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6 Ind. Eng. Chem. Fundam. 1981, 20. 6-13

Study of Kin etics of Carbon Gasification ReactionsSatyana rayana Katta' and Dale L. KealrnsChemical Engineering Research, Westinghouse Research and Developm ent Cent er, Piltsburgh, Pennsylvania 75235

The rates of carbon-steam (C-H20) and carbon-carbon dioxide (C-COp) reactions were studied in a laboratoryfluidized bed with coke breeze over a temperature range of 920 to 1040 O C at 1013kPa. Rate equations suggestedby a simplification of the Langmuir-Hinshelwood r ate expression and also Ergun's model for a fully back-mixedfluidized be d were developed for both reactions, with rate as a function of temperature and gas composition. Th esuccessof these equations in fming gasification results affords some support for Ergun's model but not in all details,and no attempt is made to prove the detailed mechanisms for the reactions in the present study. The reactionrate was found to be independent of the particle size and the inert gas concentration. The variation of the reactionrate with carbon conversion was also studied. This study forms a basis for interpreting char reactivities to be usedin projecting plant perform ance within the range of experimental conditions studied here.

IntroductionT he objective of th e prese nt stud y was to develop rateequations of practical value for carbon-steam (C-H 20) andcarbon-carbon dioxide (C-C 02) reactions and to use themfor predicting the gasification rates in pilot- and com-mercial-size gasifiers. This study is not intended to obtaina fu ndam ental equation for carbon gasification or to verifya theory. Rat her, it is to use a theoretical basis for cor-relating the data. Fu rther stu dy is needed to obtain afundamental equation.Th is stud y forms part of a continuing investigation ofcoal behavior in connection with th e development of theWestinghouse coal gasification process. Futu re stu dies willconsist of two parts: (1) he initial reactivity of severalchars an d th e variation of reactivity with carbon conver-sion; (2 ) a gasification model in which the rate equationsan d char reactivity will be used for designing the gasifieran d for identifying optimum operating conditions.A review of the recent studies on carbon gasificationreactions shows th at some of t he equations presented inthe literatu re contain a large num ber of parameters. Th einvestigators generally expresse d severe criticism about theuse of a large num ber of param eters, since any form of ra teequation can be fitted to the experimental data. Such anequation may not have any relevance to the reactionmechanism. Ra te equations based on limited data andassum ptions made on the nature of the reactions must beexam ined carefully. Following is a brief review of som eof the m odels given in order to show th e conflicting resultsof these reactions and the need to conduct additionalstudies.Von Fredersdorff (1955) noted t ha t for the C-C02 re-action a numb er of consecutive reversible and irreversiblesteps have been employed in various combinations in th eliterature to derive rat e equations. He derived four rateequations based on various reaction mechanisms andevaluated each of them by employing his experimentaldata. He presented the following rate equation, generallyknown as a Langm uir-Hinshelwood ra te expression, on thebasis of his experimental data

(1)where k is a rate constant and a an d 0are equilibriumconstants.He showed that th e same form of ra te equation can bederived from different mechanisms for the carbon gasifi-cation reactions, showing th at th e reaction m echanism isno t uniquely defined by a specific rate equation. Simplerate measurements are inadequate for evaluating a theory.

Y =kPPcoJ(1 +W C O +PPCOJ

May et al. (1958) studie d coke gasification in fluidizedand fixed beds and presented correlations for designpurposes. They derived rate constants from th e resultson the fixed-bed reactor with the a ssum ption of plug flow.Using these rate constants, they found the steam con-version in the fluidized bed to be very close to t ha t pre-dicted for a completely mixed bed, despite the length-to-diameter ratio of abou t 20. Th e flow in this fluidizedbed can be expected t o be close to plug flow rathe r tha nback-mix flow. They attribu ted this agreement to thepresence of bubb les in a fluidized bed. They showed , also,that the water-gas shift reaction failed to reach equilibriuma t low steam conversion and exceeded equilibrium a t highconversion.Squires (1961) analyzed th e dat a of May an d others. Heconcluded that in fixed beds carbon activity is highest a tthe inlet because of high steam p artial press ure an d lowhydrogen partial pressure (lowest a t the ou tlet), bu t th atin fluidized beds the carbon activity remains relativelyconstant because of periodic reactivation of the entirecarbon surface. He criticized th e use of a fluidized bed forobtaining differential rate da ta for various steam/hydrogenratios because of th e effect of t he latte r on ca rbon activity.The magnitude of this effect is unknown.Ergun (1962) conducted a comprehensive study oncarbon gasification reactions. He postulated a reactionmechanism for both C-H20 and C-C02 reactions andderived rate equations that agree well with his experi-mental da ta. In spite of this agreement and the criticalevaluation of the effect of various factors he m ade on theexperim ental data , his model has largely been ignored inthe literature. He studied the kinetics of graphite andmetallurgical coke only. Ergun (1955) had men tioned th atth e concept of th e order of reaction in carbo n gasificationstud y was controversial an d th at app aren t orders werelargely empirical factors.Turkdogan and Vinters (1970) postulated a reactionmechanism involving two rate-controlling reactions inseries-namely, th e dissociation of COP nd th e formationof CO on the surface of carbo n, for which the rea ction rateis proportional to the partial pressures of C0 2and to hesquar e root of th e par tial pressu re of CO z, respectively.They found that a t low CO content th e rate is proportionalto the squa re root of the partial pressure of C 0 2 and, inthe presence of m ore than 10% CO, th at th e rate is pro-portional to the partial pressure of COz.Rao and J alan (1972) presented a critical evaluation ofseveral theories and rate equations for the C- C 02 eaction.They concluded that a two-stage mechanism involving

0196-4313/81/1020-0006$01.00/0 1961 Am erican Chemical Society

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Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 7gasification with carbon conversion has been studied onlyto a very limited extent and has no t been very well es-tablished. A careful review of th e literatur e shows th atthere still exists a need for additional d ata on carbon ga-sification reactions for different typ es of chars an d, also,for analyzing the results in ter m s of a mea ningful modelestablished on the basis of a comprehensive study.N a tu r e o f Ca rb on G as i f ica t i on Reac t i onsfication of carbonTh e following are th e im portant reactions in t he gasi-

C +H2O - O +H2 (2)c +c02- c o (3 )CO +H2O F? COP +H2 (4 )

On th e basis of information available in th e literature, th erate of reaction of char with H 2 0 and C 0 2 appears todepend on the following factors: (a) th e nature of thecarbon (i.e., th e type of coal from which cha r is formed)and th e temperature used in the preparation of the char;(b) the change in reactivity during gasaification (increaseor decrease in th e effective surface area available for re-action); (c) th e temperature and pressure of th e reactions;(d) the gas composition (concentration of steam , C0 2,CO,and H2); (e) the mineral content of th e char; and (f ) th eparticle size if th e reactions ar e diffusion controlled.It is appar ent from a large number of studies th at th ecarbon gasification reactions are chemically controlledbelow a temper ature of about 1100 "C for the particle sizesnormally used for gasification (Von Fredersdorff, 1955).Above this temperature level the diffusion effects becomeimportant. Another importan t feature of the reactions istha t in the chemical-reaction-controlled regime, carbonconversion takes place throughout th e particle, s cificallyjust a t the surface or reaction interface (Johnson, 1975).Dut ta e t al. (1977) stated tha t for the C -C 02 eaction thesurface area occupied by pores smaller than 30 A in di-am eter is unavailable for reaction.

From a d etailed study of th e pore structures of variouscoal and char samples, Dutta et al. (1977) outlined thestructural changes that take place as he reaction proceeds.The y observed th at th e dimensions of th e solid particlesremain practically constant u p to a conversion of ab out80%. At higher conversions the solid disintegrates intosmaller fractions. T he initial pore size distribu tion an dits variation with carbon conversion would be the mostimportant factors in controlling the reactivity of anycarbonaceous material.E x p e r i m e n t a l W o r kTh e carbon gasification reactions were conducted in areactor of 3.5 cm i.d. and 30.5 cm height heated externallyby an electric furnace, a schematic diagram of which isshown in Figure 1. A sample of about 35 g of cok e breeze-1.0 +0.25 mm in size (18 X 60 mesh) was placed on thedistribu tor an d fluidized by nitrogen. Bed weights of 10and 20 g were used in a few of th e tests to de termine th eeffect of bed weight on reaction rate. T he reactor waspressurized to 1013 kPa and heated to higher than 1040OC. When steam was used the first condens ate indicatedth e beginning of the reaction. Th e bed tempe rature wasstabilized a t about 1040 "C, and a gas sample was taken.The n the bed tem perature was decreased, and gas sampleswere take n a t temperature intervals of 30 "C. Inlet gassamples were also taken. At the end of the reaction, thebed m aterial was weighed and th e product gas line wasflushed to collect fines. T he a mo unt of fines collected wasalways very small.

at char surfaces located within micropores ( 6 5rand not

oxygen exchange between th e carbon surfaze an d th e gasphase, followed by the rate-limiting carbon gasification stepand a L angm ubHinsh elwood rate expression, representeda large par t of the published data. They obtained anactivation energy of 79.6 kcal/g mol for the C-C02 reac-tion.Fuchs and Yavorsky (1975) investigated th e reactionrate s of hydrane and synthane chars with H 2 0and C02 .The y analyzed the results according toErgun's model, andtheir conclusions are essentially in agreement with his.The y obtained th e same gasification rate constant for bothreactions and r eported an activation energy of 56 kcal/molfor both reactions.Dut ta e t al. (1977) studie d th e rea ctivities of Illinois No.6 coal, Pittsburgh HVab coal, and chars made from bothin a C0 2atmosphere. Th ey correlated the change of re-action rate with carbon conversion, using a param eter thatis the ra tio of available pore surfa ce area a t any stage ofconversion to the initial available pore surface area. Theycorrelated the char reactivities with the oxygen contentsof pare nt coals with reasonable success and found th ereactivities to be almost pro portional to the surface areasoccupied by pores above approximately 15 A in radius.The y found t he ac tivation energies of all the m aterials theystudied t o be the same a t a value of 59 kcal/mol.Johnson (1974) presented correlations for char gasifi-cation kinetics from extensive experimental dat a obtainedwith a thermobalance and a fluidized bed for a tempera-tur e range of 1089 to 1366 K and a pressure range of 101.3t o 7090 kPa. His idealized gasification model consists ofthr ee consecutively occurring stages of devolatilization,rapid-rate me thane formation, an d low-rate gasification.T he last was assum ed to consist of three reactions: car-bon-steam, hydrogasification, and a thir d reaction, th estoichiometric sum of th e first two. Th e rat e expressioncontains the rate constants for each of th e three reactions,a surface area term , and a surface reactivity term , both ofwhich depend on th e carbon conversion. T hese equationshave been widely used for modeling by various investiga-tors. Th e main drawbacks of Johnson's model are th ecomplexity of its rate equations and its use of a largenum ber of param eters. Its success in predicting the per-formance of larger units has yet to be demonstrated. Thecorrelations Johnson prese nted are a pplicable only to gasescontaining steam and hydrogen.Jensen (1975) studied the C -H20 reaction in a fluidizedbed in the tempe rature range of 1040 to 1430 "C a t a t -mospheric pressure. He concluded tha t the shrinking-coremod el is applicable for the kinetics of th e reaction. He didnot study th e effect of gas composition on th e reaction rateand seems to have ignored it in obtaining the rate equationas a function of temperature. He reported an activationenergy of 19.8 kcal/mol.

Linares e t al. (1977) studied th e reactivities of severalchars in air, H2 0, and C 02. They correlated their resultswith carb on conversion as a function of t / 7 0 . 5 , where t isthe reaction time an d 70.5 corresponds to the time for 50%carbon conversion. Th ey successfully normalized theirgasification da ta a t one tem perature and gas compositioninto carbon conversion versus t / ~ 0 . 5 lots of alm ost similarshap e. Different reactions were closely described by afirst-order rate equation over a carbon conversion rangeup to 0.7 and by a cubic equation over the entire range.It would be interesting to see if sim ilar correlations couldbe obtained over wide ranges of tempe rature and re actantconcentration.Although th e initial rate of carbon gasification reactionshas been investigated in detail, the change in the rate of

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8 Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981Table I. Analysis of Coke Breeze, Wt %

ultimate analysis prox imate analysis

MixtureBed

s.G. - Steam Generator CondensateReceiverFigure 1. Flow diagram of laboratory fluidized-bed test unit.

Th e steam generator consisted of an insulated stainlesssteel boiler containing an immersion heater, a thermo-couple well, and a demister. Th e rate of steam generationwas controlled by regulating the electrical power to theheater, m easured with a precision wattmeter. A constantvoltage transformer was used to stabilize th e house powersupply. T he steam g enerator was calibrated in a series ofruns by m easuring the rate of steam generation a t differentpower levels and by determining the correction for watervapor loss during the heating-up period in separate tests.Th e steam generation r ate was found to be independentof the water level in the boiler.T he reactor was made of Inconel 600 alloy. A perforateddistributor plate and a coiled tube for preheating thefluidizing gas were pa rt of the reactor. Th e chromel-alu-me1 thermoco uples contained in a single Inconel protectiontube were used to measure and control the bed tempera-tur e. One thermocouple was connected to a precisionpotentiometer, an d the other led to an on-off temper aturecontroller. Th e reactor an d a furnace to heat it werecontained in a pressure vessel. T he furnace consisted ofthr ee heaters, each of which was controlled by a variabletransformer and m onitored continuously with a thermo-couple. Cons tant pressures were main tained in the reactoran d th e pressure vessel by two back-pressure controllers.Sam ples of off-gas for analysis were collected in evacu-ate d stainless steel sample cylinders th at were connectedto a manifold located downstream from the back-pressurecontroller. Th e gas samp les were taken by opening thebottles momentarily by means of solenoid valves ope ratedwith m anual switches.Th e rate for the C-H2 0 reaction at any temperature wasdetermine d from the tota l amoun t of CO and COz presentin the product gas and the estimated am ount of carbonin the bed at tha t time. Th e reaction rate for C-C02 wascalculated from the difference in the amo unt of CO presentin the product a nd inlet gas. T he reaction rate is definedas the weight of carbon reacted per unit time per unitweight of carbon in th e bed. Th e amou nt of carbon con-sumed d uring any period was estimated from the arit h-metic average of the reaction rates a t the beginning andthe end of th e period. This checked very well withgraphical integratio n over th e same interval. Any smallerror th at m ight have been introduced by this method isof no p ractical consequence, as th e initial weight of th esample was about 35 g and th e carbon conversion in anytest was less than about 10%.Gas analysis was performed on a B asic Gas Chromato-graph Model 8000 made by Carle Instruments. Mea-surements on pore size distribution were made with a

C 85.0 volatile matter 3.0H 0.7 fixed carbon 84.50 0.8 moisture 0.8N 0.9 ash 11.7ash 1 1 . 7Table I1

Operating Conditionstemperature 920-1040 "Cpressure 1013 kPapartial pressure of H,partial pressure of H ,Opartial pressure of COpartial pressure of CO,gas flowrate

Inlet Conditions0.0-302.8 kPa109.4-342.3 kPa0.0-213.7 kPa202.6-413.2 kPa23.7 L/min at 101.3kPa and 16 "C

Data on Fluidized Bedbed material Pittsburgh coke breezebulk density 0.16 g/cm3static bed height 4.8 cmminimum fluidization velocity 8.4 cm/ssuperficial velocity at 17.0-18.8 cm/smode of fluidization bubbling

(-1 +0.25 mm)

at 1800 "F and 101 3 kPaoperating condition s

1

0 i t I I I , I I0 0 02 0 04 0. M 0.08 0. 10 0.12Squareof Cartnn Conversion

Figure 2. Reaction rate as a function of carbon conversion forC-H,O reaction.Microm eritics mercury pen etration porosim eter Model 910series with a pressure range of 0 to 206700 kPa. Th esurface area was m easured by using COzas the adsorbateon a Micromeritics Model 2100 surface area analyzer an demploying th e Dubinin-Polanyi equation for analyzing th eresults.Th e ultimate and proxim ate analyses of Pitts burg h seamcoke breeze used in this s tudy, as percen t by weight, aregiven in Table I. Coke breeze was chosen as a referencematerial because it had been used for the initial tests onthe process development unit, is less reactive than chars,and, thus , is easier to use for a kinetic study. We pre-treated this material to remove tar by heating it up to atem pera ture of 982 "C an d then allowing it to cool to roomtemperature in a nitrogen atmosphere.Th e surface area an d pore volume of coke breeze cov-ering the pore size range of 0.01 to 100 pm diametermeasu red a bout 13.9 m 2/g and 0.68 cm3/g, respectively.(For ope rating conditions and fluidized bed data, see Table11).Th e effect of carbon conversion on the reaction rate ofcoke breeze with steam a t tempe rature s of 927 and 982 "C

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Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 9a t an inlet steam partial pressure of 309 kPa in nitrogenis shown in Figure 2. T he average values of PHZ /PH8 nthe product gas at these two temperatures are also shown.Th e variation of the reaction ra te with carbon conversionis similar a t these two temperatures. Th e curve corre-sponding to 982 "C was used to correct the results on theC-H20 reaction. No correction was applied to the resultson the C-C02 reaction, however,as th e carbon conversionwas very small.Reaction Models

According to Ergun's theory, the first step of th e C-H20and C-COz reactions on the surface of carbon may berepresented by c, +COB *c, +co (5)C, +H2O ~t C, +H2 (6 )

where C, and C, rep resent a free site and an occupied sitepossessing an oxygen atom, respectively. These reactionsare denoted as oxygen exchange reactions. Th e second stepof the reaction involves th e transfer of carbon from solidphase t o gas phase an d is represented by the following forlow conversions(7 )

Ergun postulated th at th e desorption of CO is the rate-controlling step in both reactions. He made th e followingassum ptions: th e tot al number of reaction sites (sum offree an d occupied sites) is constant; the oxygen-exchangereactions are very fast and attain equilibrium, implyingth at th e water-gas shift equilibrium is maintained in thegas phase; the com position of the gas phase inside a pa r-ticle is uniform an d identical with tha t surrounding th eparticle.He derived the following equations for C-C02 andC-H20 reactions, respectively(8)(9)

where kl and k2 are rate constants that depend on thetempera ture and type of carbon,Kl an d K2are equ ilibriumconstants of the oxygen exchange reactions, and y1 and y2ar e reaction rates per unit mass. These equations are notapplicable t o experiments under vacuum.For com plete m ixing in th e reac tor, th e ra tios PH,/PH,Oand pc o/pco for the individual reactions remain constantthroughout th e reactor, and the reaction r ate expressionsfor an isothermal fluidized bed can be written as(10)

c,- o +c,

71=k l / U +PCO/KlPCO~)YZ=k 2 / 0 +PH,/&PH,O)

Pco/Pco, =-K1 +K l k l ( l / Y J

A linear relationship between pco /pco z or PHz/PH 0 andthe inverse reaction rate would su ppo rt the validity ofErgun's rate equation.Ergun also presents rate expressions, different from (10)a nd ( l l ) , for a fluidized bed w ith negligible back-mixingof gas. The se expressions were no t used in the presentstudies.According to th e theory, the rates of carbon with H 2 0and C 0 2 hould be the same since the rate-controlling stepis the desorption of the carbon-oxygen complex from thecarbon surface. Ergun obtained higher gasification rates(- 60 percent) in the case of H 20 ,which he explained interms of a higher number of reaction sites than for COz.T he water-gas shift reaction did not reach equilibrium insome of his experiments. He suggested two explanations:(1)oxygen exchange reactions are not extremely fast as

0.61

0 . d

0. 4I /O 0. 5 1.0 1.5 2.0 2. 5 3.0

Inverse R e r t i o n Rate x I mi n-0.1

Figure 3. Determination of reaction rate parameters for C 4 0 2reaction.0.7r0 . 6 1 A

0. 2

0.11 /A Temp =10IODCJ-0. I 1 2 3 4 5

I n v er s e React ion Rate x I mi nFigure 4. Determination of reaction rate parameters for C-C02reaction.

O.7r

"'I.4 //

Temp= 9 W C

0 2 4 6 8 1 0 1 2 1 4I n v e r s e R e r l i a n Rate x I mi n

Figure 5. Determination of reaction rate parameters for C-C02reaction.postulated; (2) some sort of hindering due to pore diffusionwhich is not manifested by either dependenc e on particlesize or inert gas concentration. Ergun's the ory waa notnearly as successful for mixtures of H20 -C0 2, H20-H2, orH20-CO as it was for pure reactants.ResultsCarbonXarbonDioxide Reaction. Th e experimentaldata of t h e C 4 O Z e ac tio n were plo tte d w ith p c o / p ~ ~ ,sa function of the inverse reaction rate a t temperatures of1040, 1010,980, an d 950 "C a nd ar e shown in Figures 3to 6, respectively. Th e agreement between the results a ndErgun's ra te equation is very good. T he intercept on theabscissa gives the value of l / k l , and th e negative intercepton the ordinate gives the value of K1. The lines were

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10 Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 19810 . 7 ,

1 2 3Inverse R e l r l i o n Rate x I mi n

Figure 6. Determination of reaction rate parameters for C-C02reaction.

1 5

' 10

z 0 50.40.3 \;;;0. 10.74 0.76 a is a m 0.82 a M 0.86

I n v e rs e A b s o lu t e T e mp e ra lu re x lo3, K- 'Figure 7. Reaction constant as a function of temperature for C C O zreaction.

0 3

Temp= IWC

0 0 .2 0.4 0.6 0. 8 10 1. 2 1. 4 1.6l m e r s e Reation Rate x IO' min

Figure 9. Determination of reaction rate parameters for C-HzOreaction.1.2r 0

- 0 .21 1.0 2.0 I. 0 4.0I n v e rs e Re c t i o n Ra t e x mi n

Fi gu re 10. Determ ination of reaction rate parameters for C-HzOreaction.

1.01

0 8ON

$N 0.6Ia

0 4 /emp = 9WCo,2t\ 0 i 0 2I i0.020.74 0.76 0.78 a m 0.82 0.84

I n v e r s e A b s o lut e T e mp e ra t u re x IO3, K-Figure 8. Equilibrium constant as a function of temperature forC-COP reaction.obtaine d from a regression analysis of t he da ta. It shouldbe kept in mind t ha t the results are shown on a linear plotas opposed to a conve ntional logarithmic plot for showingth e effect of re acta nt conce ntration when observing theagreement between the d ata an d the rate equation.Th e variation of the reaction constant and the equilib-rium cons tant with tempe rature is shown in Figures 7 and8, respectively. Th e following equa tions were obtain ed

k l=0.55 X 1O l o exp(-69000/RT) (12)K1 5.86 X lo3 exp(-27000/RT) (13)

where k l s the reaction constant, min-', and T is the

0 I I I I I1 2 3 4 5 6 7 8Inverse React ion Rate x I mi n

Figure 11. Determ ination of re action rate parameters for C-H20reaction.temperature inKelvins. Hen ce, the reaction rate of C -C 02reaction can be represented by E q 8.Carbon-Steam Reaction. The resultsobtained for theC-H 20 reaction were analyzed in the same way as thoseof the C -C 02 eaction. Data a t temperatures of 1040,1010,980,950, and 920 "C re shown in Figures 9 through 13,respectively. The resultsand the form of the rate equationderived from E rgun's the ory agree very well for this re-action, also. Th e variation of the reaction consta nt andthe equilibrium consta nt as a function of temperature isshown in Figures 14 an d 15, respectively. T he followingequations were o btained for the two pa rameters

k2=4.85 X lo6 exp(-482OO/RT) (14)K 2 =2.25 X lo6 exp(-42600/RT) (15)

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Ind. Eng. Chem. Fundam., Vol. 20, No . 1, 1981 110

0.6

0. 8

I I I I I I 0

/ I

I n v e rs e Re a d o n Rate x lQ-',minFigure 12. Determination of reaction rate parameters for C-H20reaction.

0'51.10 I /

/ 10 I I I I I I4 8 I2 16 20 24 28 32

Inverse Reaction Rate x I minFigure 13. Determination of reaction rate parameters for C-H,Oreaction.

I n v e rs e A b ro lu l e T e mp e ra t u re x IO? K-'Figure 14. Reaction constant as a function of temperature forC-H20 reaction.where I t 2 is th e reaction constant, min-', an d T is thetem pera ture in Kelvins. Th e rate of C-H20 reaction istherefor e given by eq 9.T h e effect of particle size wa s investigated by studyingth e reaction ra tes of two particle size distribu tions of cokebreeze, namely, -1 +0.85 mm (18X 20 mesh ) and -1 +0.25mm (18 X 60mesh) a t 982 "C and an inlet steam partialpressure of 303.8 kPa as a function of carbon conversion.Th ere was no significant difference between th e two sizes.The effect of bed weight on the reaction rate of cokebreeze-steam reaction was studied by using bed weightsof 10 and 20 g in addition to the 35 g bed that was normallyused for th e same inlet gas composition (PHzO= -202.6,pHz =0.0 W a) . Th e results are shown in Figure 16. Note

0. 100.08

0.021 I I I I I 10.74 0.76 0.78 0.80 0.82 0.84 0.86I n v e r s e A b x l l u l e T e mp e ra t u re x IO3, K-

Figure 15. Equilibrium constant as a function of temperature forC-H,O reaction.

3 t

X1

0 . 2 1 I I I 10 IO m 30 aI n i t i a l Bed Weigh t . g

Figure 16. The effect of bed weight on reaction rate a t differenttemperatures for coke breeze-steam reaction.tha t th e bed weight significantly affects the reaction rate,the r ate increasing with a decrease in th e bed weight, ascan be expected. Wh en we plotted these results accordingto Ergun's model, we could not observe th e effect of bedweight. Som e of th e past investigations (Zielke and Gorin,1957) had assumed t ha t a t rue reaction rate could be ob-tained by extrapolating th e reaction rates a t different bedweights to zero bed weight, bu t a comparison of th e re-action rates a t zero bed weight obtained by extrapolationwith th e reaction constants obtained from Ergun's rateequation shows that the former are substantially lowerthan t he reaction constants. This, in tur n shows tha t thepractice of extrapo lating reaction rates to zero bed weightis not desirable.Th e rate equations presented here are applicable forinitial reaction r ates only. Th e variation of reaction rateof th e C-H20 reaction w ith carbon conversion is shownin Figure 2 a t temperatures of 982 and 927 "C for the sam einlet gas composition. Th e same variation can be expectedto be valid for other gas compositions as well. Johns on(1974) presen ted correlations for y(1- X)'I3 vs. X 2 withpHB/pHz asa parameter. Th e lines for th e same pressureare nearly parallel, showing that the effect of carbonconversion on the reaction rate is independen t of the gascomposition. The characteristics of pore surface area, forexample, can be expected to influence the effect of carbonconversion on the reaction rate. Th e initial increase in thereaction rate w ith carbon conversion can be explained asdue to t he opening up of pores which, in turn , results inan increase in the internal surface area. Th e subsequent

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12 Ind. Eng. Chem. Fundam., Vol. 20, No. 1 , 1981decline in th e reaction rate can be attributed to a decreasein the internal surface area.D i scuss ion

T h e low values of th e ratio of superf icial velocity to th eminimum fluidization velocity and the bed-height-to-di-am eter ratio of about 1.4 would lead one to expect th efluidized bed used in the present study to be in a bubbling,no t in a slugging, region. By estimating th e bubble risevelocity, we did indeed find t he bed to be in the bubblingregion. Hence th e assumption of back-mix flow appearsto be reasonable.A com parison of th e results of both reactions shows th atth e rate constants of the C-H 20 reaction are about 2.5 to5 times higher tha n those of the C-C 02 reaction over thetemperature range of 950 to 1040 C . Erg un (1962) ob-tained different rate constants for these two reactions,although according to his theory th e same rate co nstantsare expected. He explained this difference by reasoningtha t H 2 0 s capable of reacting with a greater number ofreaction sites tha n is COP A com parison of th e results ofthis stud y with those of Erguns study for either reactionis difficult. Th e ash conte nt in the coke breeze used hereis 11.770,as opposed to 7.4% in the coke Ergun used. Avalid comparison between the two materials cannot bemade without information on the ash composition and poresurface area. Also, the experiments in th e present studywere conducted a t a pressure of 1013 kP a, while Ergunstests were performed a t atmospheric pressure.Possible alternative explanations for the different ac-tivation en ergies obtained for the two gasification reactionsare th at t he flow in the reactor deviated from back-mixflow and th at t he sam e reaction step is not controlling inboth cases. If the latter is true , minerals present in thecoke breeze used in this s tudy would be expected to cat-alyze th e two reactions to different extents. I t is unclearwhich of these factors contributed to the appreciabledifference in th e activation energies of t he two reactions.In a s tudy on the effect of mineral matter content onthe rate of C-O2 reaction, Jenk ins et al. (1973) found t ha tthe amou nt of calcium and m agnesium present in charshad t he g reatest effect on the reactivity, while potassium,sodium , an d iron had none. T he rectivity of a char maynot be th e same in an oxygen, HzO, or C 02 atmospheresince the mineral m atter content influences each of thecarbon gasification reactions to a different extent (Tom itaet al., 1977).T he ratio of the equilibrium constants of th e C-H20reaction to th at of th e C-C02 reaction is not equal to theequilibrium con stant of the water-gas shift reaction in thepresent stu dy. We believe th at the water- gas shift reactionfailed to a ttai n equilibrium a t the exit of th e reactor, asth e steam conversion was very low. Th is conclusion issuppo rted by the work of May et al., Ergun, and Squires.In t he p resent study , steam decomposition varied from 0.1to 20% , while in Erguns study , it varied from 11to 99.6%.Th e observation that the water-gas shift reaction does notreach equilibrium at low steam conversion is certainly adrawback in Erguns theory. The present correlation maybe regarded as suppo rting the form of the Erguns rateequation rather than its theory.Erguns results show that at steam conversion of lesstha n 20% , the water-gas shift reaction is far from equi-librium and suggest th at the oxygen exchange reactionsare not very fast. In mo st of Erguns tests, steam con-version was fairly high (more than 50%),and the m easuredequilibrium c onstant of th e oxygen exchange reaction ofth e C-H20 system agreed well with t ha t derived from theC--C02 ystem. Such would not be the case if data from

a few of th e tests, where steam conversion was low, wereused in the d ata analysis. Th is observation leads to thepossibility that the equilibrium constant depends on theextent of steam conversion. In comm ercial gasifiers onecan expect th e gas flow to be closer to plug flow tha n toback-mix flow a nd the steam conversion to vary from 0 tomore than 60%. This finding implies that th e water-gasshift reaction reaches equilibrium only near the to p of thebed. Th e rate equation to be used for the design or pre-diction of performance of a reactor should, therefore,contain param eters tha t are independent of steam con-version. For design purposes, however, th e reaction ratesare insensitive to th e values of t he equilibrium constant.Th e advantages of Erguns theory are th e simplicity ofthe rate equations and th e fundam entals from which theywere derived. T he rat e equations contain only two pa-rameters: a rate constant and an equilibrium constant.The activation energies of the C 4 0 2 eaction for variouscarbonaceous materials app ear to be the same (Fuchs andYavorsky, 1975), and, hence, th e ra te co nstant for anymaterial can be established by m easuring the reaction rateat one temperature. The variation of the equilibriumconstant, formulated by Erguns theory, with tempe raturehas not been established for different materials.We have determined and reported elsewhere (Katta an dKeairns, 1980) th e reaction rates of various chars (M in-nehaha, Renton, Utah, and Western Kentucky) withsteam. The se results also show a linear relationship be-tween the inverse reaction rate an d pH2/p~&,hus showingthe validity of Erguns rate equation for different typesof carbon. T he reactivity of a carbonaceous material fora coal gasification process can thus be estimated by stud -ying its reactivity in steam, since most of the carbonconversion takes place through th e char-steam reaction.One can infer from t he analysis th at the inert gas con-centration has no influence on the rate of either reaction,and, hence, it is meaningless to express the rate as afunction of th e partial pressure of the gaseous reacta nt asis commonly done in studies on carbon gasification. Thisstudy has shown clearly that th e practice of obtaining th ereaction rate a t different bed weights an d extrapolatingthese results to zero bed weight to get true ra te is incorrect.Th e rate equations we developed in this study are ap -plicable for initial reaction rates only, as are the equationspresented in mos t studies. Th e variation of the reactionrate w ith carbon conversion mu st be determ ined separatelyfor each type of carbon. Th e me thod established hereprovides a reliable basis for comparing th e reactivities ofchars by using a simple test.An average reaction rate of char can be obtained byintegrating th e reaction r ate over the range of carbo nconversion. Th e reaction rate of any char a t a given tem-perature and gas composition is obtained from th e productof th e initial reaction rate of coke breeze as calculated fromthe rate eq uations, th e initial relative reactivity of the charwith reference to coke breeze, and t he ratio of t he averagerate to the initial rate of the char. Hence, in order todesign a gasifier or to predict th e perfo rman ce of a gasifierwith a given configuration, the ra te equations pre sentedhere sh ould be used along with th e initial reactivity of th efeedstock and t he information on t he variation of its re-action ra te with carbo n conversion in a gasification model.Conclusions

Ra te equations were developed for the C-H 20 and C-C 02 eactions with coke breeze employing a fluidized bed.Results agree well with the form of the rate equationsuggested by a simplification of L angmuir-Hinshelwoodrate expression as suggested in the Appendix and also

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Ind. Eng. Chem. Fundam., Vol. 20, No. 1, 1981 13Erguns model. Th e values of the equilibrium c onstants,however, and the activation energies of the rate param etendo not agree with those reported by Ergun. We believeth at th e water-gas shift reaction equilibrium is notmaintained a t the exit of th e fluidized bed because of thelow steam conversion in thi s study. We have presentedpossible reasons for th e above discrepancies and t he dif-ferences between Erguns model and our results. Th e rateconstant of the C-H 20 reaction was about 2.5 to 5 timeshigher than tha t of the C -C 02 eaction in the temperaturerange stu died here, an d the activation energies were 48.2and 69 kcal/m ol, respectively, for the two reactions. The reis a considerable difference in th e activation energies ofthe reaction and the equilibrium constants for both reac-tions, although the form of the rate equations is the same.Th e variation of reaction ra te w ith carbon conversion wasalso studied. Th e reaction rate was found to be inde-pendent of the particle size. Th e advantages and m eritsof E rguns model an d th e drawbacks of some of the othermodels and studies presented in the literature have alsobeen exam ined here. This investigation provides a reliablemethod to determine char reactivities and t he informationneeded for predicting gasifier performance.Acknowledgment

Th is work was performed as p art of th e Westinghousecoal gasification program under DOE Contract E F-77-C-01-1514. Th e authors appreciated th e constructive com-ments and suggestions by th e reviewers of th e m anuscript.AppendixThe following mechanism was presented by Van Fre-dersdorff (1955) for the C -C02 reaction where th e equi-librium adsorption of C 0 2on the carbon surface is followedby surface reaction and the adsorbed and gas phaseproducts are in equilibrium

(CO,) +c -2o + (CO) (A2)(CO) co (A3)(the parentheses indicate adsorbed species). This mech-anism leads to t he ra te expression

Y =k ~ c P c o , / ( l+.Pco +pPC0,) (A4)where k; =klk2/kl,a =k i / k 3 , p =k l / k ( , and uc is th eactive surface area available for reaction per u nit weightof carbon.If one considers the values of a nd p presented in theliterature a nd for the ranges of pco and pco, used in thisstudy, unity can be neglected in comparison with (cupco+ppco,). Dividing th e numerator and the denominatorby ppco,, one obtains the following equation

Y =k2ac/(l +.Pco/pPco,) 645)Von Fredersdorff proposed a similar mechanism for the

ks

which is of the same form as Erguns.C-H 20 reaction

Th is leads to the ra te expression=kfgH,O/(l +apH, +PPHzO) (A91

where kf =k l k z / k l , LY =k3//k3, and P = kl/kl. Thisequation can be reduced with the same reasoning as aboveto the followingY =k 2 0 c / ( l +WH,/PPH,O) (A101

which is also of th e sam e form as ha t presented by Ergun.Examination of the model on which the Langmuir-Hinshelwood equation was based reveals tha t the w ater-gas shift reaction equilibrium was not assumed (VanFredersdorff, 1955). Th e form of the Ergun rate equationcould be derived from the Langm uir-Hinshelwood equa-tion by assuming that the adsorption of the gaseousreactant on th e carbon surface and the desorption of theproducts a re very fast, as shown earlier. A comparison ofthe term ( d p m +ppcq) with unity cannot be made eitherfor Erguns data or for the pres ent d ata, as the values ofa an d p are not available. Ergun, however, reported t heratio of p to a,which is the equilibrium constant.Nomenclaturekl =reaction rate constant for the C-C02 reaction, min-kz =reaction rate constant for the C-HzO reaction, min-K1 equilibrium constant of the oxygen-exchange reactionK 2=equilibrium constan t of the oxygen-exchange reactionPCO, P C O ~ , H ~ , H,O =partia l pressures of CO, COz, H2 , andy1=reaction rate per unit mass of the C- C 02 eection, m i dyz=reaction rate per uni t mass of th e C-H2 0 reaction, min-lT =temperature of the bed, KX =fractional carbon conversiona, =active surface area available for reaction per unit weightLiterature CitedDutta, S.; Wen, C. Y.; BeR, R. J . Ind. Eng. Chem. ProcessDes. Dev. 1977,Ergun, S. Ind. Eng. Chem. 1955, 47(10), 2075-80.Ergun, S. Bur. Mlnes Bull. 1962, No . 598 .Fuchs. W.; Yavorsky. P. M. presented at Symposium on Structure and Re-activity of Coal and Char, 170th National Meeting of the American Chem-ical Society, Chicago, Aug 1975.J enkins,R. G.; Nandl, S. P.; Walker, P. L., J r. Fuel, 1973, 5 2 , 288.J ensen, G. A. Ind. Eng. Chem. Process Des. Dev. 1975, 14, 308-314.J ohnson, J . L. Adv. Chem. Ser. 1974, No. 131, 145-178.J ohnson, J . L.,Presented at Symposium on Structure and Reactivityof Coaland Char, 170th National Meeting of the American Chemical Society,Chicago, Aug 1975.Katta, S.; Keairns, D. L. Char Reactivities and Their Relationship to PoreCharacterlstics, presented at 180th National Meeting of the AmericanChemical Society, Las Vegas, Aug 1980.Llnares, A.; Mahajan, 0.P., Walker, P. L., J r. presented at t he 173rd NationalMeetina of the American Chemical Society, Division of Fuel Chemistw.

for the C-C02 reactionfor the C -H20 reactionHzO, respectively

of carbon

16,20-30.

~. ..New Oyleans, 1977.May, W. G.; Mueiier, R. H.; Sweetser, S. B. Ind. Eng. Chem. 1958, 5 0 ,1289.Rao, Y. K.; J alan, B. P. Metall. Trans. 1972, 3 , 2465-2477.Squires, A. M. Trans. Inst. Chem. Eng. 1961. 3 9 , 10.Tomita, A.; Mahajan, 0.P.; Walker, P. L., r. Presented at the 173rd NationalMeeting of the American Chemical Society, Division of Fuel Chemistry,New Orleans, 1977.Turkdogan, E. T.; Vinters, J . V. Carbon 1970, 8 , 39-53.Von Fredersdorff, C. G. Inst . Gas Technol. Chicago Res. Bull. 1955. No .Zielke, C. S.; Gorin, E. Ind . Eng. Chem. 1957, 49 , 396.19 .

Received fo r review October 23, 1978Resubmi t t ed April 28, 1980Accep t ed September 19, 1980