Heterogeneous kinetics of coal char gasification and combustion

Heterogeneous kinetics of coal char gasification and combustion

Pro,~ Enero) Combus;. Sci. Voi 4. pp 221-270. Pergamon Press Lid.. !978. Printed in Grea~ Britmr. HETEROGENEOUS GASIFICATION KINETICS OF COAL AND CO...

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Pro,~ Enero) Combus;. Sci. Voi 4. pp 221-270. Pergamon Press Lid.. !978. Printed in Grea~ Britmr.




NORM~ND M. LAURENDEAL The Combustion Laboratory. Sclmol q/Meci~anical Eru3ineerin9. Purdue University. West Lqfayette. lndiana 47907. USA NOMENCLATURE

Upper case symbols A A. G A~

frequency factor, area gaseous species specific external surface area of particle (crn:/g) A0 specific internal surface area of particle (m"/g) ASA active surface area B constant BO burnoff C. C, gaseous concentration (g/cm 3, atml C* carbon in char C(At carbon site occupied by species A Cs free carbon site C~ total n u m b e r of active carbon sites CI" calorific value D total pore diffusivity (cm:/s) DA molecular diffusivity (cm2/s) D~ effective diffusivity (cm2/s) D~' effective diffusivity for ash layer (cm2/s) D~ Knudsen diffusivity tcm2 is) D* D/D~ E activation energy (kcal/mol. kJ/mob H enthalpy (kcal/mol. kJ/mol) .1 mass flux (g/cm ~ • s) K, equilibrium constant for ith reaction K o,K~ overall rate coefficient on mass basis (s-1 [g/cm 3] -") K~.o.K~,,overall rate coefficient on external area basis (g' cm - : - s - ~ • [g/cm 3] -") Kn diffusional rate constant (crn/sl L pellet length/cmt Lp pore length (cm) M, molecular weight of ith species ?,' n u m b e r of pores/gm P pressure iatm. kPa) P~ products Pr Prandtl n u m b e r R particle radius (cmt R gas constant R~ overall particle reactivity on external area basis tg,cm:" sl R,, overall particle reactivit3 on mass basis (g,s g ) intrinsic reactivity (g/m-' "sl R' intrinsic volumetric reactivity (g/cm "~-sl Re Reynolds n u m b e r Sc Schmidt n u m b e r Sh Sherwood n u m b e r T temperature (K) .

Tp TSA I" I ~. I~ VM W X Xf

pretreatment temperature (K) total surface area volume specific particle volume Icm3/g! specific pore volume tcm3/g) volatile matter weight tgm) fractional conversion mote fraction of ith species

Lower case symbols a.b...~ c d .f 17 hD k /~ k' k~ /~,

k 1 / m m, mp rh~ 77 p 7" s, s'. s" t x z

rate coefficient ratios constant particle diameter roughness factor Planck's constant mass transfer coefficient {cm/s) intrinsm global rate coefficient is-Z . [g/cm 3] -") intrinsic global rate coefficient on area basis ~g. m - : s- 1. [g/cm3~ -,~) intrinsic global rate coefficient on vglume basis !g.cm -3. s- 1 . [g/cm3~-,,,} intrinsic elementary rate coefficient for ith reaction Is- 1. [g/cm 3] -~,j) intrinsic elementary rate coefficient on area basis for ith reaction ( g ' m - :" s- 1 . [g/cm3~ - , j ) ,,c[C,] k~ length total n u m b e r of gaseous species true reaction order mass of carbon atom (g/site~ particle mass (g) mass reaction rate of carbon (g/s) apparent reaction order exponential constant radius lcm) single (s = 11 or dual (s = 2} site mechanism time Is} length {cm) axial distance tern}

Greek symbols fi

fiT 7 A, c3 c 221

pore model parameter, eqn. (1091 hoLp~ D~ nondimensiona! temperature difference I~..A,, Icm) rate constant ratios, eqn. (38t pore diameter !nm! collision efficiency z Lp



r/ O

effectiveness factor fractional surface coverage of active sites

Oo o~

[c(o)]/[c,] [cA/[c,]

x Xc xo A 2 v vi

thermal conductivity chemical rate parameter (s/cm) diffusional rate parameter (s/cm 2) gravimetric stoichiometric coefficient mean free path (nm) frequency stoichiometric coefficients r/R r~ 3.14159... p intrinsic reactivity on site basis (atoms/m z. s) a~ apparent density (g/cm 3) at true density (g/cm 3) z tortuosity r o r o , r o . 5 reaction time (s) Y dimensionless time, eqn. (112) ~, ~', ~,, macroscopic Thiele modulus microscopic Thiele modulus Z active site fraction C/Co, C/C~ porosity f2 pore angle co surface energy constant

Subscripts and special symbols a adsorption, apparent A species A c surface migration C surface chemistry d desorption D diffusion e external surface area basis f reaction front g gas i,j index for species or reaction I inactive L large o bulk gas or initial conditions p pore, product s surface of particle S small r true mean value v gradient operator [ ] surface concentration [sites/m 2] I. I N T R O D U C T I O N

1.1. Background Dwindling supplies of oil and natural gas have spawned renewed interest in utilization of the world's vast co,it resources. Nuclear and solar energy will be required in the long fun; however, energy conservation and coal offer the best short term solutions. Depending on end-use and environmental constraints, coal may be utilized in four major ways-gasification, combustion, liquefaction and pyrolysis,

using three reactor types--fixed bed, fluidized bed and entrained flow.Z'2 In each case, process efficiency depends considerably on the heterogeneous kinetics controlling (1) coal char gasification with steam, carbon dioxide and hydrogen and/or (2) char combustion with oxygen or air. Devolatilization of coal occurs mainly in the 400-900°C temperature range; thus, coal behavior during most processes can be considered in two stages--rapid pyrolysis, followed by slow heterogeneous char reaction. Consequently, residence time requirements for efficient combustion are determined by char burnout. Similarly, char gasification controls reactor volume in most conversion processes producing power or synthesis gas.2.3 The efficiency of in situ gasification hinges on effective utilization of coal char left by the pyrolysis wave.* Char combustion (or gasification) in auxiliary reactors is required during gasification to substitute natural gas (SNG), liquefaction or pyrolysis to make such processes economically feasible. ~'2 In summary then, a detailed understanding of heterogeneous char reactions is important to a large variety of coal conversion schemes. Therefore, in this review we will discuss fundamental concepts influencing the chemical kinetics of both char gasification and combustion. The practitioner should find this survey useful for rate calculations, reactor modeling and process design. Thermal decomposition of raw coal produces solid char plus liquid and gaseous volatile matter: Coal


, solid (char) + liquid (tar) +gas (CH,, H2, CO),

where the tar is, of course, a vapor at pyrolysis temperatures. Char usually accounts for 30-70~ by weight of the original coal and consists mostly of carbon and ash, along with small amounts of hydrogen, oxygen, nitrogen and sulfur. The exact amount and composition of the char depends on such things as coal type, temperature, heating rate, pressure, time, hydrogen partial pressure and particle size. 5 Recently, Anthony and Howard ~ reviewed the kinetics of both coal devolatilization and hydrogasification (thermal decomposition in a hydrogen environment). Here, we consider the kinetics of the subsequent char reactions with oxygen, steam, carbon dioxide and hydrogen: C* 4- 02 ~ CO2 C* + H20 --* CO + H z C* + COz --, 2CO C* + 2H 2 --* C H , During combustion, char oxidation predominates, but attack of the char by steam and carbon dioxide is also important. During gasification, char combustion often provides heat for the endothermic H~O - C * / C O 2 - C * steps. The hydrogen-char reaction produces methane, but its contribution is usually minor compared to pyrolysis and/or hydrogasification. S'6'7 Equilibrium calculations for these re-

Heterogeneous kinetics of coal char gasification and combustion actions are given bx Walker et ul. ~' and yon Fredersdorff and Ettiott. 1.2. Scope o[ Review


reactivit? 1 d I47 R,~ =- - - - - g/s.g. H dr


where W is the weight of the organic portion of the This review is organized in the following fashion char sample. Proper interpretation of eqn. (1i 1. Introduction (Section 31 requires an awareness that heterogeneous 2. Coal and char characteristics rates are determined by the total surface area, the 3. Fundamental surface mechanisms number of reactive sites per unit surface area, and 4. Particle reaction models the local gaseous reactant concentration. Con5. Kinetics of char gasification and combustion sequently, char reactivity must depend on three 6. Directions for future research. important characteristics of the sample: (1t chemical Section 2 considers those coal and char characterisstructure: (2t inorganic constituents; and (3) potics important to reactivity, i.e.. chemical structure. rositx. Chemical structure fosters active sites b~ inorganic constituents and porosity. Active site providing dislocations, crystalline edges and heterotheory provides a fundamental interpretation of cyclic centers, Inorganic constituents promote catasurface chemistry: hence, in Section 3. we discuss the lytic activity and create further dislocations. Finally, basics of Langmuir-Hinshelwood kinetics, including pore structure fixes the total accessible surface area, chemisorption, surface migration and desorption. while controlling diffusion rates and thus the local Elementary mechanisms controlling gasification and concentration of gaseous reactants. The effects of combustion are also considered. In Section 4. overall chemical structure and mineral matter are not well kinetic models describing heterogeneous char parunderstood: the effects of porosity are fairly well ticle reactions are described of particular importdeveloped, although often misunderstood. Appreciance are the effects of pore diffusion. Recent kinetic ation for all three char characteristics is best data for gasification and combustion of char are obtained by first investigating certain properties of presented and discussed in Section 5. Temperature. coal itself. pressure and particle size are shown to be the major rate-controlling parameters• Particle size is especially importanL since various reactor types demand different char diameters: fixed bed (l-10cm}. 2.1. Coal Rank and Petrooraphy ftuidized bed 110-:-1 cm~ and entrained f~ou ~ (10-"-10-2cm). In Section 6. some areas for future 2.1.1. Rank and coal!fication research are suggested. The formation of coal from large plant masses via In this review, stress is given to the use of intrinsic Irate per unit internal surface areal rather than biochemical and geochemical processes is called o~,erall Irate per unit particle masst kinetics. The coalification. The extent of coalification determines significance of intrinsic rates is discussed in Sections the degree to which the original plant material 3 and 5. This discussion will hopefully guide future approaches the structure of pure carbon. Coal rank investigators toward proper measurement of hetero- is a measure of the coalification process, i.e., rank geneous kinetic parameters, The utilization of intrin- designates the metamorphism from plant debris te sic rates is considered in Sections 2 and 4, Of the various coal types. Coal rank thus depends upon particular importance is the development of particle knowledge of a coal's proximate and ultimate reaction models which consider changes in pore analysis (Table lk Proximate analysis parallels structure and internal surface area: in this way, carbonization: ultimate analysis indicates elemental prediction of the overall particle reactivity as a composition, Ty;pically, proximate analysis includes determination of the calorific value ICI') of the function of time can become a reality. The coal literature is voluminous and widely sample. The ASTM coal classification scheme is based on dispersed. Fortunately. previous reviews, although volatile matter for high rank coals and calorific value dated, are available to guide the novice toward understanding both the fundamentals and appli- for IoN' rank coals, since these parameters undergo cations of coal char gasification and combustion• large variations, and are thus sensitive to rank Char gasification has been surveyed by Walker et al. changes, in their respective regtmes. - InterI1959~~ and von Fredersdorff and Elliott (19631.' nationally, percent carbon (Seyter classification) is Char combustion has been considered by Thring and often used as a measure of coal rank. Typical]y, as Essenhigh 119631~, Field et al. (196719 and Mulcahy rank increases. !IoC and CV increase while VM, °;'H. % O and moisture content decrease (Table 2). High. and Smith (19691.~(' medium and low (HI,', MV, LV! volatile bituminous coals generall) demonstrate caking or agglomerating 2. COAL AND CHAR CHARACTERISTICS behavior. Both Ct" and VM (though less sol The overall chemical kinetics of heterogeneous correlate well with elemental composition, particularl? carbon, hydrogen and oxygen content. 1: char reacuons is usuall 3 measured via the char •

1 ~



TABLE I. Coal analysis definitionst t Analysis


Proximate (weight percent)

Moisture--weight loss in drying oven Volatile matter (VM)--weight loss upon slow (7mini pyrolysis in crucible to 925-950°C Ash/Mineral matter--weight of solid residue after combustion at 750°C/weight of unaltered minerals in raw coal as determined by acid demineralization or radiofrequency ashing Fixed carbon--dry ash free (daf) or dry mineral matter free (dmmf) basis, IO0-VM.

Ultimate (weight percentl

Percent carbon, hydrogen, oxygen, nitrogen and sulfur as determined by ASTM chemical methods. Thus, ?,,C + °;H +"i,O + 0;,N+',,,S = 100°,,on a daf or dmmf basis.

TABLE2. Variation of coal properties with rank t 1.1z Rank Lignite Sub-bituminous (A,B,C) HVC bituminous HVB bituminous HVA bituminous MV bituminous LV bituminous Anthracite


:°I4 (dmmf)

°gO (dmmf)


65-72 72-76 76-78 78-80 80-87 89 90 93

4.5 5.0 5.5 5.5 5.5 4.5 3.5 2.5

30 18 13 I0 4-10 3-4 3 2

40-50 35-50 35-45 31-45 31-40 22-31 14-22 < 14

2.1.2. Coal petrography Coal is a sedimentary organic rock. Rank is thus a gross over-simplification of the highly heterogeneous nature of the coal substance. Petrography is an alternative classification emphasizing the compositional description of coal as a rock material. This classification is based on visual observation of reflected or transmitted light through thin coal sections.lZ The relationship between petrographic or rank classification and chemical reactivity remains obscure in most applications.~ 3 Modern petrographic classification is concerned with the microscopic separation of coal macerals according to color and consistency. Macerals are presently considered the fundamental constituents of coal. There are three major maceral types: vitrinite, exinite and inertinite. ~2 Vitrinite is the principal constituent of coal (60-90}o by weight) and originates from the woody tissue of the plant material. It is a graphitic banded structure with a highly vitreous lustre. Exinite is the hydrogen-rich portion of the coal structure. It arises mainly from plant spores, cuticles and resins; algal and fungal bodies are also included. Inertinite is a dull granular form composed of fossil charcoal and highly decayed plant material. Maceral carbon content (~o C by weight) increases and the atomic H/C ratio decreases in the order: exinite, vitrinite, inertinite, t4 Differences in maceral composition are, however, much less noticeable for high rank coals. Maceral behavior during devolatilization indicates the strong influence of petrography, t2"t5 Vitrinite is the plasticizing, cokeforming portion of the coal structure. Exinite fluidizes and decomposes to tars and gases; inertinite

CV (kJ./g)


< 19.4 > 15 1 9 . 4 - 2 5 . 6 10-15 25.6-30.2 5-t0 30.2-32.6 3-5 33.8 1-2 34.9 <1 36.8 <1 35.4 <1

neither plasticizes nor devotatilizes. Recently, combustion efficiency has been found to be inversely related to inertinite content, inertinite apparently being responsible for the carbon content of ash particulates, tga More meaningful correlations between petrography and reactivity await further investigations. 2.2. Chemical Structure and Intrinsic Reactivity 2.2. l. Organic chemical structure 1t. 12. ~3 The complexity of coal structure requires analysis in terms of the organic functional groups that typify each atomic species (C, H, O, N, S). The fundamental carbon structure is the polynuclear aromatic (Fig. l(a)); hydroaromatic (Fig. l(b)) and aliphatic (Fig 1(c) and l(d)) structures account for most of the hydrogen. The hydroxyl (--OH), carboxyl (--COOH) and carbonyl ( ~ C O ) forms (Fig. l(e)) are the major oxygen functional groups: lower rank coals may also contain ether, quinone, methoxyl and heterocyclic oxygen structures. Sulfur and nitrogen occur as substituted aromatics (Fig. l(e)) or heterocyclics. Heterocyclic structures, especially pyridines, pyrroles and thiophenes {Fig. l(f)) predominate. A typical bituminous coal (Fig. 2) consists of a series of aromatic/hydroaromatic clusters containing an average of 2-5 rings per cluster and joined together by methylene (also, ether and sulfide) linkages, 1-3 carbon atoms in length, t2'~6'1; This arrangement promotes a complex interlocking molecular structure similar to many organic polymers. Since the clusters are only loosely connected by

Heterog.eneeus kinetics of coal char gasification and combustion













FIG. 1. Basic chemical structures jrl coal: (a) polynuclear aromatic (b = basal carbon, e = edge carbonl. (bt hydroaromatic. (c) arenes. (d) methylene bridge. (e! substituted aromatics. (fl heterocyclics









o IJ














l '



























.. 'Z',_C_H7 ST "x --


~'- ~

~ v


~ I ' -~~' / H 2


H.. ~

! t


.t_L H


~ ;'2~'@_


-h2 v



i- ~

" ""- ~ i ~



,H 0


x" " ~ " - " H I


H- C -H J











Hd. v . OH FIG. 2. A representation of bituminous coal structure (Wiser I ~). aliphatic linkages, clusters will appear on various planes and thus cross-linking and development of an extensive pore structure are favored. Aliphatic. hydroaromatic and heterocyclic bonds are more susceptible to bond breakage. 16 Therefore, during heat treatment these structures bear the heaviest responsibility for devolatilization. Chars are characterized by highly carbon-rich, polynuclear aromatic structures. In such structures, edge carbon atoms are at least an order of magnitude more reactive than basal carbon atoms (Fig. lla)l due to the availabilit3

of unsaturated chemical bonds and the higher frequency of inorganic impurities at crystallite edges. ~3. ~ Since coal rank is a measure of the approach to pure graphitic structure, we would expect that increasing rank implies a loss in aliphatic and hydroaromatic forms. Hirsch's X-ray scattering work has indeed demonstrated that the number of carbon atoms or aromatic rings per ordered cluster (flat polycondensed lamellae) increases with rank. 19'2° The implication here is that higher rank is associated



with lamellae orientation and thus reduced porosity. As expected, aromaticity increases in the order: exinite, vitrinite, inertinite. More recently, Mazumdar et a/. 2t'22 have used chemical analyses (hydrogenation/dehydrogenation plus carbonization at 600°C) to show that carbon atoms in most coals i80 < % C < 90) are distributed approximately as follows: aromatic--75°;, hydroaromatic--17°~;, aliphatic--80,o. During carbonization, aromatic carbon is primarily responsible for char formation. Tar comes from hydroaromatic carbon, while aliphatic carbon produces CH,~, CO and CO z. 2.2.2. M i n e r a l m a t t e r and trace elements "-~'~ Mineral matter (10-30°,o by weight of most coals) was probably deposited in coal seams via natural geological water flows. Four major mineral types have been found: (1) aluminosilicates (clays), such as kaolinite [AIzSi2Os(OH),,] and illite [KAl3Si3Oto(OH)2]--50°Jo by weight of mineral matter; (2) oxides, such as silica [SiO2] and hematite [Fe203]--15°o; (3) carbonates, such as calcite [CaCO3], siderite [FeCO3], dolomite [CaCO3. MgCO3] and ankerite [2CaCO3. MgCO3-FeCO3]--10°o; (4)sulfides and sulfates, such as pyrite [FeS2] and gypsum [CaSO,~. 2H20]----,~¢°~/o. Typically, mineral matter is randomly distributed in coal as ~21am inclusions. During pyrolysis, gasification or combustion, mineral matter is transformed to ash: SiO, (20-60%), AI20 3 (10-35%), Fe20 3 (5-35°o), CaO (1-20°o), MgO (1-3~o). -o/ At temperatures greater than 1300-1900K, the ash may melt and ooze through char pores to the surface of the coal. In addition to mineral matter, 20-30 trace metals are distributed through the coal structure. Some metals (boron) are organically bound to the coal molecule; others (zirconium, manganese) form inorganic bonds with mineral matter. Still others (copper) occur in both the organic and inorganic forms. Concentrations of 5-500 ppm are typical for trace elements. However, B, Ba, Sr, Cu, Mn, Sn and Zr often appear at the 500-1000 ppm level. 2"~ 2.2.3. Intrinsic char reacticity The number of active sites and thus the intrinsic reactivity of a char sample is primarily determined by: (I) the concentration of carbon edges and defects; (2) mineral matter and trace element analysis: and (3) oxygen and hydrogen content. These three chemical parameters plus char porosity account for variations in overall reactivity. Typically, porosity and concentration of carbon edges, mineral matter and oxygen increase for lower rank coals. Hence, it is not surprising that char reactivity increases substantially ~s.2~.a6 as the rank of the parent coal decreases. With increasing heat treatment temperature, however, the influence of the parent coal diminishes ase6 (Section 2.2.4}. Many studies employing extremely pure carbons

have shown that essentially all surface reaction (with non-atomic species) occurs at edge rather than basal sites. 6'zv For example, Walker er al. 6'2s find that the intrinsic reactivity ratio /~,~//~ba~,l -~ 100--1000 depending on the degree of graphitization. Further reaction occurs at edge and screw dislocations or point defects such as vacancies. -'9 Irradiation, for example, is known to create dislocations thus boosting reactivity. 6 Enhanced activity at carbon edges is presumed to be due to chemisorption by unpaired a electrons; 2s enhanced activity at defects is probably due to geometric or charge imbalances. 29 However, we should recognize that the preferred location of inorganic impurities is at edges and dislocations. 29 For example, during heat treatment, impurities are known to diffuse and concentrate at crysta[lite edges. 2s At this time, we cannot distinguish effectively between "pure" edge and impurity effects. In a sense, carbon edges and dislocations act like a catalyst, with basal carbon as the catalyst support. 29 Mineral matter and trace elements can provide direct catalytic activity to the surface. Most metals, metal oxides and salts are more or less catalytic ;29,30.31 however, iron, calcium and magnesium compounds are of prime interest, t3 As little as 100ppm Fe increases carbon reactivity over two orders of magnitude. "s'3° Recently, investigators have found that char reactivity correlates well with CaO and MgO content. 2526 Surface impurities can also affect secondary homogeneous reactions, particularly the water-gas shift, CO + H20 = CO 2 + H2 .32 The effect of mineral matter or trace elements on carbon gasification is usually explained via one of two unconfirmed theories, z9 The geometric or transfer theory suggests that an oxidative intermediate formed by reactant dissociation at a nearby catalytic site migrates to react with carbon. The electronic theory suggests that chemisorption and particularly desorption is favored at covalent or ionic carbon-metal bonds generated by electron transfer. Recently, Otto and Shelef99 found that catalyst addition does not affect measured activation energies for steam gasification. They argue that this result favors the transfer theory since here the carbon mechanism is independent of catalyst addition. The catalytic activity of an impurity det~ends on: (1) chemical form; (2) amount: and (3) inclusion size.l s.3 ~ The effect of chemical form is demonstrated by the high activity of Fe, but the much lower activity of Fe30~. 26'3°'3 t A small amount of catalyst strongly increases reactivity; larger amounts (> 1000ppm) have much less effect. Reactivity often increases with decreasing particle size due to the larger mineral matter content of smaller particles. 9'33 Similarly, catalytic activity often increases with burnoff.ts The amount of catalyst is usually not as important as distribution: i.e. many small inclusions are better than a few large inclusions. For this reason, trace elements often have a much larger effect on reactivity than mineral matter. -'~~

Heterogeneous kinetics of coal char gasification and combustion Recentl3. Walker et al. 2s'2(' have deashed chars using hydrochloric and hydrofluoric acids. After deashing, similar reactivities (with air at 500°C and CO_, at 900°C) were usually obtained for chars varying widely in rank, thus underscoring the importance of inorganic impurities. As expected, the overall reactivity of deashed low rank (porous) chars decreased compared to the original samples. However, the removal of mineral matter increased the overall reactivity of high rank chars because of higher porosities and thus increased accessibilit), to internal surface area. Chars par 3 in their oxygen and hydrogen content: moreover, oxygen and hydrogen sites should promote carbon reactivity since chemisorption on nonaromatic sites is usually favored compared to aromatic sites. 12 Thus. it is not too surprising that investigators have formulated correlations between char reactivity and oxygen content 34'3536"3' or hydrogen content. :'~ Oxygen sites, particularly of the carbonvl or heterocyclic variety, are thought to influence reactivity via electron exchange. 3a'12 Hydrogen sites are presumed to increase char reactivity by preferential oxidation 1:. with subsequent production of nascent carbon sites of high activity, zs Nitrogen and sulfur could also invite ring structure attack since r, electrons are most available at heterocyclic sites. 38


dislocations even at the highest heat treatment temperatures, e29 Based on extensive investigations. Franklin "~ has postulated the existence of graphitizing and non-graphitizing coals. Graphitizing coals (anthracite. bituminous)correspond to Hirsch's ~92° "'ordered structure". Cluster mobility and weak cross-linking encourage realignment due to cluster growth and coalescence, lamellae packing and graphitization (T > 1500°C!.1: Non-graphitizing coals (sub-bituminous, lignite) correspond to Hirsch's "open structure". In this case, heating promotes cross-linking and thus microporosity persists to at least 2000~'C. Franklin's work clearly shows that carbon edges are more prominent in chars from non-graphitizing coals than graphitizing coals.





2.2.4. Effect o f heat t r e a t m e n t Carbonization of coal induces both chemical and physical changes in the char sample. Porosity effects are considered in the following section. Here we discuss the effects of heat treatment on surface chemistry and intrinsic reactivity. During heat treatment, three major changes occur to the coal surface. First. oxygen and hydrogen at oms are lost. as shown on van Krevelen's coalification plot (Fig. 3 I. The carbonization paths short circuit the coalification band (determined by ultimate coal analyses) and meet at the carbonization pole (ClooH2,O21. Thus, above approximately 700~C, all chars have similar C - - H - - O contents. Most of the oxygen is lost at lower temperatures: heat treatment above 700:C is dominated by loss of hydrogen. A second effect of heat treatment is conversion of mineral matter to metal oxides :~L:3 AIzSi2Os(OH)4 --* A120 3 + 2SiO 2 + 2H20 CaSO~ --* CaO + SO3 CaCO 3 ~ C a O + C O 2. In addition, oxidation of trace metals and mineral matter obviously occurs under combustion or gasification conditions. Thermal annealing (T > 700-1100~C) is the third change due to heat treatment. ~2"39'4° Here microporosily and carbon edges are lost via cluster reorganization. The char structure becomes more graphitic : hence, unpaired surface electrons disappear, as verified by ESR work. as Structural defects also disappear however, impurities promote permanent

,oo° 0.2 L







Fro. 3. Effect of carbonization on char hydrogen and oxygen content (van Krevetenl 2).

Based on the above, we expect heat treatment to reduce intrinsic char reactivity due to loss of active sites. Unfortunately. unassailable evidence for this conclusion appears nonexistent: however, indirect evidence comes from measurements of overall reactivity tsee Section 2.3.3. Blackwood and McTaggart, 3" for example, find correlation of overall reactivity with char oxygen concentration (but only for molecular reactants since atomic gases react with any site, not just active ones !. Blake et al. '*° note thal the reactivity of h~ghly treated chars is nearl), constant because of a more homogeneous carbon structure. The), suggest a two site theory to explain reactivity losses during gasification or carbonization. Highly active sites [oxygen. mineral matter) are lost quickly, while less active sites (carbon edges) lose reactivity slowly. Intrinsic reactivity after extensive heat treatment or gasificgtion probably results from mineral matter-induced dislocations.




2.3. Coal and Char Porosity The overall chemical reactivity of a char particle depends on the type and concentration of active sites and the pore structure, which in turn determines the local concentration of gaseous reactant (Fig. 4). The 8L~NOPORE~


often used to measure the apparent and true densities. The apparent density o'~ is based on the volume defined by the external surface of the coal or char particle; the true density o', eliminates that portion of the total volume occupied by pores. Typically, 0"4 "- 0.9-1.4g/cm 3 (daf) and o', "-1.3-1.6g/cm 3 (daf). Determination of the true density utilizes helium as the displacement fluid since nearly all pores (6 > 4A) can be reached. Determination of the apparent density is usually done with mercury at latin since pores with 6 < 15~m cannot be penetrated. Using or= and ~r~, we may calculate the total internal volume Vg and porosity ¢,: Vs

i t t

I i




i I






FIG. 4. Concentration profile for gaseous reactant near and within a porous char particle.

pore structure is identified by: (1) the specific internal pore volume Va; (2) the specific internal surface area :Ag; and (3) the distribution of internal volume or area over pore diameter 6. Typically, V,_ 0.010.12cm3/g and As~-lOO-6OOm'-/g. The distribution over pore size determines the accessibility of internal surface area to the gaseous reactant. The large surface area donated by the smallest pores may not be available to a particular reactant unless large feeder pores exist or the kinetics are slow enough to allow sufficient time for diffusion into these micropores. Relating reactivity to As is usually difficult owing to the so-called molecular sieve effect. ~2 The concern here is the non-accessibility of large blind pores because of small feeder pores (Fig. 4). 2.3.1. Determination of pore structure 12"29'~3"46 Pore structure can be studied via a variety of methods, including heat of wetting and X-ray techniques plus electron microscopy. However, the three major methods are: (1) pycnometry; (2) mercury porosimetry; and (3) adsorption. Pycnometry is a displacement method, i.e., the pore volume is measured by first outgassing in vacuum and then measuring the volume of fluid required to fill pores greater than a known minimum pore diameter. Using various fluids (He, Hg, CH3OH, C6Hta. ), a rough pore volume distribution can be calculated. Pycnometric techniques are more




Typically, ~0 = 2-250o for coal, with higher porosities for chars. Mercury porosimetry allows determination primarily of total pore volume Vs and pore volume distribution. In this method, mercury is forced into pores at high pressure. By varying the pressure (1-1000atm), we can examine the 102-105,~ pore size range. As with pycnometric techniques, molecular sieve effects can be troublesome since blind pores may be improperly measured. By assuming cylindrical pores, a surface area distribution can be obtained from 4 dA = - d V 6


Typically, porosimetry results are presented as cumulative pore volume V vs log 6; the pore volume distribution is then the derivative d V/dlog 6 vs log 3. Adsorption isotherms allow direct measurement of total surface area Ao and surface area distribution (dA/dlog 6 vs log 6). Using eqn. (2), pore volume distribution can also be computed. The amount of gas physically adsorbed on a surface can be related to the pressure at a given temperature via the BET or Dubinin-Polanyi adsorption isotherm. By calculating the amount of gas adsorbed in the first monolayer, the surface area can be determined. Kinetic theory predicts that higher temperatures will allow penetration to smaller pores. Hence, by varying pressure and temperature, surface area distributions over the range 10 < 6 < 400,,k can be investigated, much smaller sizes than with Hg porosimetry. Adsorption techniques can be used to investigate the molecular sieve effect.*7'a'a'a'9,5° Generally, coal scientists employ both polar (CO,, CH3OH) and nonpolar (N 2, Ar, C6H6) gases; CO 2 at 298 K and N 2 at 78 K are most common. Usually, nonpolar gases give As values significantly less than polar gases. Internal area based on COz is consistent with heat of wetting methods; As based on N 2 i s m u c h less due to the molecular sieve effect. Nitrogen cannot penetrate through capillaries with 6 < 5A because of "'activated" diffusion ( D ~ e-E'ar), i.e.,

Heterogeneous kinetics of coal char gasification and combusti(m the N : diffusion rate at low temperature is so slm~ that in the course of the experimental measurements not enough time is available to fill the blind pores. Carbon dioxide monolayers migrate through capillaries because of polar interactions with the coal surface. ~ : s °

ic) 4OO (co 2 )

300200' I00,

,"3. 3 . ,"3. Coal pore structure

Pore structure is usually classified by considering three broad size ranges: (1) micropores (21 mesopores (31 macropores


1 2.5a

44- Am








CARBON ( % d a f )

~ < 20 20 < 6 < 500/~ ~J > 500/k.

This classification suggests cylindrical pores' b o a ever. electron microscopy' indicates cylindrical and conical pores• as well as flat c a v m e s . One can imagine small interstices combining these three basic shapes. Thus. the concept of pore diameter only approximates the overall pore structure. We have already seen that Hirsch's X-ra.~ work showed that (1) coal micropores reflect weak crosslinking among condensed aromatic/hydroaromatic clusters and (2) average pore size decreases with increasing rank since aromaticity and thus cluster size increase. Recently, Harris and Yust -~ found that micropores, mesopores and macropores are favored by' certain macerals, namely vitrinite, inertinite and exinite, respectively'. Thus micropores are favored and porosity decreases in high rank coals IvitriniterichL in agreement with Hirsch. Similar conclusions have also been reached using mercury porosimetry. ~'~ Note that mesopores and macropores represent "physical." rather than "chemical" cracks in the coat sample. In t h e m i c r o - m e s o p o r e range. ~i = 20-150 )k.~ '~ ~-': The molecular sieve effect is probably due to 3-8 ~, capillaries.~ 2. In the macropore range, 6 "- 103-10 ~ ,&.. thus suggesting a bimodal pore size distribution. ~: s2~~ As expected, nearly' all of the internal surface area (> 90°,,flies in the micropore m e s o p o r e range ~2.4.~,5~ However, macropores and mesopores (a > 100A) account for only 20-70°,0 of the total porosity. Gan eral. s'- have made the most complete study; of pore structure for raw coals. Using C O : and N : adsorption, they' find that the molecular sieve effect and internal area are minimized for middle rank coals (Fig. 5(a)l. Using Hg porosimetry (180 < < 29.600~1 and N : adsorption (12 < ~ < 300~kl. pore size distributions were determined and the following classification proposed : (1) m i c r o p o r e s - - 4 < c~ < 12/~: (2) transitional pores--12 < c5 < 300/~: and (3~ m a c r o p o r e s - - 3 0 0 < ,~ < 29,600.&. The authors find macropores dominate in tow rank coals while micropores dominate for high rank coals {Fig. 5(bl). Transitional (feederl pores are most influential for middle rank coals: hence, the molecular sieve effect is degraded and coal porosity minimized for these coals. ~-''-~-''-'5 Gan e t a l . find ~ "-30/~ for the ,


(b} 100-

25-~ 75-
















V2 , 95

CARBON ( % O o f )

Fro. 5. Pore structure of raw American coals: lay pore area vs rank as determined by CO: and N: adsorption. (by pore volume vs rank: t'~--macropores, V,--transitional pores. !,;--micropores (adapted from Gan etal. s2 }. transitional pores: Thimons and KisselI 5-~ find a bimodal distribution with maxima at 50 and 110/~. 2.3.3. Effect q f heat t r e a t m e n t Reactivity models for char gasification and combustion will require knowledge of the internal surface area distribution with pore size since such information determines diffusion and reaction rates within char particles. For example, macropores and transitional pores act as feeder pores, thus increasing overall reactivitx for low and middle rank chars. 25"2~ In most coal processes• pyrolysis determines the relationship between the pore structures of the char and the parent coal. Therefore. in this section•, we consider the effect of heat treatment on pore structure and overall reactivity: in the following section, we shal! consider pore structure development during gasification or combustion. Pore structure undergoes little change until devolatilization (T > 350-400~C1. U p o n pyrolysis, we expect: (11 an increase in porosity' ~:~:.39 (2) an increase in average macropore size: and (3i a decrease in average micropore ~and perhaps mesopore~ size due to volatile repolymerization, particularl\ for plasticizing bituminous coals. Thus. we anticipate no dramatic change in pore size distribution and continued molecular sieve effects. Available evidence supports these expectations at lower temperatures IT < 1300 C) and heating rates• i.e. typical carbonization conditions. 5~ At higher heating rates, volatile escape is greater and more rapid and



t250~" (°) IOOO~




these conclusions will now be considered in more detail. Chiche et al. 56 have probably made the most extensive study of pore structure changes during coal carbonization. Using adsorption (Tp < 1000°C) and X-ray (Tp > 1000°C) techniques they investigated surface area variations for heat treatment temperatures Tp ~ 500-3000°C (Fig. 6(a)). Adsorption techniques were not used above 1000~C due to molecular sieve effects. Figure 6(a) indicates that compared to non-caking coals, caking coals experience a much smaller increase in surface area and a sharp decrease for Tp > 1000°C. This loss in surface area results from sealing up of pores via coalescence, volatile repolymerization and graphitization. Toda 59 has used pycnometric techniques to study pore size changes at temperatures to 1200°C. For caking coals, both micropore and macropore volume increase, then decrease with heat treatment temperature. Above 1000°C, micropore volume is nearly eliminated, in agreement with Chiche et al. For noncaking coals, the volume of micropores plus transitional pores, changes little with carbonization temperature, i.e., development and plugging of these pores offset each other; thus the molecular sieve effect remains. Further evidence for maintenance of the molecular sieve during pyrolysis comes from Nandi er al. 5~ and Razouk et al. 5s For heat treated anthracites, Nandi et al. find that the average pore size decreases with increasing heat treatment temperature due to dehydrogenation and aromatization. In addition, they find that the internal surface area (CO, at 298 K) increases until Tp ~ 600-700°C, then drops rapidly due to graphitization. Using two sub-bituminous coals, Razouk et al. report similar results (Fig. 61b)l.











Tp ('C)



250 ZOO. 150"








Tp ('C)

FIG. 6. Effect of pyrolysis on internal surface area: (a) surface area vs heat treatment temperature for caking and non-caking coals (Chiche et al.~6), (b) surface area vs heat treatment temperature for a sub-bituminous coal--the molecular sieve effect (Razouk et al.~8). repolymerization less favored; hence, higher porosity develops, with more emphasis on micropore and mesopore contributions.'~3 In general, Ag increases most for high heating rates, low temperatures and thermosetting (non-caking) coals. 43'56'57"s8 Some of

~00 90



70 60; 50' 40 .















1 L I L











7 8 9 ~0







SOAKINGT1ME, h FtG. 7. Effect of heat treatment on char reactivity with carbon dioxide at 900~C (Blake et ul.~°}.

Heterogeneous kinetics of coal char gasification and combustion Increasing A¢ indicates micropore/mesopore development: the drop in A o is probably due to blockage of micropores. Both investigations use adsorption by polar vs nonpolar gases to investigate the molecular sieve structure. N o t e that chars with Tr _~ 600-700~C have the highest internal surface area and thus the highest overall reactivity. 4: Since high heat treatment temperatures cause loss of active sites (Section 2.2.4) and internal surface area. we would expect that heat treatment reduces overall char reactivity. Indeed. various investigators have found reactivity to decrease strongly with increasing heat treatment temperature 252634354° and soaking time 4°4: (Fig. 7). Reduced heating rates also decrease reactivit 3 owing to (I) favorable thermal annealing conditions 4: and (2) slou devolatilization and thus more tar deposition and less porosit). 4"~ Btackwood et al. 3~~-'* and Johnson 4~ find that reactivity correlates better with the heat treatment temperature (R,, m exp(lr'Tp), Tp > 700~-C) than with coal type. in agreement with Fig. 3.

2.3.4. C h a r











;-/5 ~

x (%)










v5 '


X (%)


Consider now the char remaining after coal pyrolysis. How will its pore structure develop during reaction with C O > l-I~O. O : or H , ? SIo~ reaction rates allow time for diffusion into micropores where the largest surface area is available: thus slow reactions favor development of micropores and mesopores. Faster reactions will utilize only the most accessible portion of the pore structure: thus development of macropores is favored. These simple conclusions are reinforced by the limited experimental work in this area. Detailed surface area changes during g a s - c h a r reactions were first studied by Walker et al. 6° They suggested that the biggest increases in the surface area occurred as a result of a breakdown of the molecular sieve structure, i.e. opening up of previous microcapillaries and development of new pore interconnections. Confirmation for the molecular sieve breakdown concept has recently been provided by Berger er al. ~ Lignite chars, heat treated at 1000C. were gasified with C O 2 at 900-1000:C. Lsing CO~ and C6H 6 adsorption, internal surface area changes with burnoff ( B O ) or fractional conversion X. where X = BO = 1-W;I4



were measured (Fig. 8(a)), Despite the extensive feeder pore system characteristic of lignitic chars, the results clearl} demonstrate degeneration of the molecular sieve effect during burnout. Similar results have been obtained by Johnson a~ and T o m k o ~ et al -~ Note that at 70°o B O . complete accessibility to micropore area has been achieved. Berger et al. comment that no new pores are created, but rather m~cropores and mesopores are transformed to mesopores and macropores, respectivel3. Note also

FIG. 8. Internal surface area vs burnoff during char gasification: la) breakdown of the molecular sieve effect-reaction between lignite char and CO: at 1000~C (Berger er al.611, (b) typical ,4~ vs X profiles at constant activation temperature [Johnson45 : Kawahata and Walker 62) the higher Ao values measured here compared to coals and freshl} pyrolyzed chars. Fig. 8(b) shows typical A~ vs X profiles obtained via C O : adsorption for a variety of coal chars. activation temperatures and gaseous reactants. Usually, A o increases due to micropore reactions. then decreases due to pore wall destruction and merging. The rate of Ag decrease depends, of course, on the competition between area formation and destruction. As indicated earlier, attempts to correlate char reactivit.v with A o usually fail because (1) the entire internal surface area is not accessible and [2t no known correlation exists between active and total surface area during burnout. Char reactivity clearly depends on activation temperature, pretreatment temperature, char type, pressure and gaseous reactant. In some cases. reactant penetration into the char sample is complete: 4°'45"6: in other cases, only larger pores are available. For example, Dutta et al. 3~" find that onl 3 pores with ,5> 30Jk are accessible during C O : gasification at 840-1100~C. Johnson, 45 on the other hand. finds that the average micropore size increases linearly with burnout for H a O / H 2 mixtures at 925~C. thus indicating complete penetration. F o r chars. Johnson also finds a bimodal pore size distribution with pore diameters of 20A and 1 jam as the most probable sizes: however, most of the reaction occurs on surfaces for which 6 -%<55/k. Recently. T o m k o w et al. 63 investigated internal



7'00t 600 500.

/ / 6 < 8 <200nm


3 < 8 <6rim


.~ 400-


700 600' 500

"~ 400

~..gE 300-




'~ 200.




x (%)




o ~o ;o ~o 8o ,oo


Tp.9oo'c 1

o ~o ~o ~o ~o ~oo x (%)

Fro. 9. Surface area development for different pore size ranges in xylitic semicoke (7", = 500°C) and coke (T, = 900°C) during oxygen activation (Tomkow et al.6J). surface area development (C6H 6 adsorption at 298 K) for brown coal chars pretreated at 500 and 900~C and activated with oxygen at 320-500°C. An outstanding feature of their work is the measurement of the contributions to internal surface area by various sized pores as a function of burnoff (Fig. 9). Although most of the surface area is accounted for by 6 < 30 A pores. 30-60 A pores best represent area development and coalescence, i.e., mesopores are the best indication of structural change. Note the strong effects of pretreatment temperature: (l) higher 7", allows more rapid destruction of the molecular sieve: (2) higher Tp favors micropores; and (3) overall char reactivity at larger Tp represents a compromise between reduced active site area and increased total surface area. Tomkow et al. show that the increased Ag at higher Tp is due to fewer microcapillaries, i.e. fewer molecular sieve structures. These authors also find that activation creates no new pores, but rather modifies the existing pore structure; higher activation temperatures allow greater conversion of micropores and mesopores to macropores.

where A is the pre-exponential factor and E the global activation energy. Units for/~ depend upon m and the chosen concentration units (g/cm 3, kg mol/m 3. arm*). To express /~ and rn in terms of more elementary parameters, we now consider the fundamental mechanisms occurring during gas-solid reactions. The relationship between overall (eqn. (1)) and intrinsic (eqn. (4)) reactivity will be discussed in Section 3.5. In Section 4, the influence of both boundary layer and pore diffusion on overall particle kinetics will be considered. 3.1. Chemisorption and Desorption

For any gas-solid reaction, eqn. (4) can be fitted to experimental data to determine A, E and m. Unfortunately, the resulting expression is not rigorous and only holds over limited temperature and pressure ranges. Reinterpretation of a char-gas reaction in terms of an appropriate elementary mechanism removes this difficulty. Active site theory is the basis for such mechanisms.

3. FUNDAMENTALSURFACE MECHANISMS 3.1.1. The concept of active sites An understanding of the overall kinetics or reactivity R,, of char-gas reactions requires an appreciation for the detailed interactions between gas and solid. Recall that a porous char is characterized by variations in local gas concentration (Fig. 4). Thus, at any local surface within the char particle, the local heterogeneous reaction rate is determined by the local gas concentration (if m ~ 0j. This rate is a measure of the intrinsic surface rate or true kinetics of the char-gas system. The intrinsic surface rate is usually given by /~ =/~C"

g-carbon/m-', s


where /~ is the intrinsic rate coefficient, C the local gas concentration (0 ~< C ~< C~; Fig. 4) and m the true reaction order. The rate coefficient is of course related to temperature via the Arrhenius expression [~ = Ae-e/Rr

Active site theory proposes that reactions occur at favored sites on the surface. Such sites are provided by surface irregularities; the resulting valence forces induce electron transfer causing gas-solid bonding or chemisorption. For char, we have already seen that active sites can be attributed to: (1) carbon edges or dislocations; (2) inorganic impurities ; ,and (31 oxygen and hydrogen functional groups. At each active site, the following may occur: [1) reactant chemisorption (adsorption); (2) migration of intermediates; and (3) product desorption. Both adsorption and desorption can occur via a single site or dual site mechanism. Migration allows for changes in the mobility or stability of surface intermediates. 6.~.2o2 Single site chemisorption requires one free carbon * Iatm = 101.3kPa.

Heterogeneous kinetics oI coal char gasifican,'m and combustion site and may or may not lead to the simultaneous production of gaseous species, e.g., C O : t C r --* C{O)+ CO 0 - C: -~ C(O} where C(O) denotes a carbon site filled with atomic oxygen and C/ a free carbon site. Dual site adsorption requires two free carbon sites, i.e. O : + 2C: -* 2C'(0).

Chemisorption arises from gas molecules striking the surface at locations not covered by previously adsorbed species. If 0 is the fraction of actiw" surface covered by adsorbed species, then the intrinsic rate of adsorption must be /~=&C(I-0)

k~ = Aae -E~RT


C{O) ~ C O + C : C'(O)+ C'(O) --+ C O : + C f , the former probably being the most important step in carbon gasification and combustion. Active site theory, usually presumes the following: (1) localized adsorption via collisions with vacant "active sites."; (2) one adsorbed molecule or atom per site due to strong valence bonds; (31 a constant surface (chemisorption/migration/desorption) mechanism; and (4) surface coverage less than a complete monomolecular layer. Compared to physical adsorption, chemisorption is characterized bx higher reaction temperatures, higher heats of adsorption, and often, irreversible radical mechanisms. Notice the similarity between chemisorbed species in heterogeneous kinetics and radical species in homogeneous kinetics: both play the role of active intermediates. 3.1.2. L a n g m u i r - H i n s h e l w o o d

kinetics64"6. "~

The simplest mathematical model applicable to high temperature (T > [email protected]~ gas-solid reactions was developed by Langmuir (for single site mechanismsl: Hinsheiwood later extended the model to dual site mechanisms. The following three assumptions must be added to the usual ones denoted above: (1t The surface is homogeneous, i.e. a uniform average activity can be defined for the entire surface. This assumption clearly requires a uniform distribution of active sites. (2} No interaction occurs among adsorbed species, i.e. the a m o u n t adsorbed has no effect on the adsorption rate per site. (3) Surface migration is either nonexistent or so rapid that only' adsorption and desorption can be rate-controlling In subsequent sections, alternatives to these three assumptions will be discussed. Note that the homogeneous, non-interacting surface implies that both the activation energ3 for adsorption E~ and desorption E d remain constant in time, as well as from site to site.





where C is the local gas concentration (kg,m3}, s = 1. 2 denotes single and dual site adsorption, respectively, and

Surface migration involves movement of an intermediate to a new site: hence

where C'(O) refers to a mobile site and C(O) to an inmobile (less mobile or more stable) site. Examples of single and dual site desorption are



__c-Ea . :27zMR T


from kinetic theory 64. where c is the collision efficiency and A a stoichiometric coefficient (eqn. (571). The adsorption rate /~, can be independently measured by exposing a clean surface Iheat treatment in vacuum) to gaseous atmospheres. Little is known of the mechanism of desorption: however, the rate of desorption is presumed proportional to the fraction of covered surface, i.e.. / ~ = f:~0;

s' = 1.2


where s ' = 1,2 refers to single and dual site desorption, respectively, and [q = A c e -


The desorption rate Rd can be independently measured by rapidly imposing a vacuum on the sample. Eqns (5) and (6) apply exactly for single site mechanisms, independent of site mobility. However. for dual site mechanisms, the equations presume either mobile sites or immobile sites with low surface coverage. 64 For dual site desorptiom rapid surface mobility is often required to alloa adjacent site interaction. Dissociative chemisorption ts = 2) and single site desorption (s' = t l are probably the most characteristic steps for carbon combustion and gasification. Consider now the s = s' case: assuming steady state, isothermal conditions, we have /~o = / ~ and thus from eqns (5) and 16), 0 "/~ TL-~} = aC


where a = & , i f d = __Aae~Z,_~o}:R r . Ad


Note that for a homogeneous, non-interacting surface, the parameter a is solely a function of temperature T and independent of surface coverage 0. Rearranging eqn. (7), we obtain 6-


(aC) ~-' -

l +(aC)

s = 1.2.



Assuming s = 1 and substituting eqn. (9) into eqn. !6}. the intrinsic surface rate becomes f~ = f~° = f ~ = & C , ( 1 + u C ) .



NORMAND M. LAURENDEAL system, we may easily solve eqn. (12) to give

0i =


i = 1,2

1 + a l C t -t- a 2 C 2





Assuming Langmuir kinetics, we have for the first species:

roll /

= £a.101 =



3.2. Influence of Surjace Miqration 6<6~


FIG. 10. Effect of concentration and temperature on the intrinsic rate of a system controlled by Langmuir kinetics. Comparing eqns. (4) and (10), we see that /~ can become either first or zeroth order depending upon temperature and partial pressure (Fig. 10): (1) aC<< l ~ / ~ = / < o C [ m = 1] (2) a C > l - - * / ~ = £ a [m=O]. Thus, if we fit a global intrinsic expression (eqn. (4)) to a system controlled by Langrnuir kinetics, the true order will fall in the range 0 ~< m ~< 1 depending on the partial pressure and temperature range of interest. Clearly, a simple ruth order reaction is not adequate for large variations in pressure and temperature (Fig. 10). In general, first order kinetics, i.e. adsorption control, is promoted by lower reactant concentrations (eqn. (10)) and higher temperatures (eqn. (8)). Note that either first or zeroth order kinetics also arise for s = s' = 2. Consider the s # s' case; in particular, for s = 2, s' = 1, eqns (5) and (6) give

aCO2 - ( 2 a C + 1)0 + a C = 0.

Section 3.1.2 showed that the surface coverage 0 is determined by the competition between adsorption and desorption, where adsorption refers to the reactant gas and desorption to the product gas. For Langmuir-Hinshelwood kinetics, the intrinsic surface rate/~ is obtained through the equality/~ = 1~a = Rd. Clearly, it is at this point that the assumption of rapid surface migration is employed. In some cases, however, the rate of surface migration /~¢ following chemisorption may be so slow that surface mobility becomes rate-controlling. Movement from site to site on metals, for example, is known to be activated, with activation energies E¢ -~ 5-35 kcal/mole. 6'* Obviously, higher temperatures promote rapid migration; hence, a surface reaction controlled by migration of intermediates at low temperatures may switch to adsorption/desorption control at high temperatures. Note that E, < Ea since mobility requires weak surface bonds whereas desorption requires bond rupture. If the intrinsic rate is controlled by the mobility of a single component, we have /~ =/~c = k~0



Since/~ = kaO, we see that more complex versions of eqn. (11) offer the possibility of half-order kinetics in addition to m = 0 and m = 1 (see Section 3.2). A prominent example is the carbon-oxygen reaction, which is discussed in detail in Section 3.4. 3.1.3. Effect of muhicomponent system Consider now single-site adsorption/desorption for a multicomponent system. Assuming steady state for each chemisorbed species, we obtain 65 ~ , . , C , ( 1 - Z O,)-~a.,O,=O

£"'ICt 1 + a r C 1 +azC,_"

Comparing eqns (10) and (141, we see that the second species, which may be an inert, reactant or product gas, inhibits the reaction by taking up active sites.




i= 1,2...{ (12)

where 0~ represents the fraction of active sites covered by the ith species and { is the total number of gaseous species in the system. For a simple binary

where/~¢ is the rate coefficient for surface migration. Obviously, a variety of global kinetic expressions are now possible; for example, combining eqns (9) and (15), we have

~ = £ {C\l +aC] ~c "t s = kc(aC)t/2



s= 2


1 +(aCW z where we note that the s = s' = 2 case now leads to half-order kinetics. Comparing eqns (10) and 116) demonstrates an important caveat when dealing with heterogeneous kinetics: different assumptions concerning the influence of chemisorption, surface migration and desorption often lead to similar global expressions.

Heterogeneous kinetics of coal char gasification and combustion 3.3. T t w Non-homogeneous h n e r a c t i n g Surface ~4 For Langmuir-Hinshelwood kiv.etics, we assumed a homogeneous, non-interacting surface, thus n-nplying constant values of Eo and Ed. However, for a non-homogeneous surface, the most active sites are filled first, especialb at higher temperatures where surface mobility is enhanced. For an interacting surface, filling of nearby sites creates repulsion forces thus inhibiting adsorption (and promoting desorption) of following molecules. Consequently, for the non-homogeneous, interacting surface Eo increases (and E~ decreasesl as the surface coverage 0 increases. An acceptable expression relating E, to surface coverage 0 is given by E~ = Eo~ + c%0


where Eo~ is the activation energy at 0 = 0 and c0o a surface energy constant. By analogy. E. can be related to 0 by (18b)

E d -- Eod--~dO.

Eqns (18a~ and (18bi form the basis for the so-called Temkin isotherm. Hayward and Trapnell give many examples of the importance of this isotherm for chemisorption on metals, but its significance for char-gas reactions is debatable. °6 The chemisorption rate on carbon, however, often follows eqn. l18a~ via the so-called Elovich equation. 64 Ra = Rao 8-'%"'RT where/~,,, is the adsorption rate at 0 = O. 3,4. Smlface M e c h a n i s m s .(o1" Char Gas(fication and Combustion

Table 3 lists the significant global reactions occurring during char gasification and combustion. The endothermic gasification reactions have similar rates and are thermodynamically favored only for T > 950 K. The carbon-hydrogen reaction is too slow for mosl practical applications, while the combustion step is very rapid, as expected. At temperatures approaching 2000K. the C/CO2. C/H,O and C/O: reactions probably have similar rates. ~ In this section, surface mechanisms based on elementary adsorption, migration and desorption steps are discussed for each global reaction in Table 3. For the endothermic gasification reactions, overall rate expressions derived from these mechanisms have received experimental confirmation. However. ranch-


anisms espoused for the C.'H 2 and C/O: reactions remain speculative. Later in this revte~, we will consider experimental work reporting intrinsic rate expressions and kinetic data. Such information will put our mechanistic interpretations in proper perspective. Experimental work since 1965 provides excellent evidence against direct chemisorption of molecules. Thus, in this review, the preferred mechanisms are characterized by chemisorption of radicals, not molecules. This preference is especially appropriate for chars with high concentrations of catalytic sites since metals and metal oxides promote adsorbate dissociation.°" Best evidence for dissociative chemisorption of CO., and O: to form C(OI comes from the isotopic tracer studies of Mentser and Ergun ~° and Walker e t a / . 96"-'°: respectively. In particular. Mentser and Ergun find no evidence for CO chemisorption. Support for oxygen dissociation is also provided by Marsh et al. 2°3":°" who found thal CO and CO: are produced during reaction of carbon with both atomic and moleculara8'2°: oxygen. Evidence for dissociative chemisorption of H: and H:O is given by the low pressure experiments of Biederman et al. :°5 and Wehrer et al. :°6 plus Blackwood and McTaggart's earlier work on carbon reactions with H and OH. 34 Both Blackwood and McTaggart 34 and Rosner and AllendorP 68'~69 find that O. H and OH radicals react with any carbon site on the surface, not just active ones: hence, the purpose of acuve sites is to dissociate molecular reactants.

3.4.1. C + C O 2 ~ 2 C O The principal mechanistic studies of the carbon-carbon dioxide reaction have been reported by Gadsbv et al. ~ Reif.68 Ergun et al. 36"6"'~° and Walker et al. ~9°2°6 Ergun's meticulous work at 1 atm offers convincing evidence for the following oxygen-exchange mechanism: kl:

CO 2 + C f = C O +C(O) C(O) ~ CO + Cj.

C + CO- --. 2CO C+H:O--, CO+H: C+2H: --, CHa C + 0 2 -- CO:

AH.)98(kcal/gmol) 41.2 31.4 -17.9 - 94.1


where the number of free sites C: is assumed to remain constanl with burnoff 69 Applying the steady state assumption, we have d0o

dt = kl r C e ° : O / - k l b C e ° O ° - k 3 0 °

"fABLE 3 Carbon gasification and combustion : four major reactions3'e Reaction


klb k~

Temperature range for which Kp > 1 T> T> T< T<

950 K 950K 820K 5000 K

Relative rate at 800K and 0.1 atm 1 ?,

3×i0 -~

= 0




where Ci represents gas phase concentration and 0o




0, = [ C J / [ C , ]


where the brackets indicate surface concentration (sites/m-') and C, represents the total number (occupied plus unoccupied) of active sites. By definition,

of K 133.69 is excellent.

[c,] = [ c : ] + [ c ( o ) ] or, from eqns (20), O i + O o = 1.


Substituting eqn. (21) into eqn. (19) and rearranging, we obtain 0o =



kl fCco: + klbCco + k 3" Sample weight loss is determined by the transportation of carbon atoms from the solid to the gas phase. Thus, the intrinsic site conversion rate p (Catoms/m z- s) is given by



k30 o

g/m 2.s

k Cco,_ 1 +aCco + bCco:


~,.,~ =




1 + ( C c o / K t Cco:)


where m~(g/atom) is the mass of a carbon atom. ~ubstituting eqn. (22) into eqn. (23), we have finally /~ =

An important observation regarding eqn. (24) is that /~ x [Ct]. Since the total number of active sites varies extensively among carbons or chars, prediction of char reactivity cannot be expected without prior measurement of [Cr]. Furthermore, Ergun 33"69'7° has developed convincing evidence that [Ct] is solely responsible for variations in the intrinsic surface rate/~, i.e. the activation energy for each elementary step of a surface mechanism can be measured, independent of char type. Consider, for example, the carbon-carbon dioxide reaction at lower temperatures 33 where aCco >> i and bCco 2>> 1. Equation (24) becomes


and thus the global surface rate becomes = rncp = m c [ C , ] k 3 0 o

However. strong evidence for the oxygen-exchange mechanism has recently been obtained by Mentser and Ergun. '° An isotopic tracer method using C'402, was used to follow oxygen exchange on a carbon black at 750-859°C and 1 atm. No definitive evidence for CO adsorption was found. Moreover, the equilibrium constant K1 (eqn. (26)) was calculated via independent determinations of Ag[C,]kll and Ag[C~]k t b; agreement with direct measurements

and hence eqn. (27) allows determination of both K~ and k 3 [ C , l . Note first that KI should be independent of carbon type. This conclusion has been verified by Ergun 7'33, who found (800 < T < 1400°C)

(24) KI = 4.15. l03 exp(-22.7/RT).


More importantly, since k = mc[C,]k U. a = ktb/k 3

b = klf/k 3

(25a) (25b)

Equation (24) successfully correlates existing experimental data for the carbon-carbon dioxide reaction. 6.v.v0 The oxygen-exchange mechanism suggests that CO inhibition occurs not by adsorption, but rather via reaction between carbon monoxide and chemisorbed oxygen. Following Ergun. 33'69 if we assume partial equilibration of the oxygen-exchange reaction (Grabke 2°7 contends that this assumption'fails for large C O { C O ratios), we have k~; Kl =

Cco0o .

k,---bb= Cco,.O:'


thus, the presence of CO decreases the reaction rate by reducing [C(O)] via a dynamic surface exchange mechanism, not by a simple process of filling active sites with carbon monoxide. Previous investigators, 6'7 notably Gadsby et al.. 6v have favored the latter. Indeed, the following mechanism, based on inhibition by CO adsorption, also produces a global rate expression consistent with eqn. (24): CO2 + C ~ -~ C O +C(O) C(O) --, C O + C s C O + Cs=C(CO).


= A3[C,]e-e~/"<

the pre-exponential factor cannot be distinguished from l-C,] without an independent measurement of [C,]. However, E 3 should not vary with carbon type i f [C~] is independent of temperature. This conclusion is verified for four carbon types in Fig. l l . Note that Agl-C~]k3 varies over three orders of magnitude due to variations in [C~] and A s. Independent measurement of A s for each carbon type would allow calculation of the intrinsic surface rate/~. Comparison of eqns (14) and (24) indicates that the Langmuir-Hinshelwood mechanism espoused by Ergun involves single site adsorption and desorption. However, the reader should recognize that the chemisorption reaction (R.1) may be, in reality, a dual site process composed of even more fundamental steps; for example CO2 + 2 C : - : C ' ( C O ) + C(O) C ' ( C O ) = C O + C I. If C'(CO) is a fleeting intermediate, application of the steady state approximation generates reaction (R.I) and thus the mechanism remains formally single site. The only mechanistic investigation of the carbon-carbon dioxide reaction at higher pressures

Heterogeneous kinel~cso[ coa] char gasification and combustion

is added to reacnons (R.li and {R.3i. Note that reaction (R.3')suggests the formation of other stable products after a sequence of rapid elementary steps. In this case. the coefficients in eqn. (281 become


I0 ~s



iooo ~


900 I

800 1






k =m,[C,]k ~

a = kl~ k3 c = n/c[C;]k 1f/,3 ,k 3

b = (k ].r ~ kL, )!k :,

Shaw ~,)9 has recently proposed a similar mechanism.


\ ,\



3.4.2. C-, H_,O ~ C O + H,

\\ \\



\\ , ~"



The principal mechanistic studies of the carbon-steam reaction have been reported bx Gadsby er al.-'- Long and Sykes. -~ StricklandConstable. 7; Johnstone et aI. "5 Wicke and Rossberg. ~ Binford and Eyrmg'- and Ergun. ~ As for the carbon-carbon dioxide reaction, two equivalent mechanisms have been postulated:


lOI't --

k.'\\ \

(li H:O-r-C: ~ H : + C ( O I




C(Ot ~ CO ÷C.r





FIG. 11. Temperature variation of the rate constants for the gasification step of the CO:-carbon reaction (Mentser and Ergun~'°).

(4-36 atm)is that of Blackwood and Ingeme.' 1 These authors find a higher reactivity at 790-870~C than can be attributed to the Ergun mechanism. Moreover. their global expression is of the form R=

kCm: + cC~°" 1 + aCco + bCco:


indicating a second order dependence on carbon dioxide concentration. Blackwood and Ingeme maintain that CO adsorption predominates, particularly at higher pressures. The increase in reaction rate with increasing pressure is then clearly ascribable to lower [C(CO)] and/or higher [C(O)]. On this basis. Blackwood and Ingeme suggest the following mechanism: CO2 + Cf --* CO + C(O) C ( O ) --. C O + C r C O + C ~ : CiCO) CO.~ + C(CO) --, 2C0 + C(O) CO -r CICO) --, CO2 ÷ 2 C I


A "°



1 + a C , : -,- bCH:o




Inhibition in the first mechanism is based on oxygen exchange. 69~a and in the second mechanism, on hydrogen adsorption, v2"v3"s Although the rapidity of hydrogen adsorption cannot be dismissed. 6 preference will be given to the oxygen-exchange mechanism. Significant pieces of confirmatorx evidence are: (1~ the analogy with the C/CO: reaction: (2! the agreement between experimental values of the equilibrium constant K : = k 2 / i k a ~ measured during steam gasification and calculated values based upon K : = K j K . where K~ is the equilibrium constant leqn. (261! measured during CO: gasification and K the known equilibrium constant for the water gas reaction, H : O - C O = H : +CO., :~9 [31 the agreement between E~ values as measured during carbon dioxide and steam gasification:69 {41 the evidence that H: undergoes dissociative chemisorption:S~2°" and (51 the simplified explanation of water-gas equilibrium, which commonh occurs during steam gasification, as discussed later in this section.-'~ If mechanism lit is correct, an expression for the global intrinsic rate max be written by analogy with eqn. (241: /~ =

With appropriate approximations, this mechanism can generate a global expression consistent with eqn. (28). However. a simpler, more realistic mechanism. consistent with Ergun's low pressure work. will suffice if CO: a-C{O) --+ C O + . . .


(II) H : O + C : . ~ H : + C ( O t C(O) --* CO - C I H: + C - - - C(H:I.

i 0 le, 07(


k2i. \


k = m¢[C,]k2: a = k>/k3

G0al b = k::/k~


Equation (29~ successfulh' correlates existing experimental data for the carbon-steam reactionf' -.e~ Note that. analogous to the C C O : reaction. K- can be



measured when aCH, >> 1 and bC,2 o >> 1 since eqn. (29) becomes 69 /~ =


higher rates. Also, the rate of methane formation is found to have a first order dependence on steam concentration. At 750-830°C, they report a global rate expression of the form

1 +(Cr.12,/gzCHzo)

Several investigators 32.3'*':3,75.z°6 have recognized the obvious necessity for a more elementary mechanism for the carbon-steam reaction. Dissociation of steam to OH and H is the common supposition; for example: HzO + 2Cj.,.~--C(H)+ C(OH) C(OH) + C s = C(O) + C(H) C(H)+ C(H),-~- H z + 2 C r

/~ = kCH'-°+cCZ-'° +dCm'CH2° 1 +aCH2 +bCH,o


Blackwood and McGrory assume that higher steam pressures promote conversion of adsorbed Hz to methane, thus increasing [C(O)] and consequently, the global rate. They suggest adding the following reactions to those of mechanism (II):

C(H_,)+ H20 -.CH~ + C(O) C(H2) + H: -* CH~ ---C I

C(O)-*CO+C s Evidence for dissociation of the hydroxyl radical is provided by Blackwood and McTaggart. 3'L Note, again, the presumption of dual site chemisorption, despite the single-site kinetics implied by eqn. (29). Clearly, C(H) and C(OH) must be shortlived intermediates, thus giving Ergun's simple three step oxygen-exchange mechanism. If extensive steam conversion occurs as a result of the C/HzO reaction, carbon dioxide arises as a secondary product, particularly for high ash chars. Jz In addition, water-gas equilibrium is often achieved in practical processes, especially for T > 1200°C. 7'69 These observations are consistent with- the following mechanism:7'°s'69

Using the steady state assumption for both C(O) and C(H2) and making suitable approximations, 3z they obtain a global rate expression consistent with eqn. (32). However, eqn. {32) can also be obtained from an alternative mechanism recently proposed by Shaw. t 99 If, as expected, dissociative chemisorption predominates, the reactions espoused by Blackwood a n d McGrory could be replaced by the following "straight chain" sequence:

IH2 i_.CH3 ' j'Cf [ C(H)+ H z O ~ ± ],C(O)]




CO,, + Cf ~ CO + C(O)

(R. 1)



H 2 0 + C r ~ Hz + C(O)



kza k3

C(O) --, C O + C I


The two oxygen-exchange reactions can clearly provide water-gas equilibrium; typically reaction (R.2) controls the movement toward equilibrium. Ergun 69 finds that the above mechanism also explains the kinetics of C / H 2 0 / C O 2 systems. Assuming steady state for [C(O)], the global intrinsic rate becomes


, . d c , ] {k,,coo, + h , C . : o } 1 q"kJT{ktfCco2 4- k2 fCl.l.,O+ ktbCco + k,,bCH,] ' (31)

Thus, we see that inhibition can be caused by both CO and H z as observed by Ergun s9 and Overholser and Blakely. ls°'ls3 Long and Sykes, 73 however, claim that CO does not inhibit the C/H20 reaction, while H 2 does inhibit the C/CO 2 reaction. -'°5 Some investigators suggest that H 2 0 and CO 2 prefer different sites; 69'73 in this case, eqn. (31) is obviously an oversimplification. Blackwood and McGrory 32 have investigated the carbon-steam system at higher pressures (1-50 atm). They find larger global rates than predicted by the simple oxygen exchange mechanism; moreover, methane production appears responsible for these



The C ( H ) + H 2 0 step must be much faster than the C ( H ) + H 2 step to account for the rapidity of steam vs hydrogen gasification at high pressures. 32 3.4.3. C + 2H: --, C H , Few kinetic studies are available for the C / H 2 reaction. The principal mechanistic investigations have been reported by Zielke and Gorin 7s Moseley and Patterson, v9 Blackwood 35's°'sl and Feistel et al. sz These workers all employed high-pressure reactors (5-100atm), but even under these conditions, the rate is very slow. Furthermore, there remains a dearth of reliable kinetic data and mechanistic conclusions. Here, we consider only the slow reaction between hydrogen and high temperature (Tp) char. Low temperature chars provide much higher rates due to the interaction of H 2 with pyrolysis products and oxygen functional groups, z5"~9 Such behavior is the crux of much current hydrogasification research? Most studies report that the global intrinsic rate has a simple first order dependence on hydrogen concentration, 35"79'8°'83's'* i.e. /~ = kCH,


However, Zielke and Gorin r'~ ( T = 8 1 0 - 9 2 8 ° C , P = 3 0 a t m ) and Fiestel et al. sz (T=600-1100~C,

Heterogeneous kinetics of coal char gasification and combustion 3.4.4. C + O : ---*CO:

P = 10-70atm) find



Despite extensive investigation, the mechanism of the C/O 2 reaction is probably the least understo3d of the four reactions considered in this review. There are several reasons for this unfortunate state of affairs. 9~° First. the rapid rate of this reaction obscures mechanistic studies due to: tl) mass transfer effects: (2) pore structure changes: and (3J swelling and cenosphere formation. 86 Consequently, kinetic studies are often limited to oxidation of small carbon or char particles at lower temperatures and pressures. Second. the high exothermicity of the CtO2 reaction causes uncertainty in both particle temperature and active site concentration. A solid-gas temperature difference of 200K or more is not unusual, even for particle sizes less than 100 pro. 9'8~ Surface temperatures in the 1500-2000K range can foster thermal annealing and hence reduce [Ct] during combustion. Therefore, false values for the activation energy may be measured, despite reduced catalytic effects at higher temperatures) ° Third, as experimental conditions (T, p, d) vary, the effect of secondary reactions in the boundary layer surrounding the particle change, thus making data interpretation problematic. Of particular importance here is the CO/CO: question: Are both CO and CO: primary products, or is CO2 solely a secondary product formed from gas-phase oxidation of carbon monoxide ? The CO/CO: question has been considered by man)' researchers. 6":'8,'8s'89'9° The consensus is that both CO and CO: are primary products, with the CO/CO: ratio increasing substantially at higher temperatures and lower pressures. ~ Outgassing experiments :8-s9 using oxygen-activated carbon clearly show that carbon monoxide is favored at higher temperatures (Fig. 121. A possible explanation ~°9° is


l + aC.: while Blackwood 8: (T = 650-870:C. P = 5-40atm) reports /~ =


cC~: -eCcH , 1 + aC~: +./C~: + gCc.~


at high CH4 concentrations. Under appropriate circumstances, eqn. (35) obviously collapses to either eqn. (34~ or (33). Both eqns (34) and (35) can be explained by the following mechanism :v8.8~

"H2 + C f ~ C { H 2) C(H21 + C.f ~,-~-2C(H)

2C(H)'+ H2 ~ 2C(H2) C(Hz)'4-H2~CHa + C f Zielke and Gorin '~ and Blackwood 8~ imply that surface methylene I--CH2--) could replace C(H 2) as an active intermediate in the above mechanism. The existence of C(H) was postulated since the reaction between carbon and atomic hydrogen also produces methane. 3~ An equivalent mechanism using onh' C(H) could easily be constructed from the reactions postulated in the previous section. However, corroborative evidence for any C(H) mechanism, either for the C/H 2 or C/H20 reaction, is nonexistent. Blackwood s~ shows that the global rate /~ is proportional to the oxygen content of a char sample: indeed, purified carbons have /~-~ 0. The oxygen content remains constant during gasification, an indication of oxygen-based active sites. Addition of steam accelerates the global rate significantly,838-~ probabl 3 due to C(OH) and C(H) reactions as discussed in Section 3.4.2.



E LJJ in"


(/3 LU n.' Q..

coa J










8 0



Fto. 12. Gaseous products recovered from Graphon, previously activated with 02 at 300 C. upon heating to 950~C (Laine et al.:S).



that CO is formed at carbon edges while CO~ is formed at inorganic sites. Lower temperatures favor CO 2 due to catalytic activity; higher temperatures promote utilization of carbon edges. The primary CO/CO2 ratio can be correlated by sa'9° CO/COz = A e -E/Rr, where A = 1025, E = 6-9 kcal/mot at low pressures and A -~ 1035, E "" 12-19 kcal/mol at high pressures. Secondary reactions must obviously be avoided to measure the primary CO/COz ratio. Gaseous inhibitors, low pressures and high velocities have been used; however, the relative efficiency of each technique is uncertain. In 1972, Ayling and Smith s7 used two wavelength pyrometry to measure particle temperatures during combustion of pulverized semi-anthracite (6-78 oml at 1400-2200K. Particle temperatures were also calculated via an energy balance, assuming either CO or CO2 as the primary product. Comparisons clearly demonstrate that carbon monoxide may be assumed to be the sole primary product at typical combustion temperatures. Previous investigations of carbon oxidation indicate that the true reaction order m (eqn. (4)) probably varies between zero and unity (C = Ca in Fig. 10) in the following fashion: sA°'66'gt T < 1000-1300K T > 1400-2000K

m= 0 m = l.

These results assume oxygen pressures near 0. I-0.2 atm; the wide temperature ranges very likely reflect variations in sample type and size. On this basis. Essenhigh et al. 8"66"91 discarded the usual m = 1 assumption in favor of single-site Langmuir-Hinshelwood kinetics (eqn. (10)). However, detailed mechanisms describing chemisorption and desorption were never postulated. Spokes and Benson,z°s following von Fredersdorff and Elliott v and Nagle and Strickland-Constable,~66 suggested the mechanism specified below at typical combustion temperatures:

observation that atomic species can react with any unoccupied carbon site. Reaction (R.61 accounts for the possible transformation of active sites FC,] to inactive sites [C,] at high combustion temperatures due to thermal annealing. If we neglect reaction IR.6) and assume a steady state concentration of C(O), we obtain /~ =

kC°: I + aCo:


where k = 2m£C,]k, a = 2k~/k 3

Equation (36) allows m = 0 and m = l; however, the speed of the C/O2 reaction cannot be explained unless l-C,] increases substantially for Oz compared to CO z and H,O. An alternative mechanism9z relying on C(O2) rather than C(O) is given by 02 + C f : C ( O : ) C(02) + C I -* 2 C 0

The second reaction could account for the speed of carbon combustion; however, this reaction is probably not elementary. Furthermore, the weight of evidence favors C(O), not C(O2). Since the late 1950s, evidence has accumulated ~°'65"93 showing that m = 0.5 in the temperature range lI00-1600K. More recent work 2"'42'9'* indicates that a half-order reaction can apply in general for even larger temperature ranges (650-1800K). Based on these results, a suitable mechanism for char combustion must allow for true orders of zero, one-half and unity. Recall that such a mechanism must be characterized by dissociative chemisorption and surface migration (see eqns (11) and (17)). Hence, it is not surprising that Blyholder and Eyring93 recommend the following: 0 2 +2Cf = 2C'(O)


C'(O) --* C(O)


C(O) --. CO + C i




O2 + Cf ---.C(O)+ O


O + C y - - C(O)





C(O) -~ C O + C :



C, --* Ci


This oxygen atom mechanism is consistent with /1) the extremely rapid rate of reaction between carbon and oxygen atoms 3'* and (2) the blue glow, attributed to C O + O - - - , C O z + h v , often observed around carbon particles. We note, however, that reaction (R.5) is inconsistent with Blackwood and McTaggart's

This mechanism is consistent with quantum mechanical calculations which favor mobile (twosite) chemisorption. 95 Reaction (R.8) has also been postulated by Marsh et al. z°3 and Walker et al. 96'z°2 Blyholder and Eyring93 suggest that C'(O) represents a mobile ionic bond while C(O) represents an immobile covalent (carbonyl) bond. Unfortunately, the Blyholder and Eyring mechanism cannot account for the rapidity of the C/O_, reaction at lower temperatures. Moreover, the reverse of reaction IR.7) cannot occur since experimental work has shown O2 adsorption to be irreversible for temperatures greater than -70'~C. z8'64"2°9

Heterogeneous kinetics of coal char gasification and combustion A possible alternative is the following:


Case 2. A: << iAI[


02 + 2 C 2 -'* 2C'(OI



C'(O) ~ C(O)




C(O) -* C O + C f


0 = \ --A3.'A 1


For case 1. we have two subcases: Subcase A. 4k~(l t k 3 , k 8 ) E C t ] C o :

>> k3(] ~k9/'k s)

Therefore. 0 r = 12(1 + k a / k 8) and thus k9

mdc,]k3 (1 + kg,'k~']


C'(OI -~ C O + Cf



1 + k3/k 8 ]


C'(O)-,- C'(O) ~ CO2 + C f


Reaction (R.9) is an attempt to provide faster conversion to CO at lower temperatures than allowed by reaction (R.3). Reaction (R.10) has been found by Walker et al. 96 to be responsible for primary C'O: formation. Using isotope tracer methods at low pressures, these investigators not only found positive evidence for reaction (R.10I but also eliminated previous suggestions such as

Therefore. 0o = 2k 7 [C,] Co2/k3( 1 -,- k9/k 8 ) and thus = 2mckv[C,]2Co:


F o r case 2. if we assume further

2k,o(k3/k,}2[C,] we have 0 o =

>> 2 k , ( l


(ks/k3)(kvCo,/klo) 12

/~ = m r [ C ] k s ( 1

C(O:) -* CO: + C : C O + C(O)-* C02 + C: In addition, reaction (R.10} is consistent Blackwood and McTaggart's observation that is produced during reaction between carbon atomic oxygen, a" Comparing reactions (R.9) (R.10). we see that

Subcase B. 4k.(1 +k3/ks)[Cz]Co2 << k~ll .-kg,"k81

a n d thus

+kg/k 8 {k~,:k~o) 1 :

Cg: 2


E q u a t i o n s ( 4 2 - 4 4 j d e m o n s t r a t e that the suggested

with CO 2 and and

dC~= = [C,]k,o0o/k9


dCco Equation (37) is consistent with experimental observation (i.e. C O >> CO21 since 0'o << 1 during chemical reaction. ~° The results of Laine et al. z8"89 also suggest that. in comparison to k 9 (or k3). k~o must have a lower activation energy. Application of the steady state approximation to both C'(O) and C(OI for our postulated mechanism gives h~0~-A20o+h3 = 0


where A~ = 2kv(1 + k ~ / k s ) 2 [ C , ] C o : - 2 k , o ( k 3 / k s l 2 [ C , ]

mechanism does indeed allow m = 0 (low temperatures}, m = ½ (intermediate temperatures) and m = 1 (high temperatures), in agreement with the kinetic data discussed in Section 5 of this revieu. To stmplify these equations further, we may make the following reasonable assumptions: l~ low temperatures ~ intermediate temperatures t~ high temperatures

ka/k s >> 1 k,.k~ >> I k3/k 8 <~ 1

k9/k 8 >> 1 k9.,k 8 <,. l kg,k 8 << I

Thus. we obtain rn = 0

/~ = m~[Ct]k9/2

m = 1

[~ = 2m,k~[C,]2Co:

m = ½

R = mc[C,]ksIk,'klol~'zQ)'::

~42a) (43) (44a)

Hence, we see that mobile site desorption controls at low temperatures, dissociative chemisorption at high temperatures and site migration at intermediate temperatures. Although these conclusions are reasonable, experimental work is required to verifx them.

A: = 4k41 + k a/ks)[C,] Co. + k3 (1 + k9/k 8 )

:,~ = 2k,[c,] co:

3.5. Active Site Utilization During Burnoff

The intrinsic global rate can be approximated by /~ "- rG[C,]k3(1 +kg/ks)O o


(where 0 o is given b3 eqn. (38)) since the production of CO2 contributes little to the total carbon conversion rate teqn. (37)). Consider now two possible cases: Case 1. IA1l << A2 ..

0 o = A3/A 2


The previous section demonstrates that the intrinsic rate for an).' heterogeneous char reaction is given by P, = mc- p ( [ C , ] . C,. T~


where p, the rate of conversion of carbon atoms from the solid to the gas phase ( C - a t o m s / m 2 s ) . is a function of the active site concentration [C,]. plus the local gaseous concentrations C~ and temperature T. For narrow ranges of C~ and T. we may approximate complex L a n g m u i r - H i n s h e t w o o d ex-



pressions for p by p = k[C,]C"

and thus the global intrinsic rate becomes (46)

= mc[C,]kC"

Comparing eqns (4) and (46), we see that the intrinsic rate coefficients # and k are related via /< -- mc[C,] k


Overall char reactivity R,, is usually related to the intrinsic rate/~ by an expression of the form R,, = r/A~/~,


where /~, denotes evaluation of /~ at the external surface of the sample; i.e. where C - C, (Fig. 4). The effectiveness factor i'/ (t/~< 1) represents that fraction of internal surface area Ag necessary for reaction if the local intrinsic rate were identically /~, (ex.pressions for q are given in Section 4.4). The effectiveness factor concept is a simple method of considering the continuous spatial change in local gas concentration resulting from char porosity. Combining eqns (46) and (48), and assuming an isothermal sample, we have (49)

R,. = qAgrnc[ C,]kC~' .

Therefore, sample reactivity must depend on the degree of gaseous penetration (r/), the total internal surface area (Ag) and the active site concentration ([C,]). The effect of penetration can be demonstrated by a very simple experiment. 97 Consider two porous I0


d g


I 600

I 700

I 800

I 900


FIG. 13. The effect of penetration on carbon reactivity. Relative oxidation rate vs temperature for two graphite cylinders---cylinderL has a height and diameter twice that

graphite cylinders, where cylinder L has a height and diameter twice that of cylinder S. If we now measure their relatwe reactivity R,,,L/R,,.s in oxygen at various temperatures, we obtain the data shown in Fig. 13. At low temperatures, R,,,L/R,,,s = 8 while at high temperatures, R,..L/R,.,s = 4. These intriguing results can be explained as follows. At T > 800°C, the reaction rate is fast and thus little penetration is possible: hence Rm.L/R,,.s = Ae.L /Ae.s = 4,

where A, (m'/g) refers to the external surface area of the sample. At T < 600°C, the reaction rate is slow and thus full penetration is possible: hence R,..L/R,,,s = V~.L/V~. s = 8

where V, (cm3/g) refers to the sample 600 < T < 800°C partial penetration thus 4 < R,..L/R,.,s < 8. Note that the effectiveness factor range for Duval's follows : T<600°C 600 800°C

volume. For occurs and approximate data 97 is as

rt= 1 A,/Ao < ~ < 1 q = A j A 9~-0.

A very important consequence of eqn. (49) is that

R.. ~ [C,]Ag, which implies that char reactivity is proportional, not to total surface area (TSA), but to active surface area (ASA). 'a'35 Walker et al. 's's9 have verified this conclusion by direct measurement of ASA. Oxygen is chemisorbed on the carbon surface at 300°C for 24 h; the surface complex is then removed as CO/CO2 by degassing under vacuum to higher temperatures. The amount of complex formed is a measure of the ASA, assuming one oxygen atom per carbon atom and a specific surface area of 8.3AZ/site. Other ASA measurements using H2 and CO chemisorption have confirmed the reliability of this technique, r° We have already seen that Ag fTSA) increases, then decreases during burnoff. The ASA/TSA ratio ([C,]), on the other hand, decreases somewhat initially,"-T but then increases substantially. For example, Laine et al. '8 find that for a carbon black, ASA/TSA increases from 0.3 to 3% during the first 35% of burnoff. Mentser and Ergun r° report that typically, ASA/TSA = 1-4%, but a 15~',o value is possible at high burnoff. Obviously, if ASA/TSA decreases while TSA increases, reactivity can remain constant, as suggested by Blake et al. "~° For many heat treated chars, reactivity is found to be proportional to Aq; i.e., [C,], as expected, remains constant during burnoff.98 Recently, O t t o and Shelef99 explored the relative effect of A9 vs [C,] by gasifying various heat treated chars (Tp = 1000°C) in steam (17.5 torr) at 800-900°C. Reactivity was found to vary over four orders of magnitude, with graphite the least reactive and a lignite char the most reactive. By measuring TSA, the authors showed that A9 differences account for most of this variation: FC,]

Helerogeneous kinetics of coal char gasification and combustion varied by "'only'" a factor of ten. Excluding lignite. they find that R,, ~ ,4 o to within a factor of three. Recall that t-C,) is promoted by carbon edges, inorganic (particularly, metallic) impurities and heterocyctic (particularly. oxygen) sites. If. for a given reactant, oxygen sites are important, then [C.] and/~ could decrease with BO due to oxygen site depletion. If metallic impurities were the only active sites, then intrinsic reactivity could remain constant during burnoff If carbon edges predominate, then /~ could increase with BO because of pitting: however, at higher temperatures, thermal annealing may occur, reducing [C~ and thus reactivity. Active site concentration can, of course, be stabilized by heat pretreatment: subsequent burnoff experiments must obviously be carried out at temperatures below the pretreatment temperature.








R increasing r J

~...t1~ I

. ,1












DISTANCE FROM PARTICLE CENTER Fro. ]4. Reactant profiles both external (> R) and internal ( < R ) to a porous char particle.

Heterogeneous gas-solid reactions involving a single char particle are governed by an intricate coupling of transport phenomena and chemical kinetics. The overall reaction scheme can be described by the following basic events: (1) diffusion of mass (reactant and product gases) and heat across the b o u n d a r y layer surrounding the solid particle: (2! diffusion of mass (and heat) through the porous structure of the particle; and (3) reaction of gases with solid surfaces within the particle. Section 3 of this review' has addressed the third topic: the effects of chemisorption, surface migration and desorption have been considered and appropriate expressions for the intrinsic reactivity /~ derived. In this part, we discuss the effects of mass transport. By so doing, we will be able to develop expressions for the overall particle reactivity R,, in terms of/~ and various char and transport properties. Such expressions will. of course, allow us to model overall kinetics for gasification and combustion processes.

intrinsic reactivity /~ increases, the reactant concentration profile both within and outside the particle varies as depicted in Fig. 14 tthe nomenclature has been chosen to be consistent with Walker et al. 6). Curve I represents the case for which chemical reaction within the particle is slow with respect to diffusion, thus allowing an essentially constant reactant profile across the gas film and throughout the particle. Here. the overall reactivity R,, is controlled by the intrinsic chemical reactivity /~. Under these conditions, burnoff vs time curves for all char types and reactant gases should be similar, since. as indicated in Section 2.3. most chars have similar pore structures and pore development during reaction. Indeed. recent work by Walker eta/. 1°° finds that for various chars and reactants lair at 1 arm and 405°C, CO2 at 1 atm and 900°C, steam at 0.022 atm and 910~C and H 2 at 27.2atm and 980°C), all burnoff data can be correlated by



a char

0"37 / t_~._'~3 ! '

4.I. The



Mass Transport Particle Reactivity



Consider a heterogeneous char-gas reaction at typical process conditions : T = 1000-2000 K. P = 1-20atm, d = I lam-10mm. Under such conditions, what will be the effects of reactant diffusion, both in the boundary layer and within the char pores, on overall reactivity R,,? How will changes in temperature, pressure and sample size affect the overall reaction mechanism ? A quantitative response to these fundamental queries is a major goal of this review. In this section, however, the effects of mass transter will be discussed in a simple qualitative fashion to introduce the reader to some basic




of radius


As the

' , -"

" t '


~ 0 . 5




where z0. ~ is a normalization parameter defined as the value of t at X = 0.5. Obviously, %.5 is a good relative measure of the intrinsic reactivity/~. As /~ increases, the diffusion rate, first within Icurves a and II) and then external to the particle, cannot keep up with the chemical rate: hence, the development of concentration profiles as indicated by curves a'. b, IV and finally IIl (Fig. 14). Obviously, as R increases, less and less of the particle volume becomes accessible to high gas concentrations. For curve III, chemical reaction within the pore structure is so rapid with respect to diffusion that the reactant gas concentration approaches zero both within and at the particle surface. Thus, the overall reactivity is controlled solely by boundary 1 .....






I 1¢1

I-klJ n.-


~<< 1 Ea ~ 0

rt < I . / 2

~'a= I12~" t


-.L. T

I~a = El.

FtG. 15. The three ideal zones representing the change of reaction rate of a porous char with temperature (Walker er al.6). Curve IV denotes the ideal case where the intrinsic rate is fast enough to completely consume any reactant gas near the surface; thus, the overall reactivity is again controlled by the intrinsic surface reactivity. Both curves I and IV therefore depict physical zones in which the intrinsic or true global activation energy can be measured; however, the intrinsic frequency factor can only be measured under zone I conditions since the surface area for reaction is not usually known for zone IV. If, for example, we assume reaction upon every collision,1° then the minimum ratio of internal to external area is r~52 42 (AP/As)'ain rc6z/4 ~' where 2 is the mean free path and thus the minimum penetration depth of the reactant gas. Assuming 2 = 5000 A and 6 = 100 A, we have (A~c'A~)~i. = 200, certainly a strong indication that intrinsic combustion rates cannot be measured by assuming that only the external surface area is important. In practical cases, the reactant gas profile most probably lies between curves a' and b. Here, both bulk and pore diffusion affect overall reactivity. The combined effects of intrinsic reactiyity and diffusion occur, with neither having sole control of the overall reactivity R~,. The reader should note that the curves in Fig. 14 only apply at a given instant of time. Realistically, the reactant profile changes continually during burnoff, as verified by Walker et al. via porosity measurements within reacting carbon rods. 6 The reaction order may even change during burnoff or along a pore due to Langmuir-Hinshelwood kinetics. The preceding is clearly indicative of the complex interactions required to model a heterogeneous char-gas system.

Walker et al. 6 have used temperature as a measure of intrinsic reactivity to discuss the relative importance of any one step in the overall reaction scheme. Three ideal zones (zone IV was not considered) were defined (Fig. 15). Zones [ Ilow temperature) and III (high temperature) correspond to curves I and III in Fig. 14..Zone II (intermediate temperatures) represents control by chemical reaction plus internal pore diffusion only, as indicated by curve II of Fig. 14. The intermediate zones ~ and b (Figs 14 and 15) represent transitions between the ideal cases. Curves a and II are obviously approximations to the practical case since the surface and bulk reactant concentrations are presumed equal. However, in many cases, such approximations are quite suitable. Figure 15 also indicates the effects of temperature on effectiveness factor r/ and apparent activation energy Ea. 6 F_.. is the measured overall activation energy, including any effects of mass transport (Section 4.2). Under zone I conditions, the apparent (Ea) and true (E0 activation energies are obviously equal; moreover, ~/= 1 as implied by eqn. (48). As diffusion effects increase, r/decreases since less of the total internal area A9 is used; E, also decreases, as will be shown later. The point to be made here is that diffusive effects must be considered to avoid mistaken identifications of apparent with true kinetic parameters. The relative influence of various experimental parameters on the controlling mechanism for overall char reactivity is shown in Table 4. Temperature (T), pressure (P) and particle size (d) are process parameters, while porosity (0} and active site concentration [C,] are char properties. Note that parameter values consistent with low intrinsic reactivity (T, P, EC,] low) and high particle accessibility (d tow, ff high) favor zone I. Zone III is favored

Heterogeneous kinetics of coal char gasification and combustion TABLF 4. Influence of experimental parameters on controlling mechanism for overall char reactivity Parameter*






Zone I Zone I1 Zone Ill




k M H


* k indicates a 1o~. M a medium and H a high value of each parameter. for the opposite case. Zone II. i.e pore effects, is most favored since it represents "average" values of the various experimental parameters. Therefore, realistic overall models should focus on pore (and bulk} diffusion with zones I and III being the natural result of a particle model applied at either extreme. Quantitative verification for the trends shown in Table 4 will be given in Sections 4.3., 4.4, 4.6. and 5.1. 4.2. Basic Modeling Concepts and Assurnptions 4.2.1. Definitions






Overall char kinetics (eqn. (1)) are often correlated by an expression of the form a ~'s 3. ~0 ~. ~o: R,~ =

1 (l-X)

dX dt

= KoC ~


to the intrinsic reactivity on a site basis. Therefore. the volumetric (k') or surface (/~t rate coefficient can be related to the intrinsic rate coefficient k, thus allowing measurement of a fundamental rate coefficient insensitive to variations in [C,] and Ag. as discussed in Section 3.5. Table 5 also lists the relationship between overall and intrinsic reactivity discussed previously teqn. (48)). This expression (1) considers the effects of mass transport, (2) allows for variations in A o and [C(] and (3) relates measured and fundamental kinetic constants, since R~, = K , C 2 = t I A o n b [ C , ] k C



K~. the measured or apparent rate coefficient is given by K~ = A , e -E°/Rr (52a) while k, the intrinsic or true rate coefficient on a site basis, is given by k = Are -E':Rr. (52b) While the relation between the apparent and true activation energies, E~ and E,, or the apparent and true reaction orders, n and m, is not yet evident {it will be later), we see immediately that the apparent frequency factor A s depends on A o and [C~]. This observation alone accounts for much of the confusion in the coal literature. 4.2.2. Determination qfl the intrinsic rate coe~cient [:

where C o is the ambient concentration and Ko the overall rate coefficient. Investigators usually take Ko A e -E'Rr where E = E o + c X B (c and B are constants} accounts for loss in reactivity with extent of reaction. Obviously. such expressions are merely curve-fitting procedures and cannot lead to enterpretation in terms of the fundamental kinetic parameters espoused in Section 3.4. Table 5 lists the important definitions and notation used by most workers concerned with detailed kinetics calculations. The overall particle reactivity is the desired quantity, both in terms of process predictions and fundamental experimental measurements. In this review. Rm is the preferred form of the overall reactivity. The external surface area expressions have also been used. particularly for char combustion. R,~ and Re must. of course, be expressed in terms of C,. not C o (Fig. 4). to allou for fundamental interpretation: however, both C~ and Co expressions have been used for data correlation. In most modeling work. mathematical convenience dictates that the intrinsic reactivity be expressed as a global, rather than a L a n g m u i r - H i n s h e l w o o d rate. The global expression can be obtained from the appropriate L a n g m u i r - H i n s h e l w o o d expression by neglecting product inhibition and investigating the limits of the resulting rate equation. F o r example, eqns (241 and (291 can be approximated by allowing 0 ~< m ~< 1. For global kinetics, the intrinsic reactivity can be expressed on either an area or volume basis (Table 5~. In both cases, this reactivity can in turn be related =

Jpl-c', 4 4


The total particle reaction rate is given b.~ R,, = O?Ao+ A~IR , = 07A~+,4~)~C~


where A 0 and A,, are the specific internal and external surface areas, respectively. For "'non-porous" particles (zone IV). r/A~ < .4~ and thus R,, = A e k"C ~ . (54) Knowledge of C, via surface probing or boundary layer calculations now allows determination of /~.9 TABLE 5. Definitions for heterogeneous kinetics I. Overall particle reactivity* (11 Mass basis (g/s g) R,~ = K oC~o= K sC~

(2! External surface area basis (g/s. cm: I** R~ = K,.,.C~. = K,.sC7 R, = ?a,,R~

II. Global intrinsic reactivity+ (1) Site basis (sites/m: • s) o = k[C,]C-

(2) Area basis (g/m=-st ,~ = ~ c - ' /~ = . ~ ,

.'. ~ = m d C , ] k

(3~ Volume basis.(g/cm 3 s ) R = k'C ~ R ' = c;aAaR

" k' = o a A e ~

III. Relationship between particle and intrinsic reactivity R,~ = 71Xd~ ~ = ~ . 4 f i C ; * Reactivity usually refers to the organic carbon content of the char sample, i.e. gin-C/gin-char, s. ** -,, = 1'~ A,,: characteristic sample dimension. + Intrinsic reactivit.~ is usual!}' calculated per unit internal surface area



Knowledge of I-C,] then allows determination of the fundamental rate coefficient k since/~ = mcl-C,]k. As discussed previously, eqn. (54) is a reasonable approximation for porous particles, if the intrinsic reactivity is high enough (some combustion conditions), as shown by curve IV of Fig. 14. Recall that, here, determination of k will allow calculation of the true activation energy E,, but only an estimate for the pre-exponential factor ,4,. In most cases, gAg >> A e and thus from eqn. (53),

R.. = ,A~C;".


Unfortunately, pore diffusion often predominates (r/ < 1) and thus determination of /~ is difficult. However, if zone I conditions can be arranged, eqn. (55) reduces to

R,, = A fiC'~.


Since Cs = Co for zone I (and [I), eqn. (56) allows for direct determination of/~. This, of course, is the exact meaning of the phrase, "in zone I, the overall particle reactivity is controlled by chemical kinetics". Equation (54) represents chemical reaction only at the particle surface, whereas eqn. (56) represents an equal reaction rate throughout the particle volume. Hence, for zones III and IV (Fig. 14), the particle diameter decreases continually with burnoff, while the apparent density remains constant. For zone I, on the other hand, ao decreases continually., while d remains constant. These conclusions are often used to determine the extent to which a particular experimental system is bulk diffusion or surface kinetics controlled (Section 5.1.). 4.2.3. Basic modeling assumptions Conceptual and mathematical convenience dictates certain simplifying assumptions appropriate to heterogeneous reaction schemes. The following basic assumptions will be incorporated into all models discussed" in subsequent sections: (1) spherical symmetry (2) intrinsic reactivity modeled as a global, ruth order irreversible rate expression (3) all gas-solid reaction occurs within the particle (4) isothermal particle (5) psuedo steady-state analysis (6) gaseous reactants are dilute species in an inert component. The first assumption allows simplified onedimensional solutions to the species conservation equation; cylindrical and planar systems have also been considered.6'65., o3,1oa,.1o5 Assumptions (2) and (3) allow use of the global intrinsic reactivity expressions in Table 5. Langmuir-Hinshelwood kinetiizs would require simultaneous solution of two or three species equations; hence, only global expressions have been employed by most investigators. The isothermal assumption eliminates the energy equation and thus simplifies the analysis considerably. Justification comes from a simple heat balance which

gives for the maximum temperature drop across the particle :29

fT = I---~ T~' max =


where T~ and T, are ihe temperatures at the center and surface of the particle, respectively; D is the diffusion coefficient, AH the heat of reaction and x the thermal conductivity. For AH = - 4 0 k c a l / m o l , T~=1250K, x = 4 " 1 0 - 3 c a l / K ' c m ' s (typical of high temperature chars), D = 10-1cm/s (Knudsen diffusion corresponding to 6 = 400A), and C~ = 5.10-Smol/cm 3 (a partial pressure of 5atm), we find that /~r = 0.04. According to detailed calculations performed by both Bischoff~°6 and Weisz and Hicks, ~°7 isothermal conditions may be assumed to good accuracy for t/3rl < 0.05. Weisz and Hicks also show that for fast exothermic reactions, the temperature profile flattens out considerably as the center of the particle is approached; the temperature gradient is highest near the e x t e r i o r surface. Similarly, McGreavy' and Thornton ~°s find that the temperature drop across the boundary layer dominates that across the particle for gas-solid systems. They further show that if all thermal resistances are lumped into the boundary layer, the isothermal particle model is a very good approximation to the non-isothermal case. Non-isothermal calculations, i.e. simultaneous heat and mass transfer, have been considered by Wen and, Wei 1°9 and Lih and Lin. 1~° The pseudo steady-state approximation has been shown to be valid for gas-solid reactions by both Bischofft i t and Wen. i t : The dilute species approximation permits two simplifications: {1) binary diffusion theory can be used to model a multicomponent system; and (2) isobaric conditions can be assumed, i.e. volume changes and thus convection within pores can be neglected. Approximate methods for dealing with non-dilute systems (Stefan flow) have been presented by Thiele t13 and FrankKamenetskii. 65 Mulcahy and Smith t° show that for a system with 80°; inert gas, the maximum error in overall reactivity R,, is about I0°~. In view of the basic assumptions listed above, our general gas-solid reaction scheme simplifies to the three fundamental processes considered in Section 4.1: gas film diffusion, pore diffusion and surface kinetics. Each process must be accounted for and properly coupled into the overall system. The distinguishing factor that separates the existing models is the method used to describe diffusion through the porous solid. Modeling of intrinsic surface kinetics and boundary layer diffusion is relatively standard. 4.3. Mass Transport Phenomena for Char Reactions For each carbon reaction in Table 3, we may define a gravimetric stoichiometric coefficient

A = ,Vtc/v~Mg,


Heterogeneous kinetics of coal char gasification and combustion where % is the molar stoichiometric coefficient for the reactant gas and M S M g is the molecular weight ratio of carbon to reactant gas. For combustion, we have seen previously that carbon monoxide is the prtmary product at high temperatures; hence, the surface reaction is usually, assumed to be C + ½ 0 2 --* CO(A = 3,/4) rather than C + O , --* C O d A = 3/8). The xrnportance of eqn. (571 will become apparent in the following subsection, where we link carbon reaction rates to mass diffusion rates.

To an excellent approximation, 9



where d~ is the mass flux of reactant gas (g/s. cm:) at the surface, h v is the mass transfer coefficient (era/s) and C o - C ~ (g/cmYt is the concentration difference across the boundary layer (Fig. 4). Since the overall particle reaction rate must be related to the amount of reactant arriving at the surface, we then have (58b)

where K o is by definition the diffusional rate constant (overall mass transfer coefficientl. C o m b i n ing eqns (58). we obtain K D =

Ah o :

where we have assumed a constant average boundary layer temperature T. Substituting eqns [64) and (65) into eqn. (63i. we find

12AD xCo R"'D =

2AD, d


and thus from eqn. (58b), 2ADa

R~ = - ' - y - - t C o - C s ) .



whether the particle is porous or nonporous. Note that R,,.D is the highest possible reactivity; if Rm < R,,.z~ then chemical effects are operative. We may now calculate the total reaction time for film diffusion control z~ by noting that the particle mass, m v = ~no~d 3, is related to R,,. v for a carbon particle by 1 d m v = Rm.o. m v dt

Using eqn. (67) and integrating, we easily obtain the famous d:-law: do -d


where d is the particle diameter, DA the binary diffusion coefficient for species A and Re the Reynold's n u m b e r based on particle diameter. Typical values for c are 0.30 < c < 0.35. 9"1° At high temperatures, a reasonable approximation is Sc = pr ~- 1. For a stagnant atmosphere or pulverized char particles (d ~< 1001am). Re = 0: hence we have from eqns (59) and (60), K° =


Thus. film diffusion tends to be rate-controlling for large samples: small particles encourage chemical control. Equation (63) holds independent of pore diffusion effects: thus, for pure b o u n d a r y layer control (zone III), we have





thus, knowledge of h D is required to calculate K o. The mass transfer coefficient hD can be obtained from Sherwood N u m b e r correlations. F o r a sphere. ~~'~ Sh = - - = 2.(1 +cRel/2Scl/a), D,

= --~-~-(xo-x~

R., cc TY'4P°d -2.

The universal approach taken to model gas film diffusion is to use a simple integrated form of Fick's Law. i.e.

R~ = K o ( C o - C ~ ) = A J s.



4.3.1. B o u n d a r y laver diffusion

d~ = hD~Co-C~),




8ADACo t



where d o is the particle size at t = 0. Based on eqn. (68), we now find that the total reaction time is • z D = ~:Dd o2


o, ~cD = 8ADACo'



Under combustion conditions, extensive data demonstrate conclusively that eqn. (69) predicts burning times for a variety of chars if do >1 200~tm 1°. Zone IIL however, is not normally favored under gasification conditions (except perhaps at T 2000 K) due to the slower intrinsic rates compared to combustion.

162) 4.3.2. Pore diffusion models

F r o m Table 5, R e = 7o,R,,: for a spherical particle, 7 = d/6 and therefore from eqn. (62), R,,


12ADa aod_, (Co-C~}.


The literature contains numerous methods for mathematically' describing gaseous diffusion through complex pore structures. In general terms, however. most pore diffusion models are of two basic types: macroscopic or microscopic. In the macroscopic



approach, an empirically derived effective diffusivity D e represents the flow resistance throughout the particle. Gas transport from the exterior surface to any internal point within the particle is modeled using Fick's Law, i.e. Ja = -

De dCa dr '

where Ja is the mass flux (~cm 2- s) of species A and Ca its local concentration (g/cm3). The majority of existing models can be classified as macroscopic. In the microscopic approach, diffusion through a single pore rather than the entire porous particle is considered. The overall particle is depicted by an appropriate combination of single pores. Flow through an individual pore is modeled using capillary diffusion theory. According to capillary diffusion theory, isobaric flow through a cylindrical pore may involve molecular diffusion, Knudsen diffusion and surface migration. 11s Surface migration will only occur for a mobile chemisorbed layer and is usually neglected. Molecular diffusion becomes the predominant mode of transport whenever the pore size is large compared to the mean free path of the diffusing species (6/J, a > 10). The molecular diffusion coefficient (Da) for binary gas systems is a function of both temperature and pressure, as shown by eqn. (64). Knudsen diffusion, i.e. molecular transport via collisions with the walls of the capillary, occurs primarily when the pore size is small with respect to the mean free path (6/2 a < 0.1). For a smooth pore, the diffusion coefficient for Knudsen flow can be expressed as 115 Otc.4

3 \~m a ]

Note that DKa is independent of pressure, but is linearly proportional to pore diameter. According to Youngquist, lzs the combined effects of both Knudsen and molecular diffusion can be modeled to a good approximation for an isobaric system by using the overall pore diffusion coefficient, (70)

Compared to the microscopic approach, macroscopic models suffer due to difficulties in making a priori calculations for the effective diffusivity D,. Usually, investigators rely upon experimental measurements; correlations of the form De=cqJ p

p = 1,2,3

A~O N -- - (Tz62/4)-r '


where z - 1/sin f2 is the so-called tortuosity. The numerator in eqn. {72) represents the void area on the external surface; the denominator represents the area circumscribed by a cylindrical pore intersecting the external surface at an average angle ~, i.e. the area of an ellipse. Wheeler proposes ~2--45 °, implying r = x/~-. The length and diameter of an average pore can be obtained by equating the total predicted and experimental void volume and surface area: 7t62 L N'---~- p = V~


N . rolL,,-f(I - ~) = Ag,


where f is a surface roughness factor. For smooth non-intersecting (and thus non-porous) pores, the j ( 1 - t ~ ) factor in eqn. (74) reduces to unity. Simultaneous solution of eqns (73) and (74) gives the average pore diameter: 4Vg 6 = -~-J(1 -~0) =

4~f ~0(i-~0).



Substitution of eqn. (72) into eqn. (73) gives the average pore length:


D = ~ a +~-~xa)

simple porous slab. 65 Wheeler depicts the particle as a system of cylindrical pores (N pores/g), each pore being of a theoretically determined average length L and diameter 6. The pore structure is homogeneous and interconnected; the pore direction is random and any surface (internal or external) consists of a fraction ~O of pore mouths and a fraction 1-~O of solid material. Based on these assumptions, the number of pores/g is given by

v~ L , = A,$, = 7r.


Following Frank-Kamenetskii, 65 we now consider diffusion through a porous layer coritaining nonintersecting cylindrical capillaries. The mass flux can be modeled via an effective diffusivity, dC J, = - D,-~x,


or as a summation of the flux through each pore, dC D dC Jp = - D . . . . . dl r dx'



are often employed. 6' 1t 2. ~t 6.~ x7 A constant value lbr the effective diffusivity is near,'y always assumed. Equation (71) shows, however, that D, varies with both time and position within the sample. A more satisfying formulation of the effect of porosity on effective diffusivity comes from an application of Wheeler's classic pore model ~ls to a

where D is the pore diffusion coefficient, given by eqn. (70). Note that in eqn. (78), conversion from a coordinate system along the pore to one perpendicular to the slab surface is accomplished via the tortuosity r. Since J, and Jp are related by Jr = (9t62'4~ - - - : - - } NJp

Heterogeneous kinetics of coal char gasification and combustion we have from eqns (77) and (78j, De =

where D'c is the constant effective diffusivity for the porous ash. Integrating across the ash layer {R > r > r r) and normalizing with respect to the constant particle radius R yields

zA e •

Substituting from eqn. (72). we obtain finally De =

ryAD'e ri7¢ = 4~ZR2R(--ff~_r j(C~-Crt





Assuming z = \:,'2, we get D~ = DO~2, the expression for effective diffusivity espoused by Satterfietd? ~4.4. Macroscopic Models

The most simplistic macroscopic approach to modeling gas-solid reactions is the classic unreacted shrinking core model. ~°3'~°9 As the name implies, this model depicts reaction as taking place along a symmetrical front that recedes towards the center of the particle (Fig. 16t. As the reaction front passes any

e: =, 7










Flo. 16. Unreacted shrinking core model.

given point within the particle, total conversion of carbon occurs; moreover, an ash layer can form about the central unreacted core. Figure 16 shows the sequential operation of three basic processes: gas film diffusion, ash layer diffusion and surface reaction at the central core. Gas film diffusion can be modeled by expressing eqn. (58b) as ~fi¢ = 4r~R2Ko(Co- C~)


where rh, is the constant mass reaction rate of carbon (g/st. In terms of ash layer diffusion, rh~ is given by ri2¢ = 4rtr2 AD'~ ~ r ,



where the particle reactivity has been expressed on an external surface area basis (Table 5). Combining eqns (81), (82) and (831 to eliminate C, and C:, we have fin ally rnc Re = 4~R2 = Ke,oC o


1 R(R-rf) -~-~D4 - - - r:AD'~


where Keo=.


", 2

,i~, = 4~R ~ (': \,,R,I]

4.4.1. Unreacred shrinking core model




where C: is the gas concentration at the reaction front r = r:. For a simple first order reaction, the normalized rate at the reaction front is given by r



R 2 "\-~ +_--g2:--~- ) " r: K~..c/

Equation (84) is the classic result of the basic unreacted shrinking core model. Note that the overall rate coefficient Ke.o reflects three basic resistances--ffinn diffusion, ash diffusion and chemical reaction, any of which can become ratecontrolling. Clearly, non-unity reaction orders can be considered via a simple modification of eqn. [82): Shen and Smith I2° allow further variations, i.e. changing particle size and reversible surface reaction. The unreacted core model is probably the best simple representation of gas-solid systems)~2 As r: decreases, the shift in rate-controlling step is adequately modeled by eqn. (84): moreover, the ash layer resistance can easily be omitted, thus successfully modeling fluidized bed combustion) I~:~° However. if the sample is characterized by (1) slow reaction, (2) high porosity or (3) small size, heterogeneous reaction will occur internally rather than at a well-defined surface. Indeed, Calvelo and Cunningham ~:~ show that for most practical situations, where the gas film resistance is minor, the shrinking core model is almost completely restricted to nonporous solid reactants. Therefore, for the majority of char reactions, except perhaps combustion of larger samples, a progressive conversion model is required. 4.4.2. Progressive conversion models Progressive conversion schemes represent a general approach for macroscopically modeling heterogeneous reactions involving porous solids. The object of such models is to obtain a solution for the effectiveness factor q. and thus from eqn. (55/, for the reactivity R,,. Two types of progressive conversion model are extant (Fig. 17t. Type 1 assumes no ash zone: type 2 allows the existence of an ash layer. Type 1 models are usually applied to fiuidized bed or








~¢j~'G&S FILM










I\ ?C.-O.-.L : I/J, /




z rr p-

[ Z uJ ~J








1 R










FIG. 17. Progressive conversion models: types 1 (no ash zone) and 2 (ash zone). entrained flow systems, or to fixed beds during the initial reaction phase. Type 2 models find most application in the later phases of reactions occurring in fixed beds. In the type 1 model, the reactant gas profile within the porous particle is modeled using a differential equation of the form

1 d r2O,


r 2 dr

= 0



where the stoichiometric coefficient A converts the reaction rate term from g/crn 3 .s of carbon to g/era 3' s of reactant. Note that eqn. (85) depicts the simultaneous occurrence of both diffusion and surface reaction. The boundary conditions are given by D, dC

-~r =ha(C°-C~) dC --=0 dr

@ r=R

@ r=0,

(86a) (86b)

where eqn. (86a) accounts for diffusion across the gas film and eqn. (86b) maintains a zero gas flux at the particle center. In dimensionless form, eqns (85) and (86) become 1 d / 2 .dqG o.


~2 d~

dW = (Rho~ O*-(1-q') " d~

\D,,,, ]

dqs --=0


@ ~=0


@ ~= 1

(=7) (88a) (88b)

where qs - C/Co, ~ = r/R and D ] =- DjD .... where De., is the value of the effective diffusivity at the

the well known Thiele modulus,

(k'Co'- l,~t:'2 ~ = R LA--~--~-=.=)


which represents the characteristic ratio of reaction to diffusion rate for a particular gas-solid system. Low values of ~" imply zone I conditions; high values zone II conditions (Fig. 15). Thus. as expected, zone I is favored by decreasing values of particle size, temperature and pressure. In the type 2 model, a porous ash layer void of solid reactant is assumed to develop outside the inner core (Fig. 17). Thus, two separate zones exist throughout the reaction: the diffusion or ash zone and the reaction zone. For. the ash zone, the reactant gas profile is defined by the simple diffusion equation, i d /.:


~ZdeL~ D=--~-) = 0


where D;* is the non-dimensional effective diffusion coefficient for the ash layer. Equation (87) adequately describes the reactant profile within the reaction zone. The boundary conditions

dq s /Rho'~ D'*--=~--~.~)(1-W), d~

o'/dV' "t"~-,) r":

= o " {d'%_ \d~) :

dqs --=0


@ ~=0

@ ¢=1


@ ~. = 4:

(91b) (91c)

account for gas film diffusion and particle symmetry, as well as mass flux continuity at the reactiondiffusion zone boundary. Representative solutions to both types of progressive conversion model have been obtained for a

Heterogeneous kinetics of coal char gasificauon and combustion


TABLE6. Representative solutions to progressive conversion models Investigation



Film diffusion

Effective diffusivity

Aris ( 1957 iI o~ Roberts and Satterfield (1965) ~:-" Tien and Turkdogan (19701:°~ Mehta and Aris (1971)~o.~ Ausman and Watson (1962) a2-~ Ishida and Wen (1968) 12'* Wen (196811 ~2

1 1 1 1 1.2 1.2 1,2

1 0-i * 0-2 ] 1 I 2


Constant Constant Constant Constant D~ = D'~ = constant D~ ,~ D'~ = constant D~ ~ D'~ = constant


No Yes Yes Yes Yes Yes

Delr~ va D'elr)

*The irreversible mth order reaction is replaced here by the modified Langmuir-Hinshelwood expression R = kC/(l +aC'i where C denotes product concentration. realistic case of variable effective diffusivity and nonunity reaction order has not received extensive attention. Only Mehta and Aris 1°-' consider ruth order kinetics; Roberts and Satterfield aBa present results for a simplified L a n g m u i r - H i n s h e l w o o d expression, i.e. product inhibition is neglected. Tien and Turkdogan 2°~ allow both product inhibition and volume changes. Analytical solutions for a first order reaction for both model types 1 and 2 have been obtained by Ausman and Watson ~23 and Ishida and Wen. ~24.~2_~ Ishida and Wen ~:4 consider a particle having constant yet different diffusivities in the ash and reaction zones (D e ~ D'e). Comparisons between the progressive conversion and unreacted shrinking core models are drawn, in general, they find that for /> 100. the type 2 progressive conversion model and the unreacted core model are identical. Wen 1~2 considers the effects of ruth order reactions, changing particle size and variable diffusivity, but presents limited results. Typically, he assumes the effective diffusivity to be related to porosity by eqn. (71). As expected, the effectiveness factor increases with burnoff due to concurrent increases in porosity; moreover, higher values of r/ are obtained compared to the D e = D', case. Wen claims that the use of constant effective diffusivities is acceptable in most circumstances. Modifications to the basic progressive conversion model have been developed by several investigators. Szekely e t al, I2~'I:':'12s'129 have proposed a variation known as the grain model. In this model, the reacting particle is represented by an array of small spherical grains (Fig. 18a). The dimensions of the array can be related to the particle porosity. Diffusion within the fixed array of grains is modeled by a constant empirical effective diffusivity. Surface reaction is assumed to occur only within the spherical grains, as described by the shrinking core model. This approach can be used to study the effects of porosity, i.e. grain size and grain size distribution, on the reaction rate of porous particles. Abed and Rinker ~3° have used a similar approach to study the effects of volume change: i.e, the isobaric assumption is relaxed and convective flow within the particle is considered.


Peterson depicts the porous solid as a system of uniform cylindrical pores with random interconnections (Fig. 18b). The reaction rate is assumed proportional to the surface area available within the pores. Assuming each individual pore enlarges uniformly (remains cylindricall, Peterson obtains a necessary" relation between pore diameter and particle porosity. Diffusion is again modeled via a constant effective diffusivity. (o)











FIG. 18. Modified pore structures for the progressive conversion model: (a)grain modal (Evans and Szekely 126 ), (b) random monomodal pore model (Peterson131), Ic) random bimodal pore model (Wakao and Smith a32 L A comparative study of progressive conversion models, including the Peterson and Szekely approaches, is presented in a review bv lshida and Wen. a25 This study shows that for low temperature. kinetically controlled reactions, the particle reaction rate is, as expected, the summation of the reaction rate of individual grams or pores. F o r high temperature. diffusion controlled reactions, all progressive conversion models can be approximated by the shnnking core model through proper use of an



"equivalent" rate constant. Thus, to a large extent, the various progressive conversion models are indistinguishable when applied to practical burnoff problems. Wakao and Smith '32"133 have developed a progressive conversion model with a bimodal pore size distribution. The solid is assumed to consist of many microporous grains compressed together forming a pellet. The interstices between the individual grains comprise the macropore system of the pellet. The effective diffusivity is modeled via a statistical sum of three possible flow paths (Fig. 18c): (i) through the macropores; (2) through the microporous grains; and (3) through macro- and micropores in series. Reaction is assumed to take place solely within the microporous grains. Cunningham and Geankoplis ~3~ expand this. model to include trimodal pore size distributions. In a review of models for porous media, Youngquist it5 concludes that though such polymodal distribution models have been successful in predicting gas fluxes through pellets made of compressed powders, their general applicability to naturally porous materials is questionable.

and ~/=

tanh (I)



respectively. Aris ~°~ also shows that the ~/ vs Thiele modulus curves for various geometries are nearly equivalent (10% maximum error) for a first order reaction if the Thiele modulus of eqn. (93) is modified to give cV -

7(k'/AD,) 112.


In addition, Mehta and Aris demonstrate that the ~/ vs Thiele modulus curves for ruth order reactions (m /> 0) can be approximated by the first order curve (20% maximum error) if the Thiete modulus of eqn. (96) is further modified to give65'~°5

,F!m+ 1)k'C,'-l.Tl'2 (I)" = 'L




Effectiveness factor vs Thiele modulus curves for various pellet shapes are shown in Fig. 19 for a first

\X 4.4. 3.

Effects of pore diffusion


Much physical insight into the effects of pore diffusion can be obtained by considering the type 1 progressive conversion model with constant effective diffusivity and negligible gas film resistance. F o r a first order reaction and a symmetrical pellet of arbitrary shape, the species equation (see eqn. (87)) becomes ~o¢ V~2qJ-q)2~P = 0






r.v, tNn~'~. ) ~ - - - - F L A T PLATE


"t7 o~


where • ~. C/C~, ¢ = r/L and the Thiele modulus is

= L(14IAD,)1/2.


In eqns (92) and (93), L represents the half width of a slab, the radius of a cylinder or the radius of a sphere. The boundary conditions for the case of no film resistance (C, = C°) are given by dW


d¢ W=[

0.01 [ 0.1








FIG. 19. Effectiveness factor vs Thiele modulus for various particle shapes and negligible gas film resistance. Exact solution for m = l; good approximation for m t>0 (Arisl°¢).

@~=o @ ~=L

Using these boundary conditions, eqn. (92) can be solved for the gas concentration profile within the pellet. The effectiveness factor can then be derived from r / = C/C~ =




where C is the average reactant concentration within the pellet. Solutions to eqns (92) and (94) are given by Aris: 1°4 for the planar and spherical geometries, the effectiveness factors are

= tanh ~/'~


order reaction. The applicability of these curves to ruth order reactions is verified by Fig. 20. Figures 19 and 20 show that the reactivity is controlled by surface kinetics 01 = 1) for q~,. < 0.5 (zone I) and by pore diffusion (~/= I/q~,,) for ~,, > 5.0 (zone II). As the reaction rate increases, the gas penetration distance and thus the effectiveness factor (the fraction of total internal surface area used for reaction) decreases. 65'~°3 The region 0.5 <~,,, ~< 5'.0 is not uncommon for char gasification and combustion; obviously, the simultaneous occurrence of reaction and diffusion must be considered. The effect of pore diffusion on apparent kinetic parameters can be demonstrated by considering particle reactivity under zone II conditions. For an

Heterogeneous kinetics of coal char gasification and combustion




O. I






FIG. 20. Effectiveness factor vs r/O~ for a fiat plate, negligible gas film resistance and variable order (Mehta and Arisl°5).

ruth order reaction, the reactivity is given by R , = Ag/~C-g = k'~--g


t7 a



C-g - ~C7 = ~



Combining eqns (98) and (99), we obtain

R,. = rlkt C~m /a, = k t C~m /%¢.,.


Substituting for the Thiele modulus from eqn. (97), our final result becomes 6~


= 6_F2ADe ]'": aadLm+l k,C~.~


where for a sphere, 3' = d/6. Equation (101) indicates that the overall particle reactivity is the geometric mean of the diffusion and reaction rates. Note that under zone II conditions, R= m d - ~, while for zone I. 17 = 1 and thus from eqns (98) and (99), R,, is independent of particle slze. In other words, for zone I, n~ ~ V,: for zone II. m~ m A,. Comparing eqns (51) and (101), we see immediately that the apparent order and activation energy are related to the true order and activation energy by n=

m+l "~

E,~ = E,/2.

(102a) (102b)

Equations (102a) and (102b) demonstrate convincingly the necessity of considering diffusional effects when attempting te measure true kinetic parameters. Pore structure likewise affects the relation between

apparent and true parameters; for example Carberry ls5 finds that for a bimodal system, n = (m + 3),/4 and Eo = E,/4. In this section, we have excluded boundary layer effects. Mehta and Aris 1°5 give results for the case of gas film resistance, but no simple correlation of the type shown in Figs 19 and 20 is possible. The R,, expression given by eqns (98) and (99) can be used for the film diffusion case by calculating C, from

R~ = ~Ao~C ~ = Ko(C~-C~).


Alternatively, some investigators prefer redefining the effectiveness factor as 105. ~1: r/ -



and calculating particle reactivity from R,, = r/AJ~Co~.


4.4.4. Utility of macroscopic models Macroscopic models have been used with reasonable success to predict overall characteristics, such as conversion-time relationships and particle effectiveness factors. Despite its severe limitations, the unreacted core approximation is still being used to model char combustion in fluidized beds. 2~° Progressive conversion models have received experimental substantiation for the case of carbon oxidation in inert porous solids (catalyst regeneration), 211 but their suitability for char reactions remains in doubt due to the unknown relationship between effective diffusivity and burnoff. Experimental work is especially needed to establish the relationship between local pore structure (Section 2.3! and effective



diffusivity. Recently, Smith and Tyler 9'*'1'~9 have used a type 1 progressive conversion model (eqns (55), (95a), (97), {103)I and D , = Dq,/2 (eqn. (80)) to calculate for the first time intrinsic reaction rates from overall char combustion data. This methodology implies important new opportunities for utilization of progressive conversion models and thus the need for improved effective diffusivity predictions. The relative simplicity of the macroscopic approach in part explains its general popularity. However, this approach is not suitable for predicting specific reaction details, such as the variation of Ag, Vg, q9 or pore size distribution with burnoff. Such information is important if char reactivity is to be maximized, as in activated carbons. Detailed calculations of this kind require the development of microscopic models.

described by the following species conservation equation ~°3 1 d[.









where a(z) is the local pore diameter, ,~ the intrinsic rate coefficient for the ruth order reaction, and D(z) the overall pore diffusion coefficient (eqn. (70)). The effect of gas film diffusion as well as pore symmetry are accounted for by the boundary conditions dC -D~z =ho(Co-C 0 dC = 0 dz


@ z=0

(106at (106bl

(~! z = Lp

where Lp is the pore length (eqn. 176)). In dimensionless form, eqns (105) and (106) become

4.5. Microscopic Models Microscopic modeling of reactions between gases and porous solids is generally broken down into two steps: (I) development of a reaction model for the single pore; and {2) prediction of the overall particle reactivity in terms of the single pore result. Step (2) will be discussed later in this section; first, we consider the single pore model.


dW d~ 2 + :t--~- --* q~a~p,. = 0

D* d ~ = # ( v dq~ d~



,g ~ = 0



{108a) (108bt


4.5.1. The general single pore model Typically, the single pore is modeled as a smoothwalled, open-ended capillary of known geometry (Fig. 21). A gas film can be assumed to exist between



GASFILM+ ~ / /







2 d~ -

t r



pore diffusivity and D, is the initial pore diffusivity at the pore entrance. The parameter ~ is defined as


/ ]" ~


where W = C / C o , ,=-,.'Lp, D*=-D/Ds and f l = hoLJD r The parameter /~ represents the bulk to


w 0 Z 0 0 t.9





Z FIG. 21. The single pore model.

the bulk gas outside the pore and the pore entrance. Axial diffusion of reactant occurs simultaneously with surface reaction along the pore wall. The reactant gas profile within the pore is



where ¢ - 6/~, and 6s is the initial pore diameter at the pore entrance. The value of = characterizes the effect of variations in pore diameter and diffusivity on the reactant gas concentration profile. For a cylindrical pore of constant size, = equals zero. As in macroscopic models, the Thiele modulus, defined as 4> =


1 dD*

+ o

\ ,AdD /



represents the ratio of reaction rate to diffusion rate. The main difference between • (eqn. (89)) and 4~ (eqn. (110)) is the pore diameter 6 and diffusivity D. Both 6 and D can vary with axial distance z and thus 4> will not be an invariant system parameter unless the pore is modeled as a constant diameter cylinder. Equations (107) and (108) define the steady-state reactant gas concentration profile within a single pore. For a given z, the rate of change of pore diameter is given by d6 I i - ~)f-rca-~C ~ = ~ , . ~ 6 ' - - : dt for smooth, non-porous capillary wails, we then

Helerogeneous kinetics of coal char gasification and combustion

obtain d~ --=q)~ d)"


where )'is the dimensionless time. T =




Gt~s By repetitively solving eqns (107) and (111), the reactant gas concentration profile and pore shape can be calculated as a function of time. In this way, the contribution of a single pore to the overall particle reactivity and burnoff can be predicted)36 Prior to the recent work of Kriegbaum and L a u r e n d e a u ) ~6'21: the complete ruth order pore reaction model as stated in eqns (107-112) had not been solved. However, solutions to some simplified forms of the model were available in the literature. Table 7 summarizes the relevant investigations. The


boundary layer diffusion, are applicable to the single pore model if ~ = 0. It is for this reason that the Mehta and Aris 1°~ investigation is included in Table 7. Wheeler's classic analysis of the constant diameter cylindrical pore assumes a first order reaction with no gas film resistance. 29'1°3:1~ For this case, eqn. (113) becomes d2tI, d~: 4)2~ = 0 (1t4) with boundary conditions given by T=I

ca ~ = 0

dSv --=0

~i ~ =


(l15a) (115b)


The solution to eqns (114-115) is T=

cosh 4) (~ - 1) cosh 4)

TABLE 7. Investigations of the general single pore model Investigator Wheeler (1951)~ is Petersen (1957P 3~





0 2d~


0 2d~



Roberts and Satterfield (1965) ~2:

0-1 *

Thomas (1966) ~a~


Mehta and Aris (1971)~o~


Kriegbaum and Laurendeau (1977) :~:



0 2d~ J ---+-d~ D*

0-~ dD* d~


*The irreversible ruth order reaction is replaced here by the modified Langmuir-Hinshelwood expression, .~ = kC/(1 + bC). +The general Langmuir-Hinshelwood case leqns (24J and (29)i is also considered in this analysis. classic analytical solution is presented by Wheeler. 1Is Roberts and Satterfield 122 consider the effect of L a n g m u i r - H i n s h e l w o o d kinetics, but without product inhibition. Peterson T M allows pore growth, while Thomas 13v considers the conical-shaped capillary. Numerical solutions for the ruth order reaction, with boundary layer resistance, are provided by Mehta and Aris. 1°~ Kriegbaum and Laurendeau 2.: consider Knudsen diffusion and pore growth, as well as L a n g m u i r - H i n s h e l w o o d kinetics.

and hence -=

1 '-P(~)d~= 2-tanh 4). ,0 4)

The Thiele modulus becomes

d)2~ ~ = 0


substituting from eqns (751 and (761, we obtain

f ~ °A .f:"~I,'2 =

For a constant diameter cylindrical pore, a = 0 and thus eqn. (107) becomes (1 13)

with boundary conditions given by eqn. (108i. Recall that eqn. (113) is identical to the governing equation for the type 1 progressive conversion model, as applied to a slab of constant effective diffusivity. Therefore, the numerical results of Mehta and Aris (Table 61 for the ruth order reaction with or without


t/ ~ x\ 1/2 =

4.5.2. T h e constant diameter cylindrical pore

dZ~t, d~2

for a first order




where we have assumed a smooth, non-porous pore. N o t e that the Thiele modulus has now been expressed in terms of measurable particle properties. For the catalytic cylindrical pore. 4) is a system constant, independent of axial distance. A comparison of eqns (116) and (llTt with eqns (95a) and (97) (recall eqn. (80)) demonstrates again an important point: the microscopic and macroscopic approaches are equivalent if both the pore diameter and effective diffusivity remain constant.




The overall particle reactivity can now be obtained from the single pore result by calculating the rate of mass loss (g/s) for one pore:

rhc.p = rc6LpkC = nfLvrlkC s.






Multiplying by the number of pores per gram, we obtain the particle reactivity

for smooth non-porous pores, we then have eqns (72), (75), (76) and (117),





/ rJ








{A'~kAD~c,c~tanhqS. R,. = \ "/z: f


Equation (119) is the necessary link between pore structure and particte reactivity. Note. however, that eqn. (119) only applies for an invariant pore structure.


t,i :,i//~////~,,'1 ~


4.5.3. Pore structure models If pore structure is not allowed to change, i.e. effective diffusivity and pore diameter remain constant, then the macroscopic and microscopic approaches are equivalent. However, for coal chars, pore structure development must be considered. Since the effective diffusivity cannot as yet satisfactorily model pore structure change, the microscopic approach must be emphasized. Hence, in the general pore model, we must allow ~ # 0. Even more important, pore models incorporating interactions between neighboring pores must be developed. One pore model for non-catalytic gas-solid reactions that allows for pore interactions has been proposed by Szekely and Evans. 126 In this model, cylindrical macropores of uniform diameter are assumed to penetrate a semi-infinite slab perpendicular to the free surface at equally spaced intervals (Fig. 22). The solid regions between the macropores are presumed to react according to shrinking core theory. A developing ash layer maintains the initial macropore geometry. By properly accounting for the interaction between the propagating reaction fronts, the overall reactivity is found to maximize with time. The microscopic approach has also been used to model solids containing various pore size distributions. Carberry ~3~ considers a bimodal distribution by picturing the porous solid as a system of cylindrical macropores having uniformly sized cyl= indrical micropores branching off, perpendicular to the macropore walls. Reaction is presumed to occur solely within the micropores; the macropores simply provide for gas transport throughout the particle. Both micro- and macropores are analyzed by using the single pore model; reaction in the macropore is defined as a function of the micropore effectiveness factor. A similar model that considers uniform macropores and a distribution of micropores has been proposed by Mingle and Smith. t3s Unfor-

, ~ i



FIG. 22. Application of the single pore model to a porous particle (Szekely and Evans 1z6). tunately, both models do not account for pore growth. A statistical model that considers non-catalytic reactions occurring within particles having a pore size distribution has been developed by Hashimoto and Silveston. t39 Population balances are used to consider pore size growth, initiation of new pores and coalescence of adjacent pores. Particle properties are formulated as moments of the pore size distribution. The model provides good agreement with the burnoff data of Kawahata and Walker, 62 e.g. Ag, Vg, ~b and 6 vs BO. Unfortunately, predictability is in large part a result of the model's ten empirical parameters. 4.5.4. Utility of microscopic models The usefulness of the microscopic approach can be demonstrated by the recent work of Kriegbaum and Laurendeau. t36'-'12 In this investigation, the porous char is modeled as a system of individual conical pores, radiating from the center to the surface of a spherical particle. Each pore is assumed to consist of a tubular capillary bounded radially by a nonporous carbon sheath. The carbon sheath is in turn bounded radially by non-porous ash. The ash serves to limit the radial growth of the pore. As in Sections 4.3.2 and 4.5.2, the dimensions of the individual pores are determined by equating the experimental and theoretical structural properties of the particle, e.g. pore surface area, pore volume and carbon fraction. A bimodal pore size distribution is considered, in line with the experimental results presented in Section 2.3. By integrating over all porores, predictions caq be made for internal surface area, pore volume and carbon burnoff as a function of reaction time. Pore volume and surface area predictions are in good agreement with experiment for

Heterogeneous kinetics of coal char gasification and combustion macroporous chars, but in poor agreement for microporous chars. This result is to be expected since the opening up of blind pores is not yet considered by the model. For kinetically controlled gasification reactions, particle burnoff predictions are in excellent agreement with the experimental curve (see eqn. (50)t of Walker et al. ~°° over the first 70~/o of burnoff. Moreover, comparison with the data of Dutta et al. 36 reveals that the model can predict values of z0. ~ to about a factor of two. Differences above 70~0 conversion are again to be expected, for the model assumes independent pores while reality requires inclusion of pore coalescence and particle fragmentation. In comparison to macroscopic models, microscopic models (ll require no empirical parameters such as the effective diffusivity and (2) utilize only intrinsic kinetic constants, The latter is especially advantageous since intrinsic data offer the best opportunity for "universal" kinetic parameters, i.e. dependent only on the chemical structure of the char. On the other hand. the microscopic approach must postulate a reasonable pore structure model, particularly if blind pores and pore coalescence are to be considered. Thus, we see that successful microscopic modeling will require measurement of both intrinsic rates and pore structure changes during burnoff. Such models will then reflect in detail the essence of overall char reactivity: the union of intrinsic surface kinetics and developing pore structure, each dependent on local reactant concentration. 4.6. Special Features q f Combustion Compared to gasification, combustion presents some unique properties worthy of further discussion. These characteristics derive from the high rapidity and exothermicity of the combustion reaction. The effects of sample size and thermal annealing are especially pertinent.


and hence 1







Equation (120) states that the overall rate coefficient Ke.o depends on both chemical kinetics (Ke.st and film diffusion (KDI. Obviously, bulk diffusion controls at low values of KD/Ke. ~. Since Ke.s ~ e -E/Rr and K v T~'"~/Pd (eqns (61) and (64)), we have KD/K~'" ~

TV/4e-E/RT Pd


and thus diffusive control is favored by high values of pressure, temperature and particle size. Practical combustors usuall) operate at P = l atm. T ~_ 1500°C; thus. particle size will largely determine if chemical kinetics must be considered. Should surface kinetics control, the total reaction time can be calculated from 1 dm r = Ke,oC o m r dt


where mp is the particle mass. Assuming a constant apparent densit} and integrating, we obtain zc = r:cd,,


where Go


~c = 2 K e . o C o

Here, the initial particle diameter d,, represents sample size after swelling: typicall~ dch,,/dco,z ",1.5 8.86 Equations 169) and (122) are compared in Fig. 23. Diffusive control is likely for do >i 100gin and chemical control for do ~< 1 }am. Both film diffusion and chemical kinetics are important in the pulverized coal range (1 < d,, < 100 ~tmt. 10 4

4.6.1. T h e role o f diffusion For man), years, the speed of the C-O2 reaction promoted the belief that (1) bulk diffusion is always rate-controlling and (2) char combustion always occurs at the particle surface, i.e. pore diffusion is negligible. In the early 1960s, Essenhigh et al. 8"j'~°'~4~'~42 disproved the former; in the earl)' 1970s Field 143'1'~ and Smith et al. 94"14s-1~1 disproved the latter. The role of bulk diffusion can be .analyzed in a simple fashion by considering the competition between chemical kinetics and film diffusion.8'~4° Assuming a first order overall reaction at the particle surface and negligible gas phase reactions, we may write R e

10 2 -

LIJ pt.9


Z n." :3 ~D




IO-e I0

I0 2

IO s


= K~.,,C,, = K~,sC~ = K o ( C o - C A ; INITIAL PARTICLE DIAMETER (t~m)

therefore C~=

,K D

K v + K~.~


FIG. 23. Burning times for carbon combustion in air at 1atm and 1500"C--Kv = 1000s/cm: and K c = 1s/cm [Beer and EssenhighJ4o1



In recent years, the role of pore diffusion during pulverized coal combustion has received extensive experimental investigation. In the late 1960s. several electron microscope studies of partly reacted bituminous coal particles suggested internal burning within 1 ~tm sized pores.152,153,15~ Subsequent theoretical work predicted that complete penetration requires 6 > 10gm; if d < l gin, pore effects predominate while c5 < 100 A favors reaction only at the external surface of the particle.t° Recently, Field 1'~3"t'~'* and Smith et al. 9'*'145-t51 gained conclusive evidence for internal burning during pulverized coal combustion. First, they find that R,, < Rm.~ (eqn. (67)), which indicates at least partial control by surface chemistry. As expected, Rm "" R,~.~ only for the largest particles (d = 100gin) at the highest temperatures (-,. 2000 K). Second, both the apparent density and particle diameter usually decrease with burnoff. Sometimes, ~r, will decrease only slightly, implying minimal penetration; other times, d will decrease only slightly, implying nearly full penetration. In general, both internal and external reactions occur simultaneously. Third, in most cases, R,,oc d -~, an indication of zone II conditions (eqn. (101)). For d < 20 )am, or T < 800K, zone I is favored, especially tbr highly porous bituminous and lignite chars. ~'.5''5°'~5t Fourth, Smith and Tyler,~9 using pulverized semianthracite, find that q < 0.25 for d > 50 gm, while --.0.25-1.0 for d < 251.tm. These values of the effectiveness factor are consistent with zone II conditions. 4.6.2. Boundary layer models A unique characteristic of combustion is the possibility of homogeneous reaction within the boundary layer due to the overall reaction CO +½02 ~ CO2. The elementary step controlling this global reaction is C O + O H - - * C O 2 + H, which explains why CO to CO2 conversion is so sensitive to minute additions of steam. The fundamental question here is the relative location of the CO conversion process. The overall stoiehiometry and surface temperature obviously depend on whether CO is converted to CO2 at the particle surface, within the boundary layer or outside the boundary layer. 9'~55'~$6'15r In general, the location of the CO oxidation front is regulated by the particle size (d) and bulk gas temperature (To), for these two parameters largely determine the competition between the rates of carbon monoxide diffusion and combustion. ~s5'~56 Since for diffusion R ~ , d - t (eqn. (62)), larger particles and higher temperatures favor conversion near the surface; smaller particles and lower temperatures favor conversion outside the boundary layer. Based on the above, previous investigators have attempted to simplify the boundary layer calculation by using either the single film 9'~5s or double film 159'160'16t model (Figs 24(a) and ~b)). In the single film model, both CO and C O : are considered

to be primary products; no reaction occurs within the boundary layer, but CO oxidation may occur outside the layer) This model also can be extended to consider CO oxidation at the surface, in which case CO z is presumed to be the only primary product. 9 Ayling and Smith s7 find from surface temperature measurements that the single zone model is applicable for particle diameters less than 100 ~am. In the double film model, CO oxidation consumes all of the incoming oxygen before it reaches the surface. The resulting CO, diffuses away from the reaction front in both directions. At high temperatures, the C O 2 + C - - - 2 C O reaction is the only heterogeneous step. This model has received support from microprobe observations of both CO 2 and temperature peaks away from the particle surface. t 62.103.~64 Wicke and Wurzbacher estimate that the double film model is adequate for particle diameters greater than l mm. t62 However, some workers ~°'t65 doubt the necessity for the C O 2 + C --, 2CO step. In the important regime 100 ~tm < d < 1000 gm, a continuous film model (Fig. 24(c)) must be used since the four major reactions could occur simultaneously. Here, non-zero concentrations of CO, CO2 and 02 are allowed at the particle surface; CO: and temperature still peak within the boundary layer. Various modifications of this model t55 neglect C+Oz--*CO2(high To) or C + C O , . - * 2 C O (tow T,,). The continuous film model allows carbon monoxide oxidation to occur anywhere within the boundary layer depending on particle size, bulk gas temperature or water vapor content. '5~'t6°'~62 The surface concentrations of 02 and CO2 are not assumed, but rather are predicted by the model. The general continuous film model has been considered by Caram-and Amundson ~56 and Annamalai and Durbetaki. ~65 Both studies report that the surface concentration of oxygen decreases with increasing surface temperature: Annamalai and Durbetaki also show that the surface carbon monoxide concentration peaks with increasing surface temperature. Caram and Amundson t~6 find that the temperature and carbon dioxide peaks appear, and thus the surface oxygen concentration is zero, for To >t 1200 K. Since only moderate temperatures are required for CO combustion, we would expect that particle size determines the conditions under which the continuous film model collapses to either the single or double film model. Indeed, Caram and Amundson find that for d < 501am, the single film model applies, while for d > 5 ram, the double film model is a reasonable approximation. 4.6.3. Rate reduction at hiyh temperatures Carbon reactivity measurements at high combustion temperatures ~66-~'° often demonstrate the behavior shown in Fig. 25: R,, sooner or later decreases with increasing temperature, but eventually resumes its upward march. This behavior, though usually obsern'ed for combustion, is not unique to

Heterogeneous kinetics of coal char gasification and combustion

( C] )


S~gle Film Model C+ I/2 0 2 --CO C+ 0 2 - - CO 2

iC°T n-LU ~"




" ¢


( b ) Double FiLm Model C+CO 2 -- 2 C 0 CO + I / 2 0 2 - CO2


(c) Continuous Film Model


C+1/2 0 2 --CO


C+ O2 - - CO2 C+CO 2 - - 2 C O CO+1/2 O2--CO 2

~ - - " ~ C O Rs




FIG. 24. Boundary layer models for char combustion: (a) single film model, (b) double film model. (c) continuous film model (Basu et a l . , t ~ -~ Caram and Am undson t so ).

combustion, since the steam and carbon dioxide reactions sho~' sunilar profiles.9"l~'~72 These profiles have often been at least partly attributed to such things as (1) reduced pore penetration, especially at the low pressures often used in high temperature work• (2) dissociation to atomic species or (3) Langmuir-Hinshelwood kinetics with reverse adsorpt i o n 9-' However. the most accepted explanation is thermal annealing. "~'a66 a process in which active sites become inactive due to micropore coalescence,

structural ordering and catalyst deactivation (Section 2.2.4). Assuming a combustion/thermal annealing mechanism similar to that discussed in Section 3.4.4. Nagle and Strickland-Constable, following Blyholder and Eyring. ]9-~ derive the following semi-empirical expression ~66 /~=

kCo2 - Z+krCo:( 1 -Z), 1 + aCo~


where 7, is the fraction of sites which are highly active, I - Z the fraction of nearly' inactive sites and k~ the rate coefficient for inactive sites. At stead) state. 7. is determined by


i6/, = k t C o (1 - Z ) . >,. p,-



I 1500i2000







where /~6 is the rate coefficient for annealing. Recently. Park and Appleton found that e q n 4123) adequately correlates graphite and soot oxidation data at 1700 < T < 4000K and 0.05 < Po: < 13 atm. ]6~~7° No elementary mechanism, however. has as yet been convincingly established, 5. K I N E T I C S O F C H A R G A S I F I C A T I O N COMBUSTION



FK;. 25 Carbon reactivit~ for combustion at high temperatures (Lewis ~'~ i.

In the past, measurerrlent of important char parameters such as specific surface area. active site



concentration or sample impurities has rarely been attempted. The determination of pore surface area as a function of burnoff is obviously a minimum requirement for obtaining global intrinsic rate coefficients on an area basis (Table 5). Such measurements have only been reported in the recent work of Smith and Tyler. 9'*'98't'.9 In the opinion of this reviewer, any compilation, comparison or interpretation of non-intrinsic kinetic data is fraught with uncertainty. For example, a review of overall or elementary frequency factors on a mass basis (Table 5) would only produce a miasmic tabulation owing to unknown values of specific surface area. Fortunately, activiation energies are more easily compared (if pore diffusion effects are accounted for or eliminated) since A9 is relatively independent of temperature for heat treated chars. However, if Aa varies substantially during burnoff or if the pore surface area or active site concentration of a particular sample vary with temperature, then the measured "true" activation energy will be in error. Furthermore, any activation energy differences may be difficult to reconcile if the impurity level changes significantly either during burnoff or among carbon samples. ~~ The difficulties described above are the major reasons why previous reviews have been unable to achieve experimental/theoretical cohesiveness. Since carefully measured intrinsic data are still scarce, this reviewer sees no reason to attempt the full unification process at this time. Instead, an attempt will be made to amplify on the elementary mechanisms discussed in Section 3.4 by choosing only those investigations providing (because of sound experimental technique) well defined values of true activation energy and reaction order, both elementary and global. Early studies were invariably influenced by mass transfer. Consequently, we will emphasize, for the most part, work published after 1960; earlier work can be found in previous reviews. We will also emphasize the few well conceived investigations dealing with or related to char reactivity; t79 the extensive work on graphite and other high purity carbons has been reviewed by Lewis.~:t Apparent kinetic data for the char-oxygen reaction is considered here because of its application to intrinsic kinetics. Overall data for the char-CO 2 and c h a r - H 2 0 reactions are not included because of lack of consistency and the high degree of empiricism associated with most of the relevant investigations. Overall rate expressions for these two reactions for pre-1963 work can be found in the review of yon

Fredersdorff and Elliott. r More recent data for the char-CO2 reaction is given by Dutta et al. 36 Tyler and Smith 9s and Fuchs and Yavorsky. ~sz For H,_O and H20/Hz mixtures, the work of Johnson, s3 van Heek et al. ~ 5 and Feistel et al. sz are most applicable. Taylor and Bowman 2~3 provide overall CO: and H_,O data for sub-bituminous chars. 5.1. E x p e r i m e n t a l M e t h o d s and A n a l y s i s Heterogeneous kinetics can be cast into proper perspective by first considering the relevant experimental techniques: (a) fixed or fluidized beds; (b) thermogravimetric analysis; and (c) entrained flow (Fig. 26, Table 8). The fixed/fluidized bed can be FRITTED MATERIAt


~o o,:: o o o o o o¢/oo ooo~oo o o¢ F j~oooo~ ,0= ~.p#








!/,/,J f jJJ,A "-'-~-FURNACE

r"j , / , / -

f f-.Js7



FIG. 26. Experimental techniques for determination of char kinetics: (a) fixed/fluidized bed, (b) thermogravimetric analysis (TGA), (c) entrained flow method. operated in either the integral (large height) or differential (small height) mode. ~73 Continuous sampling in the differential mode allows direct determination of elementary kinetic mechanisms, but experimental errors can be large due to small product concentrations. The integral mode bypasses the above problem, but requires a plug flow or perfectly stirred reactor approximation. ~73 In general, the fixed bed allows utilization of a wider range of particle sizes, but the fluidized system provides a nearly isothermal bed. In both methods, kinetic data and stability can be assured by

TABLE8. Experimental ranges for heterogeneous kinetic methods Method Fixed/fluidized bed Thermogravimetric analysis Entrained flow

Residence time Is)

Temperature (K)


t -600 30-6000 0.05- l0

500-1500 500-1300 600-2200

1-400 0-100 1-500


Heterogeneous kinetics of coal char gasification and combustion TABLE 9 Effect of heterogeneous reaction zones on theoretical and experimental parameters related to overall reactivit 3 Zone

R, eqn

Overall rate coefficient*





ero vs X+



















- 0





K~ = A#k




6 V2AD~ 11 : K , = ~-~ | r n + 1 o,,4gf:

m+ 1





* R.. = K~CF:





K, = - -


- 1

d vs X~"

R , . . v = KoCo

**R,,KdP: p = - 2 . - 1 , 0 + cro--apparent density : d--particle diameter : X--fractional conversion : D--decreases : C---constant

monitoring exhaust gas flow rate and species concentrations. The calculated and experimentally determined burnoffs can be compared to check for systematic errors. 98 The thermogravimetric s3`~ o~ and entrained flo~ ~43'~"s'~'~ methods are usually limited to global intrinsic kinetics. T G A operates via continuous monitoring of sample weight; extremely low pressures are quite feasible. In the entrained flow method, particles can be introduced either with the preheated gas or in a central tube, as shown in Fig. 26(cl. Gases and solids are sampled downstream of the center jet. Isothermal conditions are rarely maintained: solids sampling and precise knowledge of local stoichiometry can present difficulties. Usually, the reaction order is obtained by varying the reactant concentration at constant temperature, while the activation energy is calculated by varying the temperature at constant partial pressure. An obvious problem here is that A o or [C[] may change with experimental conditions." This difficulty can be minimized by using (lJ a common pretreatment temperature greater than the temperature range of the experiment. (2} direct Ag and I~ measurements and (3i a narrow burnoff range. The latter can be accomplished by maintaining low burnoffs, i.e. 5-10% ~'3 or bx periodic modulation of reactant concentration. 9s~-~ Reactant modulation is also an excellem technique for discerning elementary mechanisms and rate data: other methods include (1) monitoring all product species rather than a single one. (2i identifying the nature of the adsorbed species and (3) isotopic tagging. ~~

Two additional items, sample temperature and mass transport effects, must be considered to assure reliable kinetic data. Obviously, the data must be based on particle rather than gas temperature. To maintain isothermal conditions across the gas film, preheal is often required. F o r rapid reactions, an energy balance is needed to predict the particle temperature, particularly for entrained flow.S 7,~ 45., 47 Traditionally, bulk diffusion has been eliminated by Ill high velocity flows, 166 (2) small particle s i z e s ) ' ° (3) low pressures 93'169 or (4) surface microsampling 1.6 The boundary layer can also be controlled, though not eliminated, via a variety of newer techniques: (11 rotating disk] ~" (2) stagnation flow *w and (3} diffusion cell. 1"2 However, only the third method is applicable to char particles. The effects of both bulk (zone IIIt and pore (zone II) diffusion on apparent reaction order, activation energy and various experimental parameters are shown in "Fable 9. N o t e that if bulk diffusion controls, intrinsic kinetic parameters cannot be obtained: however, for zone II, the true parameters can be calculated from the apparent parameters. Direct measurement of the global intrinsic r i t e coefficient ~ is possible in zones I or IV (Table 9, Fig. 14), though for porous particles, the existence of a well defined zone IV is doubtful. Using eqn. (124}.

d3aa 1 -X

= - -


we see that for zone I. a~ = a,.o(1 - X ) , while for zone IV, d = d o ( 1 - X ) ~ ' 3 ; in zone II. on the other hand, both ao and d decrease with burnoff. Variation of the

TABLE 10. Intrinsic global rate coetticients ~ for char gasification and combustion Investigation


Smith and Tyler {1972}~Semi-anthracite Smith and Tyler f1974t "a Lignite char Tyler and Smith {1975t9~ Petroleum coke


Temperature (K)

O: O: CO2

1400-2200 630-181(t 1020-1 lg()

Reactant pressure tatm ~ m 0.1-0.2 0A -0.2 0.25-1.15

k(g.m- : .s- a. atm- ")*

1 5.5 10Sexp(-40.0/RT)+ 0 1.3- 10'~exp ( - 32.6/RT)'t 0.6 3.0.105 exp ! - 53.0/RT}

*R = 1.987 10- -~kcalgmoi-K * Determmed b3 eliminating pore and bulk diffusion effects via eqns (55 t. 180 ~. ¢95a I. 1971 and (103 I.



TABLE 11. Intrinsic global kinetic parameters for carbon dioxide gasification Investigation


Gadsby et al. 11948}67 Overholser and Blakely (1965) ~s° Blake et al. (1967) .*0 Turkdogan and Vinters (1969) ~s~ Lewis ( 1970I 1~i Tyler and Smith (197519s Fuchs and Yavorsky 11975)lsz Dutta et al. (1977) 36

Coconut char Graphite Coke Graphite, coconut char Carbon Petroleum coke Chars Chars

T, K

P, atm

975-1075 1050- 1300 1125-1175 975-1475 -1020-1180 1025-1175 1115-1365

1 I i 10-3-10 -1 18-35 I


E, kcal 'tool

1 0.7 -0.5 1 0.6 0 1

59 55-60 57 68 58-66* 51-57 55 59

* Review : E, = 80-90 kcal/mol for ultra-pure carbons, particle size and velocity are the easiest methods of discriminating between zone I and zones II and III. In summary then, we note that Table 9 is a particularly useful guide to the experimentalist who wishes to determine the effects of mass transfer on intrinsic chemical rates. Few values of the global intrinsic rate coefficient 1~ are available in the open literature (Table 10). To this author's knowledge, no reliable values for elementary intrinsic rate coefficients (on an area basisl have been reported. The lack of both global and elementary data reflects the paucity of Ag vs BO measurements. Obviously, rate coefficients on a site basis, requiring [C,] measurements, remain but a vivid dream (see, however. Laine et a/.:s'sg).

investigation; its suggestion of an alternative L a n g m u i r - H i n s h e l w o o d mechanism probably deserves further research. These global results can, of course, by interpreted via the appropriate L a n g m u i r - H i n s h e t w o o d expressions (Sections 3.4.1 and 3.4.2) to obtain information on the activation energies of the elementary steps,

5.2. Carbon Dioxide and Steam Gasification

as shown in Table 13. Tables 11 and 12 suggest roughly E l : ~- 55-65, E2.f ~ 45-65 and E 3 ~ 45-60 kcal/gmol. Detailed L a n g m u i r - H i n s h e l w o o d investigations for carbon dioxide and steam gasification are listed in Tables 14 and 15. Note the lack of data in the last decade, particularly for the c a r b o n - s t e a m reaction. The relative ease in measuring equilibrium constants rather than rate coefficients lends credence to the tabulated values of E t : - E 1 b and E 2 f - E 2 b . The investigations of Ergun et al. are particularly trustworthy. Mentser and Ergun give the first direct measurement of both E l / and Elb. Pursley et a/. t89 have presumably determined Elb by measuring the rate of carbon deposition on glass surfaces. Binford and Eyring :~ probably provide the most reliable data for steam kinetics. Taking everything into account, and assuming Et : - E ~ b "" E 2 : - E , b ~- 20kcal/mol, Tables 14 and 15 suggest E l : -- 55, Elb = 35, E , : ~- 45, E2b '" 25 and

Literature values of the true order and activation energy for both carbon dioxide and steam gasification are shown in Tables I1 and 12. Nearly all investigations were performed in a fixed or fluidized bed, or by thermogravimetric analysis. Typical particle diameters were 0.1-3.0ram. In most cases, the sample impurity level was high enough to duplicate char conditions; for ultra-pure carbons ( < 5 p p m of impurities), the activation energy was often ~ 25kcal/mol higher than that for impure samples.6. ~7 t Comparison of Tables 11 and 12 shows a much higher degree of uncertainty for HzO gasification than CO,. gasification. In general, m "- 1 for P < l a t m and m ~ 0 for P > 15atm. 6'36't71 The widest ranges of temperature and pressure are provided by Turkdogan and Vinters ~sx and van Heek et al. Iss The former is a particularly well done


CO, +C: = CO +C(O)


Ib 21"

H,.O + C : = H 2 + C ( O )


2b 3

C(O)---, C O + C / .


TABLE I2. Intrinsic global kinetic parameters for steam gasification Investigation Zielke and Gorin (1957) ss Blakely and Overholser (1965) ~s 3 Stewart and Diehl !1972) ~s.* van Heek et ai. (19731ts5 Fuchs and Yavorsky (19751 ts-' Kayembe and Pulsifer 11976)186 Kaftanov and Fedoseev i1976) 21~ Linares er al. (1977) 187

Sample Disco char G raphite Chars Chars Chars Bituminous char Graphite Lignite char

T. K

P, arm


E,, kcal/mol

1090-I200 1050-1200 1175-1275 875-1375 1025-1175 875-1125 1175-1475 1025-1205

1-30 1 1 1-70 18-70 1 -(8.5-23)" 10-3

0,1-1.5 0.7 0.6 0 0 -1 06

40-75 ~ 50 34-40 36-50 ~ 50 61 70 42

Heterogeneous kinetics of coal char gasification and combustion


TABLF 13 Limiting intrinsic conditions for carbon dioxide and steam gasification Reaction




aCco <" 1

1 +aCco+bCco:

bCco: << 1

C + C O : ~ 2CO

aCco <~ 1 bCco: >> 1 C+H20--CO+H,


aCH: ~-' 1

1 +aCH+bCn~o

b C t t : o << ]

aCH: <~ 1 hCH: o >> 1

E ~ = 6 0 k c a l / g m o l . Since E ~ y - E a b > O and Ea.r - E = b > 0. C O and H : inhibition should become less effective at higher temperatures, as d e m o n s t r a t e d experimentally by n u m e r o u s investigators. 6'''69'7-~ The p r o p o s e d E l : value is s u p p o r t e d by Mentser and Ergun v° and F u c h s and Y a v o r s k y ) 82 The E 3 value is consistent with Ergun 33. Mentser and Ergun 5~ and Binford and Eyring. ~7 Both E~: and E a are fairly consistent with the coke study of Hottel et aI. ~88 E=: and Eab are most in need of fu-ther verification. 5.3 H ydrooen Gasification Little work has been d o n e on the intrinsic rate p a r a m e t e r s for hydrogen gasification, either global or elementary. Table 16 presents some results for the true reaction order and activation energy. Obviously, no r e c o m m e n d a t i o n s are possible. 5.4. Combustion Overall char c o m b u s t i o n results, expressed as R¢ = A e x p l - E,/RTIC",,











are listed in Table 17. Pre-1965 data are not included for two reasons. First, corrections for b o u n d a r y layer diffusion were not m a d e : thus, C, is u n k n o w n . Second. the particle t e m p e r a t u r e was invariably assumed equal to the gas temperature. Field 1.3 and Smith et al. 14s-~'s'Is°'~5~ instead use a simple energy balance to calculate the particle temperature. This temperature can be as much as 2 0 0 K greater than the gas temperature. Mutcahy and Smith ~46 show that. without this correction, c o m p u t e d values of the apparent activation energy can be a factor of two higher than the correct value. The tabulated values of a p p a r e n t order, activation energy and frequency factor (Table 171 were obtained in entrained flow furnaces (d "- 20-100 ~tmJ at a total pressure of about one atm. The exception is Field et at.: 9 they base their results primarily on a re-analysis of previous data using large carbon sampies. ~ ' ~ ~ = Typically, the data in Table I? duplicate experimental results to within a factor of two. Since the various Carbons examined by Field et al 9 are probably much less p o r o u s than typical char samples, we can assume zone IV conditions and thus

TABLI~ 14. Activation energies for elementary reactions of the C + CO: --, 2CO system* Investigation Ergun (1956/33

Sample Graphite. Activated carbon

Walker et aL (1959)~

Carbon +

Blackwood and lngeme (1960) v~

Coconut char

T. K


1075--1675 975-1675






Elb .













Ergun (1961)69







yon Fredersdorffand Ellion (1963) v

Anthracite. coke






Hottel et al. (1966) lss







Purstey et al. (1966) 1~






Turkdogan and Vinters 1197012°°

Graphite. coke

1075- 1475







Mentser and Ergun (1973170

Carbon black






Strange and Walker (1976) ~ °







* All activation energies in kcal/gmol. + Reviex~ paper. ** High purit: graphite. ; Assuming E, = 60kcal gmol. ,' Assuming reaction (RI bl is the rate controlling carbon deposition step


NORMAND M. LAURENDEAU TABLE 15. Activation energies for elementary reactions of the C + Investigation


Johnstone et al. (1952) r5 Wicke and Rossberg (1953) r6 Binford and Eyring (1956) 77 Blackwood and McGrory (1958) 32 Walker et al. (1959) 6 Ergun (1961) 69 von Fredersdorff and Elliott (1963) r

Graphite Graphite Graphite Coconut char CarbonS" Coke Carbon*

H20 ~


+ H2


T, K





1135-1210 1275-1475 1175-1575 1025-1105 -1275-1475 --

13-32 -43 60 ~ 71 -13-62

27-51 --30 --27-82

---30 -20 --

82-112 56 60 30 60-69 -60-112

* All activation energies in kcal/gmol. -t-Review paper. Er ~- E, "- 36kcal/gmol. 193'194 C o m p a r i n g with the reamining activation energies listed in T a b l e 17, we see that in m o s t cases, pulverized char c o m b u s t i o n occurs in zone I1. This conclusion is consistent with c o n c u r r e n t m e a s u r e m e n t s of particle size a n d apparent density vs burnoff (Section 4.6.1.). N o t e t h a t Sergeant a n d Smith's results m o r e closely a p p r o a c h zone 1, in agreement with their o b s e r v a t i o n of large voids t h r o u g h o u t the char structure, tS° Table 17 suggests a true activation energy of 3 2 - 3 8 kcal/gmol. Any estimate of the true order is clouded by the n a r r o w range of oxidizer pressures used in the experiments to date. Intrinsic kinetic d a t a for c a r b o n a n d char combustion are s h o w n in T a b l e 18. T a k i n g everything into account, we see that the true order varies between zero and unity approximately as f o l l o w s . l . o . 2 7 , 9 3 . 9 ' * , 149,168, i 95

m~-0 m~-0.5 m'-- 1.0

T ~< 9 0 0 K 900 1500K.

on Rodriguez-Reinoso er al., 27 Mulcahy a n d Smith, t° Smith a n d Tyler 94 and Lewis. tvt In particular, Lewis tvt shows that E ~ = 3 5 - 4 5 k c a l / gmol for impure c a r b o n s and E,--- 50-60 kcal/gmol for ultra-pure carbons. H e u c h a m p s a n d D u v a l t96 suggest two parallel reactions on separate sites to explain this p h e n o m e n o n : E, = 6 0 k c a l / g m o l for c a r b o n edges a n d E,-~ 3 6 k c a l / g m o l for catalytic sites. A similar m e c h a n i s m may a c c o u n t for measured variations in activation energy at all orders for both c o m b u s t i o n a n d gasification. Table 19 presents results for oxygen c h e m i s o r p t i o n and desorption on c a r b o n surfaces. In the desorption process, however, the oxygen is desorbed as c a r b o n oxides. Thus, the zeroth order activation energy is chosen to be 7 0 - 8 0 kcal/gmol, in line with the d a t a reported by H a y w a r d and Trapnell 6"* a n d Blyholder a n d Eyring. 19s Table 19 also suggests that the activation energy for a d s o r p t i o n is 15-20 kcal/gmol, a figure we will refer to shortly. Consider now the c o m b u s t i o n m e c h a n i s m proposed in Sectfon 3.4.4:

This result is similar to previous estimations by T h r i n g a n d Essenhigh, s M u l c a h y a n d Smith x° a n d Lewis.'Tt Such b e h a v i o r is c o m p a t i b l e with L a n g m u i r - H i n s h e l w o o d kinetics, as s h o w n by Fig. 10 a n d Section 3.4.4. L a n g m u i r - H i n s h e l w o o d behavior is also depicted by the recent results of P a r k a n d A p p l e t o n : ~v° at 2500K, m = 1 for Po_, < l a t m a n d m ~- 0 for Po,_ > 5 atm. Tables 17 and 18 suggest the following correlation between true order a n d activation energy: m = 1 m = 0.5 m = 0

Et - 3 0 - 4 0 kcal/gmol E, = 4 0 - 5 0 kcal/gmol E, "" 7 0 - 8 0 kcal/gmol.

T h e first order activation energy relies heavily on the work of Field et al., 9 S m i t h et al. l'~'5-tSt and Laine et al. 89 T h e half-order activation energy is based mostly


0 2 + 2 C , --- 2C'(O) ks

C'(O) ---, C(O)


C(O) ---,ksC O + C :



C'(O) ~ C O + C : klO~

C'(O) + C'(O) - , c u 2 + C : .


(R.9) (R.10)

Recall that this m e c h a n i s m allows m = 1 at high t e m p e r a t u r e s (eqn. (43)), m = ½ at intermediate t e m p e r a t u r e s (eqn. (44a)) and m = 0 at low temperatures (eqn. (42a)), in agreement with Table 18. Recall also that the m = 1 case is controlled by reaction (R.7), i.e. surface chemisorption. Hence, as suggested by Table 19 and Essenhigh et ~ / / . 6 6 , 9 ! the m = I

TABLE 16. Intrinsic kinetic parameters for hydrogen gasification Investigation


T, K

Blackwood (1959, 1962) s°'sl

Coconut char

Lewis (1970) tvl


625- 875 1275-1650

Tomita et al. (1977) s4




P, atm 5-40 0.01-180 0.01-180 7-28


E,, kcal/mol



0 [

~38 70-85



Heterogeneous kinetics of coal char gasification and combustion


TABLE 17. Overall kinetic data for cha; combustion including corrections for boundary layer diffusion and surface exothermicit y* Investigation


T. K

Po~,. atm


Eo, kcal/mol

A, g / c m : - s a t m "






Field et a l (1967) 9


Field (1969) ~"3

Sub-bituminous char





Mulcahy and Smith (197111'.°

Anthracite, petroleum coke, bituminous and lignite chars




~ 15

Smith (1970) ~":

Anthracite char






Smith (19711 ~

Petroleum coke Anthracite char Bituminous char

1200-2270 1200-2270 1200-2270

0.20 0.20 0.20

1+ 1+ 1+

18 I7 16

20 10 8

Smith (1971)J'~*







Sergeant and Smith (19731 ~s°

Bituminous char





Hamor, Smith and Tyler (19731TM

Lignite char






* K~., = A exp( - E , / R T I where T is the particle temperature "t n = 1 a s s u m e d a c t i v a t i o n e n e r g y s h o u l d be 1 5 - 2 0 k c a l / g m o l r a t h e r t h a n 30--40 k c a l / g m o k as s u g g e s t e d p r e v i o u s l y . A p o s s i b l e e x p l a n a t i o n for t h e a b o v e d i s c r e p a n c y is t h e fact t h a t m o s t i n v e s t i g a t o r s ( T a b l e s 18 a n d 19) e i t h e r a s s u m e first o r d e r k i n e t i c s or v a r y o x y g e n concentration over such a narrow range that any d e v i a t i o n f r o m first o r d e r k i n e t i c s w o u l d be difficult to discern. I n d e e d , it is i n t e r e s t i n g to n o t e t h a t (11 t h e m o r e r e c e n t e v i d e n c e ~°'-';'9. a n d (2) t h e t w o inv e s t i g a t o r s c h a r a c t e r i z e d by t h e l a r g e s t o x i d i z e r p r e s s u r e r a n g e -'7'9' r e p o r t i n s t e a d h a l f - o r d e r kinetics.

For these reasons, the following revised assignment b e t w e e n t r u e o r d e r a n d a c t i v a t i o n e n e r g y m a t be more appropriate : m = 1 m = ½ m = 0

E,-~ 15-20kcal/gmol E, = 3 0 - 5 0 k c a l / g m o l E~ -~ 7 0 - 8 0 k c a l / g m o l .

T h e a c t i v a t i o n e n e r g y r a n g e for t h e m = ~ case i n c l u d e s r e p o r t e d d a t a ( T a b l e s 17 a n d 18) for b o t h h a l f - o r d e r a n d first o r d e r kinetics. T h e l a r g e r a n g e w o u l d n o t be u n e x p e c t e d if, as s h o w n in S e c t i o n

TABLE 18. Intrinsic kinetic data for carbon and char combustion Investigation


T. K

Po:, atm

Blyholder and Eyring (1957) 19: Blyholder and Eyring (1959) 9"~ Walker (195916 Thring and Essenhigh [ 19631 s Laine e: al. t1963) :s Laine et at. (1963) 8~ Essenhigh er al. (1965) ~6

Graphite Graphite Carbon, chars Carbon. chars Carbon Carbon Carbon

875-1075 I0-6--10 -4 1075-1575 10-6-10-'~ . . . . . 800-1550 ~ 0.2 850-950 5 10-5 575-950 (,1-661.10--' 950- 1725 0.03-0.21

Rosner and Allendorf (19651 a68


Field et al. (1967) 9 Mulcahy and Smith ( 1969 )ao Smith and Tyler (1972) 149 Gray et al. (1"974)9a

Carbon Graphite Semi-anthracite Sub-bituminous char

1100-I 300 1450-I700 950-1600 1200-1600 1400-2200 1300- 2000

~ 10- a ~ 1 0 -3 0.01-0.21 -0.1--0.2 0.05-0.10

Smith and Tyler (197419'* Rodriguez-Reinoso et al. (1974127 Dutta and Wen (1977137

Lignite char Graphite Chars

630-1800 775-875 700--850

0.1-0.2 (8-791,10 -3 0.21


E,, kcal/mol

0 0.5 1 0 1' 1' 0

80 2-80 ° 46-58 ~ 25-45 ~ 44 43-46 4&



0.5 l 1 0.5 1 0 1 0--0.5 0.5-0.6 1'

62 0 36" 35-60: 400 37 ~ 6 33 ~ 47--53 3t

° E, approaches 2 kcat/mol at the highest temperatures. Literature review. ' m = I assumed. Based on a reanalysis o f T u et al. 191 e Literature review : based primarily on a reanalysis o f T u et al..t 9 ~ Parker and H ouel: 76 and Golovina and Khaustovitch.~ 92 assuming a non-porous carbon surface. r Literature review: E, increases from 35 to 60 kcal/mol as the graphite impurity level decreases) ~ Determination of/: for a char. hBased on a reanalysis of Field. ~'~3



TABLE 19. Activation energies for oxygen chemisorption and desorption on carbon surfaces Investigation Gulbransen and Andrew t 1952)9" Blyholder and Eyring (1957) 19s Hayward and Trapnell (1964) 6`* Mulcahy and Smith (1969) ~° Spackman et al. (1976) *2

E,,kcal/mol -4-8 1-23 10-20" 6-19t

Ed, kcal/mol 40 80 72-74 50-70* --

*Estimates based on requirements for transition from chemical to mass transfer control. rE,, depends on site activity, increasing as the more active sites are filled. For T > 600K, most of the 0 2 is chemisorbed on the least active sites (16-19 kcal/mol).

3.4.4, half-order kinetics are largely controlled by surface migration, a process presumably sensitive to surface impurities. If the proposed mechanism and activation energies are valid, eqns (42aL 143) and (44a) give {m = 0) (m = 1)

E9 = 70-80kcal/gmol E7 = 15-20kcal/gmol (m = 4_) Es +½(ET-E,o) - 30-50kcal/gmol. The E9 value is not unrealistic and the E7 value is, of course, consistent with Table 19. Independent measurement of reaction {R. 10) is particularly needed since Elo determines E 8. Obviously, the mechanism and activation energies assumed here are not yet based on solid experimental evidence. These uncertainties will hopefully prompt the development of new experimental and analytical procedures to properly measure both true order and activation energy for char combustion. 6. DIRECTIONS FOR FUTURE RESEARCH

In terms of future applications, research on heterogeneous char kinetics ought to be mainly concerned with the reactivity of various chars with oxygen, steam and carbon dioxide. The effects of various catalysts, particularly metallic impurities, on reactivity should be investigated. Of importance here is the relationship between reactivity and the degree of contact between the catalyst and the carbon surface. The dearth of high pressure reactivity data must be corrected: moreover, the temperature range of heterogeneous kinetics studies should be broadened. The latter may be accomplished by (I} considering fundamental phenomena so that data influenced by mass transport can be interpreted correctly or (2) developing new experimental techniques. Fundamental experimental research ought to be concerned with such things as the measurement of intrinsic rate constants and true reaction orders, rather than development of simple reactivity correlations. More optimistically, determination of elementary rate constants should be a prime goal, so that truly predictive models based on first principles

can be developed. [n particular, we should investigate or measure: If) The effect of devolatilization and burnoff on pore volume, pore size distribution, total surface area and active surface area (2) The variation of pore volume, pore size distribution, effective diffusivity, total and active surface area with particle diameter during burnoff (3) Intrinsic rates on both a surface area and site basis (4) True kinetic parameters (E,A,), both global and elementary. The last two points are extremely important: we must determine to what extent activation energies and frequency factors are independent of char type. once the kinetic data have been corrected for A s and [C,] changes. Can E, and A, be correlated with derived or fundamental surface properties such as petrographic composition, crystal orientation, defect structure or atomic bond energies? In a more scientific context, modern electron and ion spectroscopic methods used in catalysis research should be applied to coal chars to study the details of specific site adsorption, desorption and chemical transformation, t 97 Fundamental theoretical models need to be developed in order to compare char burnoff predictions with the experimental results anticipated in the previous paragraph. The future of macroscopic models depends on more suitable expressions for the effective diffusivity. Microscopic models ought to b e emphasized; they should consider: (1) The relation between R,, and/~, e.g. changes in Thiele modulus with time and position (2) Combined molecular and Knudsen diffusion (3) L a n g m u i r - H i n s h e l w o o d kinetics, or at least intrinsic rate expressions with non-integer orders (4) Pore development; i.e. for an initial pore size distribution, allow the expansion and intersection of pores due to surface reaction. Of particular importance are the effects of blind pores, pore coalescence and particle fragmentation.

Acknowledqements--Preparation of this review was supported in part by the United States Department of Energy under Contract E(49-18)-2029: Gasification in Pulverized Coal Flames. The assistance of Mr. Richard A. Kriegbaum in the preparation of Section 4 is appreciated. The final version of this paper owes much to the detailed comments and suggestions by one reviewer of the original manuscript. REFERENCES 1. HOTTEL. H. C. and HOWARD. J. B., New Energy Technology: Some Facts and Assessments. MIT Press, Cambridge, MA (1971). 2. HAMMOND, O. H. and BARON, R. E., Am. Sciem. 64, 407 (1976).

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(Manuscript received 12 September 1 9 7 7 ; in revised f o r m 6 M a y 1978)