Modelling fluidized bed combustion of high-volatile solid fuels

Chemical Engineering Science 57 (2002) 1175–1196www.elsevier.com/locate/ces

Modelling !uidized bed combustion of high-volatile solid fuels

Fabrizio Scala, Piero Salatino ∗

Dipartimento di Ingegneria Chimica, Universit�a degli Studi di Napoli “Federico II”–Istituto di Ricerche sulla Combustione–C.N.R.,Piazzale V. Tecchio, 80–80125 Napoli, Italy

Received 23 February 2001; received in revised form 12 December 2001; accepted 12 December 2001

Abstract

A model of an atmospheric bubbling !uidized bed combustor operated with high-volatile solid fuel feedings is presented. It aims at theassessment of axial burning pro3les along the reactor and of the associated temperature pro3les, relevant to combustor performance andoperability. The combustor is divided into three sections: the dense bed, the splashing region and the freeboard. Three combustible phasesare considered: volatile matter, relatively large non-elutriable char particles and 3ne char particles of elutriable size. The model takes intoaccount phenomena that assume particular importance with high-volatile solid fuels, namely fuel particle fragmentation and attrition inthe bed and volatile matter segregation and postcombustion above the bed. An energy balance on the splashing zone is set up, taking intoaccount volatile matter and elutriated 3nes postcombustion and radiative and convective heat !uxes to the bed and the freeboard.

Results from calculations with a high-volatile biomass fuel indicate that combustion occurs to comparable extents in the bed and in thesplashing region of the combustor. Due to volatile matter segregation with respect to the bed, a signi3cant fraction of the heat is releasedinto the splashing region of the combustor and this results in an increase of the temperature in this region. Extensive bed solids recirculationassociated to solids ejection=falling back due to bubbles bursting at bed surface promotes thermal feedback from this region to the bed ofas much as 80–90% of the heat released by afterburning of volatile matter and elutriated 3nes. Depending on the operating conditions asigni3cant fraction of the volatile matter may burn in the freeboard or in the cyclone. ? 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Modelling; Fluidization; Fuel; Attrition; Biomass; Combustion

1. Introduction

Combustion or co-combustion of non-fossil solid fuelsis gaining consideration as a result of the increasing priceof fossil fuel resources, the abundance of di<erent typesof wastes to be disposed of and the global warming con-cern. Non-fossil solid fuels include several types of biomass,peat, municipal, agricultural and industrial wastes, burnedalone or in combination with fossil fuels. Fluidized bedcombustion (FBC) stems out as one of the most promisingtechnological options in the fuel-to-energy chain due to its!exibility with respect to the fuel mix and the possibility toaccomplish e>cient and clean operation.Extensive experimental investigation has been carried out

to date on the feasibility and performance of the !uidized bedcombustion of di<erent alternative fuels (La Nauze, 1987;Saxena & Jotshi, 1994; Anthony, 1995). However, funda-mental work on the comprehension of the basic mechanisms

∗ Corresponding author. Tel.: +39-81-768-2258; fax: +39-81-593-6936.

E-mail address: [email protected] (P. Salatino).

taking place during conversion of these fuels has receivedcomparatively less attention.Alternative fuels have, in general, physical and chemical

characteristics much di<erent from fossil fuels, so that thebehavior of these two kinds of fuels in FBC is very di<erentone from the other:

(1) The interactions of emitted volatile matter with the!uidized bed can assume a great relevance: the largecontribution to the overall heat release coming from ho-mogeneous combustion of volatile matter emphasizesthe importance of mixing=segregation phenomena withrespect to !uidizing gas and bed inert solids. The loca-tion of volatile matter combustion signi3cantly a<ectsthe heat release pro3les along the combustor. This is-sue is strictly connected to the extension and locationof heat exchange surfaces, to the pathways to pollutantsformation, to the reliability and safety of combustor op-eration.

(2) The loosely connected or even incoherent structures ofchars left behind by devolatilization lead to a more pro-nounced impact of particle attrition phenomena. Fine

0009-2509/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved.PII: S 0009 -2509(02)00004 -0

1176 F. Scala, P. Salatino / Chemical Engineering Science 57 (2002) 1175–1196

char generation by attrition, together with large intrin-sic oxyreactivity of char, signi3cantly a<ect the fate ofchar and of ash residues.

The most common approach to the assessment of in-bedsegregation=combustion of volatile matter has been rep-resented by the “plume” model, independently derivedby Park, Levenspiel, and Fitzgerald (1980, 1981) andStubington and Davidson (1981) and extended by By-water (1980) and de Kok, Nieuwesteeg, and van Swaaij(1985). The model assumes that volatile matter forms anoxygen-starving plume rising through the bed. Combus-tion of the volatiles occurs as a di<usion !ame at theplume boundary. Stubington, Chan, and Clough (1990) andStubington and Chan (1993) proposed a multiple discretedi<usion !ame model which accounts for devolatilizingparticles stepwise motion to the top of the bed under the ac-tion of the ascending !uidizing gas bubbles. None of theseapproaches, however, considers hydrodynamic interactionsbetween the devolatilizing fuel particle and the surrounding!uidized suspension, but reference is made to segrega-tion mechanisms typical of mixtures of inert particles. Onthe contrary, there is experimental evidence that segrega-tion of gas-emitting particles occurs according to mecha-nisms much di<erent from those relevant to !uidization ofnon-reacting particles. Yates, Macgillivray, and Cheesman(1980), Atimtay (1980) and Pillai (1981) observed volatilebubbles formation around devolatilizing fuel particles.Davidson (1992), while discussing experimental results ofMadrali, Ercikan, and Ekinci (1991), suggested that thesebubbles may act like a lift for the fuel particles towards thebed surface, resulting in particle segregation on top of thebed and release of volatile matter directly in the freeboard.Also Nienow and Rowe (1976) and Prins (1987) showedthat fuel particles tend to concentrate in the proximity ofthe bed surface during devolatilization. The e<ect of thehydrodynamic interaction between the stream of volatilematter emitted in the devolatilization stage, the suspensionof the !uidized particles and the fuel particle motion itselfhas been investigated both experimentally and theoreti-cally by Fiorentino, Marzocchella, and Salatino (1997a, b)in incipiently !uidized beds. The analysis of these inter-actions suggested that the released volatiles may form“endogenous” bubbles around the devolatilizing particles,lifting coarse fuel particles to the bed surface. Eventually,devolatilization is completed at (or close to) the bed sur-face and a large fraction of the volatile matter is releaseddirectly in the freeboard, where it burns. Mechanistic stud-ies on devolatilization-induced segregation have only beencarried out so far in bench scale reactors at relatively lowgas super3cial velocity. On the other hand, occurrence of“strati3ed combustion” is commonly reported whenever!uidized bed combustors are operated with high-volatilefuels feedings. This reinforces the idea that fuel segregationcannot be ruled out even at the relatively large gas super3-cial velocities at which full-scale boilers are operated. Local

temperature increase just above the bed surface has been re-ported in most experimental works addressing high-volatilefuels combustion and is direct consequence of strati3edcombustion (Peel & Santos, 1980; Hampartsoumian &Gibbs, 1980; Gulyurtlu & Cabrita, 1984; Achara, Horsley,Purvis, & Teague, 1984; Jovanovic & Oka, 1984; Leckner,Andersson, & Vijil, 1984; Andersson, Leckner, & Amand1985; Irusta, Antolin, Velasco, & De Miguel, 1995).The extensive bypass of volatile matter with respect to

the bed calls for better consideration of volatile matterpostcombustion in the freeboard. van der Honing (1991)showed that burnout of volatile matter bypassing the bed islimited by the oxygen mixing rate in the lower section ofthe freeboard which depends on “turbulence” establisheddownstream the bed. The loss of the sharp distinctionbetween dilute and emulsion phases and the establish-ment of turbulence over a broad spectrum of length- andtime-scales (Horio, Taki, & Hsieh, 1980; Pemberton &Davidson, 1984) positively a<ect volatile matter afterburn-ing. On the other hand, extensive bed solids recirculationassociated with solids ejection=falling bed due to bubblesbursting at the bed surface promote thermal feedback fromthe splashing zone to the bed and partly mitigate the con-sequences of volatile matter afterburning (Martens, Opden Brouw, & van Koppen, 1982; Turnbull & Davidson,1984).Operation of FBC 3ring alternative solid fuels is gener-

ally associated with higher combustion e>ciencies com-pared with coal, provided that residence time of the fuelparticles in the bed is long enough (Leckner et al., 1984;Andersson et al., 1985). On the other hand, carbon 3nesare formed to a large extent by attrition and fragmentationof coarse particles, as reported by Gulyurtlu and Cabrita(1984) and Gulyurtlu, Reforco, and Cabrita (1991). Re-cently, Arena, Cammarota, and Chirone (1995a), Arena,Cammarota, Chirone, and D’Anna (1995b), Arena, Chi-rone, and Salatino (1996) Salatino, Scala, Chirone, andPollesel (1997), Salatino, Scala, and Chirone (1998) andScala, Salatino, and Chirone (2000) compared the over-all combustion–attrition behavior of a subbituminous coalwith those of four waste-derived fuels. Attrition and frag-mentation turned out to be far more extensive in the caseof high-volatile fuels. This feature re!ects the propensityof such fuels to give rise, upon devolatilization, eitherto highly porous, friable chars or even to a multitude offragments of very small size. Combustion e>ciency is di-rectly determined by the relative extent of the combustiontime scale and of the residence time of char 3nes in thebed which, in turn, is related to elutriation. Fixed carbonfrom high-volatile fuels is converted via the generation of3nes followed by their postcombustion over their residencetime in the bed to an extent comparable with that of directcombustion of coarse particles (Salatino et al., 1998; Scalaet al., 2000). Despite quantitative assessment of attrition iscurrently available only for few high-volatile fuels, the verynature of these fuels leads to the expectation that extensive

F. Scala, P. Salatino / Chemical Engineering Science 57 (2002) 1175–1196 1177

attrition be a general feature associated with the course of3xed carbon conversion.Few models speci3cally addressed !uidized bed com-

bustion of high-volatile or alternative fuels. Oymak, Sel-cuk, and Onal (1993) modi3ed a previously developed FBCmodel in order to match experimental temperature and gasconcentration pro3les obtained during lignite combustion.According to this model all fuel volatile matter is releaseddirectly in the splashing region. Fuel particles attrition wasneglected. Irusta et al. (1995) presented a three-phase FBCmodel for a high-volatile fuel, incorporating attrition andfragmentation phenomena. Devolatilization was assumed tooccur partly in the freeboard and partly in the bed, the rela-tive extent depending on an adjustable parameter (the “inter-nal devolatilization degree”). Comparison with results frompilot plant operation with a lignocellulose waste showed thata signi3cant amount (20–40%) of the volatiles burned inthe freeboard. Borodulya, Didalenko, Palchonok, and Stan-chitis (1995) proposed a modi3ed two-phase plume modelfor biomass combustion in !uidized beds, taking into con-sideration combustion of volatiles and char in both bed andfreeboard but neglecting particle attrition and fragmentation.The model predicts that up to 40% of the volatiles may burnin the freeboard.The present work aims at modelling !uidized bed com-

bustion of high-volatile fuels with an emphasis on thee<ect of volatile matter segregation=combustion and ofthe mode and extent of fuel attrition. The relevance ofthese phenomena to combustion e>ciency and to the axialburning pro3les is assessed with reference to a biomassfuel, whose behavior during FBC has been extensivelystudied in the past (Salatino et al., 1998; Scala et al.,2000).

2. Theory

A steady-state one-dimensional model of a bubbling !u-idized bed combustor operated with high-volatile solid fuelsis presented. The combustor is lumped into three sections:the bed, the splashing region and the freeboard. The modelis based on material balances on 3xed carbon, volatile mat-ter and oxygen in each combustor section. The frameworkof the model is reported in Fig. 1. The combustion pathwaythat goes from the raw fuel (0) to the combustion products(P) proceeds via the formation of three phases, representedby the square-shaped blocks: volatile matter (V ), coarse char(C), made of relatively large non-elutriable particles directlygenerated from the raw fuel, and 3ne char particles (F) ofelutriable size generated by attrition of the coarse ones. Thegeneral notation to express mass !ow rates from the I thphase to the J th phase in the K th section of the reactor isFIJ; K , where I and J can take the values 0; V; C; F; P;and K can be bed, sp (splashing region) or fb (freeboard).Ec; K is the unburnt 3xed carbon escaping the K th reactorsection. CO2 and H2O are the ultimate combustion products

Fig. 1. Material balances on combustibles in the reactor.

(P). Gaseous pollutant formation has not been consideredin the model.The model is complemented by an energy balance on the

splashing region written under the assumption that heat re-lease by volatiles and 3nes postcombustion in this zone isbalanced by thermal !uxes to the bed and to the freeboard(Fig. 2). Heat extraction through the walls in this regionis neglected due to the small aspect ratio (height=diameter)of the splashing zone. The notation qSJ; H is adopted to de-note heat !uxes (referred to unit bed cross-section) fromthe splashing region (S) to the bed (J = B), the freeboard(J = F), the ejected bed particles (J = P), the elutriatedcarbon 3nes (J = E), the gas (J = G) and the volatiles(J = V ) entering the splashing zone. H refers to the heattransfer mechanism, either radiative (H = R) or convective(H = C).A layout of the model is provided in Fig. 3. Assumptions

and equations relative to each section of the combustor areseparately detailed hereinafter. Further details on the modelare given elsewhere (Scala, 1998).

2.1. The 6uidized bed

Bed !uid dynamics is modelled according to thetwo-phase !uidization theory (Toomey & Johnstone, 1952;


Fig. 2. Heat !uxes in the di<erent combustor sections.

BED Material balances

SPLASHING REGION

Material balances Energy balances

FREEBOARD Material balances

Output variables

VVolatiles segregation/combustion submodel

Fuel/char communition submodel

Splashing region fluid dynamics

Fines elutriation submodel

Volatiles mixing/combustion submodel

Char combustion

kinetic submodel

Bed fluid dynamics

Model parameters and operating variables

Fig. 3. Flow diagram of the model.

Davidson & Harrison, 1963): gas in the bubble phase isin plug !ow, gas and solids in the emulsion phase arewell stirred. An average bubble size is assumed and calcu-lated according to Darton, La Nauze, Davidson, and Har-rison (1977). If the bubble size is larger than 0.6 timesthe inner bed diameter, the bed is treated as being in theslugging regime (Clift & Grace, 1985, Chapter 3). Thebubble–emulsion phase mass transfer coe>cient is calcu-lated according to Sit and Grace (1981). Bed temperature istreated as a design variable rather than being the result of anenergy balance. The bed is isothermal and the gas is at thesame temperature as bed solids. All particles (fuel and inertmaterial) are assumed to be spherical. The inert bed parti-cles are not subject to attrition but maintain their initial sizeand are coarse enough not to be elutriated signi3cantly fromthe bed. Steady bed inventory is assumed and no balance oninert material is considered.It is assumed that the fuel particles are made of three

di<erent components: volatile matter (where all fuel-boundhydrogen and oxygen end-up), 3xed carbon and ash. For thepurpose of computations, fuel moisture content is lumpedwith volatile matter. It is assumed that char particles contain


Table 1Material balances in the bed

Coarse char T1F0C = FCF; bed + FCP; bed

T2F0C = F0xfcxcoarse

T3FCP; bed = kCP; bedWC; bed

T4

FCF; bed = F0Cn1n2�3nefc

�coarsefc

(dF

d0

)3+ kCF; bedWC; bed

Fine char T5F0F + FCF; bed = FFP; bed + Ec; bed

T6F0F = F0xfc(1− xcoarse)

T7FFP; bed = kFP; bedWF; bed

T8Ec; bed = kelWF; bed

Volatile matter T9F0xvol = FVP; bed + FV; bed

T10FVP; bed = fF0xvol

T11FV; bed = (1− f)F0xvol

Oxygen T12

CbedO2

= C inO2

{1− Ubed

ebed[Ubed − (Ubed − Umf) exp(−X )]

}

+

{F0Yvolf[1− exp(−X )]

AX [Ubed − (Ubed − Umf) exp(−X )]

}

T13

ebed =e

�bedT14

�bed =Yfc(1− Ec; bed

F0xfc) + Yvolf

Yfc + Yvol

only 3xed carbon and ash. Monosize fuel feed containingno 3nes is considered. Therefore, 3nes in the bed are onlythose produced by attrition and fragmentation of coarsechar and those resulting from the shrinkage of coarse parti-cles down to elutriable size. Either over-bed or submergedfuel feeding can be considered in the computations. In ei-ther case, consistently with the one-dimensional feature ofthe model, it is assumed that fuel particles are e<ectivelyspread across the combustor cross-section upon feeding.An integral material balance on 3xed carbon, based onan average size of coarse carbon particles in the bed, isused instead of the di<erential particle population bal-ance, leading to a signi3cant simpli3cation of the modelequations.

2.1.1. Material balancesTable 1 reports 3xed carbon (in coarse and 3ne phases),

volatile matter and oxygenmaterial balances in the bed alongwith expressions for each term.It is assumed that primary fragmentation of the fuel par-

ticles upon devolatilization is instantaneous upon feeding tothe bed. Both coarse and 3ne particles can result from pri-mary fragmentation. Particle swelling or shrinkage duringthis stage are neglected.

Calculation of the overall char combustion kinetic con-stants kCP; bed and kFP; bed is detailed in Appendix A. The3nes elutriation constant kel is evaluated with a correla-tion proposed by Geldart (1986). The 3xed carbon mass!ow rate associated with 3nes generation from coarse charparticles (FCF; bed) is the sum of two contributions: 3nesresulting from the shrinkage of coarse particles down toelutriable size and 3nes produced by attrition and=or per-colative fragmentation of coarse char particles (Chirone,D’Amore, Massimilla, & Salatino, 1984; Arena, Chi-rone, D’Amore, Miccio, & Salatino, 1995c). kCF; bed is the3nes generation constant by abrasion and=or percolativefragmentation.As discussed in Salatino et al. (1998), two approaches

can be adopted to express the carbon 3nes genera-tion constant kCF; bed depending on the relevant attritionmechanism:

(a) Combustion-assisted-attrition. Fines generation ratedepends on the combined e<ects of surface abrasionand of combustion-induced loss of particle connectiv-ity (Chirone, Massimilla, & Salatino, 1991). The 3nesgeneration constant is evaluated as

kCF; bed =kab(Ubed − Umf)

dC; (1)


where kab depends on the material properties, on theinert bed material size and on oxygen concentration inthe bed.

(b) Fragmentation by peripheral percolation. During thecourse of combustion porosity at the particle surfacereaches a critical value (that depends on the fuel charstructure) and the cortical region collapses producinga multitude of 3nes (Kerstein & Niksa, 1984; Salatino& Massimilla, 1988). In this case 3nes generation isproportional to the carbon burning rate at the particlesurface. The 3nes generation constant can be written as

kCF; bed = "kCP; bed ; (2)

where

"=(1− Vash − #cr

#cr − #0

): (3)

#0 and #cr are the char initial and critical porosities andVash is the volume fraction of ash in the char particle.The RHS of Eq. (3) represents the ratio between thefraction of the 3xed carbon detached as 3nes fromthe coarse char particle on the verge of percolationand the fraction of carbon burnt (Walsh, Dutta, Cox,Saro3m, & Beer, 1988; Walsh & Li, 1994). From Eq.(2) it follows that

FCF; bed = "FCP; bed ; (4)

that is, the 3nes generation rate is proportional to thecoarse char combustion rate.

The actual average diameter of the coarse particles in thebed is expressed according to Chirone et al. (1984) andArena et al. (1995c):

dC = 0:8d0

[n1

(n2 + 1

2

)]−1=3

; (5)

where n1 and n2 represent the char particle multiplica-tion factors due to primary and secondary fragmentations,respectively.The average size of the 3ne char particles is considered

as an input parameter. This assumption is based on the ex-perimental evidence that the size distribution of elutriated3nes is approximately independent of operating conditionsand is only related to a “natural grain size” of the char tex-ture (Arena, D’Amore, & Massimilla, 1983).Calculation of the fraction f of emitted volatiles burn-

ing inside the bed, for either over-bed or submerged fuelfeedings, is based on theoretical and experimental work ofFiorentino et al. (1997a, b). These authors carried out ex-periments based on submerged single-particle feeding in in-cipiently !uidized beds and observed that volatile matterreleased in the pyrolysis stage form “endogenous” bubblesaround the fuel particle which, in turn, may lift the particleitself to the bed surface. Two segregation patterns were ob-served: the single bubble segregation (SBS) pattern, whenthe 3rst volatile bubble alone lifted the fuel particle to the

bed surface; the multiple bubble segregation (MBS) pattern,when the particle lagged behind the 3rst generated bubbleand a chain of two or more volatile bubbles was formed lift-ing the particle to the bed surface along a stepwise trajectory.Regardless of the segregation pattern, after reaching the bedsurface the fuel particle remained segregated thereon as faras devolatilization took place. Accordingly, the value of fhas been evaluated as follows:

(a) Over-bed feeding. Fuel particles fed over-bed pyrolyzewhile being strati3ed at the bed surface. As a conse-quence f = 0.

(b) Under-bed feeding. The fractional volatile matter burn-ing in the bed is assumed to be equal to the fractionof volatiles emitted during the particle uprise from thefeeding point to the bed surface. The remaining volatilematter is directly emitted in the splashing zone. Theparticle rise time to the bed surface depends on the seg-regation pattern of the fuel, as observed by Fiorentinoet al. (1997b).

SBS pattern: The devolatilizing particle is assumedto rise with the volatile bubble at a constant velocitygiven by

vr = v∞r + (Ubed − Umf); (6)

where v∞r is the experimentally determined particlerise velocity under incipient !uidization conditions. Thetime elapsed from particle injection to segregation is

'r =hbedvr

: (7)

MBS pattern: The time for particle segregation at thebed surface is given by the sum of an induction timeduring which the devolatilizing particle remains nearlystill at the feeding point and an uprise time (Fiorentinoet al., 1997b):

'r = 'i +hbedvr

; (8)

where 'i is determined from experiments and vr is cal-culated from Eq. (6).In either case the fraction of volatiles emitted and

burned in the bed is expressed as

f = 1− exp(− 'r'd

); (9)

where 'd is a characteristic fuel devolatilization time,given by

'd = kddm0 : (10)

The devolatilization constant kd is a function of the fueltype and of the bed temperature. A value of m= 2 hasbeen assumed in Eq. (10).

Fuel particles remain segregated at the bed surface as faras devolatilization is active. Once devolatilization is com-plete, char particles are assumed to be evenly dispersedthroughout the dense phase of the bed.


Table 2Material balances in the splashing region

Fine char T15Ec; bed = FFP; sp + Ec; sp

T16FFP; sp = Ec; bed*F; sp

T17

*F; sp = kFP; sphspUsp

Volatile matter T18FV; bed = FVP; sp + FV; sp

T19

FVP;sp =

(CbedO2

UmfA

Yvol

)+ QentrCsp

vol = F0xvol(g+ h)

Oxygen T20

CspO2

= C inO2

(esp − 1)esp

TbedTsp

T21

esp =e�sp

T22

�sp =Yfc(1− Ec; sp=F0xfc) + Yvol(f + g+ h)

(Yfc + Yvol)

Calculation of the actual oxygen concentration in thedense phase of the bed is based on the assumption thatall the in-bed emitted volatiles burn in the bubble phase.Derivation of the oxygen balance in the bed is detailed inAppendix B.

2.2. The splashing region

The vanishing of the distinction between bubble and emul-sion phases in the splashing region and the establishment ofturbulence associated to bubbles bursting (Horio et al., 1980;Pemberton & Davidson, 1984; van der Honing, 1991) makegas mixing more e<ective in the splashing region than in thebulk of the bed. Accordingly, the splashing zone is consid-ered well stirred as regards both the solids and the bulk ofthe gas phase and isothermal as regards the gas phase. Nosecondary air injection is considered.Solids present in this region consist of ejected bed parti-

cles and elutriated 3nes. No coarse char particles are presentin the splashing region. In spite of the experimental evi-dence that solids concentration decays along the splashingzone, uniform distribution of ejected bed particles through-out this region is assumed. Clustering of bed particles is ne-glected as suggested by Benoni, Briens, Baron, Duchesne,and Knowlton (1994).Bed solids are ejected from the bed into the splashing

region by bubble bursting at the bed surface, according tothe mechanism proposed by George and Grace (1978). Theinitial ejection velocity of bed particles at the surface of thebed is related to the bubble bursting velocity:

vS;0 = .Ubub; s: (11)

The bubble size at the bed surface is calculated accordingto Darton et al. (1977). Typical average values of . arebetween 1 and 3 (Do, Grace, & Clift, 1972; George & Grace,1978; Berkelmann & Renz, 1991; Fung & Hamdullahpur,

1993). A conservative value of . = 1, i.e. initial particleupward velocity equal to that of the bursting bubbles, hasbeen assumed in the computations.The mass !ux of ejected inert bed particles at the bed

surface is (George & Grace, 1978; Pemberton & Davidson,1986):

FS = 0�S(1− 1mf)(Ubed − Umf): (12)

A broad range of uncertainty characterizes the value of theparameter 0 (George & Grace, 1978; Pemberton & David-son, 1986; Briens, Bergougnou, & Baron, 1988; Baron,Briens, Galtier, & Bergougnou, 1990; Fung & Hamdullah-pur, 1993; Milioli & Foster, 1995). In this work we assume0 = 0:01 in accordance with experimental results by Pem-berton and Davidson (1986).The height of the splashing region is calculated as

the maximum height reached by bed solids in theirejection=fall-back trajectories. This height, together withthe average residence time of the ejected bed particles inthe splashing region and the average relative velocity be-tween the particles and the gas, is calculated by solving theequation of motion of a spherical inert particle ejected inthe splashing region, neglecting the drag force. The solutionof the approximated equation of motion di<ered from thatobtained from the detailed equation of motion (consideringthe drag force as suggested by Do et al., 1972) by ¡ 20%,in the average.The volumetric fraction of ejected bed solids in the splash-

ing zone can be calculated as

"S; sp =FS'S; sp�Shsp

: (13)

2.2.1. Material balancesTable 2 reports 3xed carbon (in 3ne phase), volatile mat-

ter and oxygen material balances in the splashing regionalong with expressions for each term.


The 3xed carbon material balance is formulated as-suming uniform postcombustion of elutriated carbon 3nesduring their residence time in this region. kFP; sp is theoverall 3nes combustion kinetic constant in this region,whose calculation is detailed in Appendix A. Values of thechar 3nes average diameter are assumed equal to those ofin-bed 3nes.It is assumed that volatiles bypassing the bed burn in the

splashing region by the sum of two mechanisms (fractionsg and h in Table 2): (A) nearly-premixed combustion ofvolatile matter with oxygen issuing from the dense phase ofthe bed as interstitial gas and (B) non-premixed combustionwith the oxygen issuing from the bubble phase. The 3rstprocess is assumed to take place instantaneously at the bedsurface. The second process is assumed to be controlled bymacromixing of volatiles and oxygen associated with gasentrainment from the bulk of the gas phase into the so-called“ghost” bubbles (Pemberton & Davidson, 1984). The totalgas entrainment rate in the splashing region is calculated asthe product of the number of ghost bubbles present in thesplashing region and the single bubble entrainment rate. Thenumber of ghost bubbles present in the splashing zone isgiven by the product of the bursting frequency of bubblesat the bed surface and their residence time in the splashingregion, that is

Qent = Qent1bub

6(Ubed − Umf)A3D3

bub; s

'gb: (14)

The gas entrainment rate at a single ghost bubble and thebubble residence time in the splashing region are calculatedaccording to Pemberton and Davidson (1984), assumingvortex ring behavior and growth rate given by Maxworthy(1972)

Qent1bub =

36D3

bub; s(Ubub; s − Umf)5; (15)

'gb =15

(1

(Ugb − Usp)− 1

(Ubub; s − Umf)

): (16)

Ugb in Eq. (16) is the ghost bubble velocity at the upperlimit of the splashing region, calculated according to Pem-berton and Davidson (1984). The parameter 5 is taken as1=(3Dbub; s) as suggested by Hamdullahpur and MacKay(1986).Volatiles concentration outside the ghost bubbles is as-

sumed to be constant along the splashing region and equalto the volatiles concentration issuing from the bed de-pleted by nearly-premixed combustion at the bed surface(term A).

2.2.2. Energy balanceTable 3 reports the energy balance in the splashing re-

gion along with expressions for each term. Heat release byvolatile matter and 3nes postcombustion in this zone is as-sumed to be balanced by convective and radiative thermal

!uxes to the bed and to the freeboard. The convective heat!uxes are associated with increase of sensible heat of gas,volatile matter and 3nes upon crossing the splashing zoneand of ejected inert bed particles during their trajectory inthe splashing region.The inert solids convective heat !ux to the bed is evalu-

ated assuming that the ejected particles are uniformly dis-persed in the splashing zone at a temperature TTP averagedover their residence time in the splashing zone. 6 is the ratiobetween the total exposed surface area of the ejected par-ticles in the splashing zone and the cross-sectional area ofthe bed:

6 =6"S; sphsp

dS: (17)

The gas convective heat transfer coe>cient hS; C is cal-culated using a correlation suggested by Palchonok, Brei-tholtz, Borodulya, and Leckner (1998) for Nusselt numberfor convective heat transfer around particles in the splashingzone. The actual ejected particles temperature TP is calcu-lated by solving the unsteady state energy balance around asingle ejected particle in the splashing region, as reported inTable 3. An order of magnitude evaluation of particle Biotnumber ensures that temperature is uniform throughout theinert particle.Radiative !uxes are calculated according to the zone

method (Hottel & Saro3m, 1967). The following absorbing=emitting zones are considered:

(a) the bed;(b) the freeboard;(c) the ejected bed particles (treated altogether as one

zone);(d) the absorbing=emitting gas embodying the contribution

of the elutriated carbon 3nes.

The 3rst two zones are treated as two parallel in3nite grayplanes, at a distance equal to the splashing zone height, con-3ning the gas and the gray ejected bed particles. The entiretreatment is based on geometrical optics, since the particlesize is much larger than the relevant radiation wavelengths.The global view factors of the system 7IJ referred to thecross-section of the bed are calculated from the geometricalview factors of the system and the emissivities of the fourzones, as detailed in Appendix C.

2.3. The freeboard

Gas and particles in the freeboard are in plug !ow andisothermal with temperature Tfb treated as a parameter. Thefreeboard height is given by the total reactor height minusthe expanded bed and splashing region heights.

2.3.1. Material balancesTable 4 reports material balances on 3xed carbon (in 3ne

phase), volatile matter and oxygen in the freeboard alongwith expressions for each term.


Table 3Energy balances in the splashing region

Overall energy balancein the splashing region

T23H sp

A= qSG; C + qSV; C + qSE; C+qSP; C + qSB; R + qSF; R + qSP; R

T24H sp = FFP; sp|VHfc|+ FVP; sp|VHvol|

T25

qSG; C =FG

AcG(Tsp − Tbed)

T26

qSV; C =FV; bed

AcV (Tsp − Tbed)

T27

qSE; C =Ec; bed

AcF (Tsp − Tbed)

T28qSP; C = 6hS; C(Tsp − TTP)

T29qSB; R = 87SB(T 4

sp − T 4bed)

T30qSF; R = 87SF (T 4

sp − T 4fb)

T31qSP; R = 87SP(T 4

sp − TT 4P)

Unsteady energy balancearound a single ejectedbed particle

T32dS�ScS

6dTPdt

= qPPS; C + qPPS; R + qPPB; R + qPPF; R

T33qPPS; C = hS; C(Tsp − TP)

T34

qPPS; R = 87PS

6(T 4

sp − T 4P)

T35

qPPB; R = 87PB

6(T 4

bed − T 4P)

T36

qPPF; R = 87PF

6(T 4

fb − T 4P)

Table 4Material balances in the freeboard

Fine char T37Ec; sp = FFP; fb + Ec; fb

T38FFP; fb = Ec; sp*F; fb

T39

*F; fb = kFP; fbhfbUfb

Volatile matter T40FV; sp = FVP; fb

Oxygen T41

CfbO2

= C inO2

(efb − 1)efb

TbedTfb

T42

efb =e�

T43

�=Yfc(1− Ec;fb=F0xfc) + Yvol

(Yfc + Yvol)

The 3xed carbon material balance is formulated assum-ing postcombustion of elutriated carbon 3nes during theirresidence time in this region. kFP; fb is the overall 3nes com-bustion kinetic constant in this region, whose calculation is

detailed in Appendix A. Char 3nes average diameter is equalto that of in-bed 3nes.Volatile matter escaping the splashing region, if any, is

assumed to burn completely and uniformly in the freeboard


Table 5Model parameters

Fuel

xfc, dimensionless numbers 0.193 xcoarse, dimensionless numbers 1xvol, dimensionless numbers 0.792 n1, dimensionless numbers 1xash, dimensionless numbers 0.015 n2, dimensionless numbers 3Yfc; kmol=kg 0.016 Vash, dimensionless numbers 0.002Yvol; kmol=kg 0.025 kd; s=m2 1.5e+5�coarsefc ; kg=m3 90 v∞r ; m=s 0.3�3nefc ; kg=m

3 230 'i; s 0dF ; m 1:0e− 4 VHfc; kJ=kg 34000k0; 1=s atm 1:2e + 8 VHvol; kJ=kg 11500Ea, kcal=kmol 32000 cV ; kJ=kgK 4.2n, dimensionless numbers 0.76 cF; kJ=kgK 1.5#0, dimensionless numbers 0.91 1char , dimensionless numbers 0.8#cr , dimensionless numbers 0.955 kC; W=mK 0.1dpore, m 1:4e− 6

Bed inert particles�S ; kg=m3 2540 1P , dimensionless numbers 0.6cS ; kJ=kgK 0.8 kS ; W=mK 2.91mf , dimensionless numbers 0.43

Combustordbed ; m 1.13 1B, dimensionless numbers 0.78WS; bed ; kg 1400 1F , dimensionless numbers 0.99htot ; m 5.0

and in the cyclone. This assumption prevents the assessmentof any unburnt volatile matter at the exhaust, but is consis-tent with the main focus of the model that is the establish-ment of axial burning (and temperature) pro3les along thereactor.

3. Results

3.1. Evaluation of model parameters

The model has been applied to a high-volatile biomassfuel (Robinia Pseudoacacia) extensively characterized inthe literature (Masi, Salatino, & Senneca, 1997; Salatino etal., 1998; Scala et al., 2000). Numerical values of modelparameters used for calculations are listed in Table 5.Most of the parameters have been estimated accordingto available literature data. Fuel-related parameters havebeen taken from Masi et al. (1997), Salatino et al. (1998)and Scala et al. (2000). Fuel devolatilization parametershave been evaluated according to the experimental resultsof Fiorentino et al. (1997b). In particular Robinia wasfound to behave according to the SBS devolatilizationpattern. Following Salatino et al. (1998), 3nes generationwas assumed to be controlled by peripheral percolativefragmentation.Dry fuel particles have been considered. The volatile mat-

ter yield has been approximately taken as per ASTM prox-imate analysis. The heat capacity of the volatile matter has

been assumed equal to that of propane. The heat of com-bustion of the emitted volatile matter depends on the fuelcomposition and has been determined from the net calori3cvalue of the fuel, knowing the 3xed carbon and volatile mat-ter mass fractions and the heat of reaction associated with3xed carbon combustion.The gas emissivity in the splashing region has been calcu-

lated following the method suggested by Hottel and Saro3m(1967), with the aid of the diagrams reported by the au-thors. Calculation has been carried out considering the con-tributions of both CO2 and H2O evaluated at the tempera-ture and partial pressures relevant to the splashing regionand also the contribution of the burning carbon 3nes dis-persed in the gas. The bed emissivity has been evaluatedfollowing Palchonok (1998). The freeboard emissivity wasset to 0.99 as the freeboard behaves much like a black bodycavity.Bed column inner diameter and sand inventory in the bed

(giving the static bed height) are indicated in Table 5. Thegas distributor was a perforated plate with 400 holes.Model results are analyzed with reference to a set of

base-case values of operating variables. The analysis hasbeen further extended to assess model sensitivity to selectedoperating variables.

3.2. Base-case computations

Values of operating variables adopted in base-case com-putations are listed in Table 6. Submerged fuel feeding was


Table 6Operating variables and results of model computations

Shaded area refers to base case computations.

considered in the base case, despite the prevailing currentpractice is represented by over-bed feeding, with the aim ofassessing to what extent could this option be re!ected byenhanced in-bed volatile matter burning.Output variables chosen to characterize the performance

of the !uidized bed combustor are:

1. Coarse and 3ne char loadings in the three regions of thecombustor;

2. Fraction of volatile matter burned in the three regions ofthe combustor;

3. Oxygen concentration in the dense phase of the bed andin the splashing region;

4. Fixed carbon and total combustion e>ciencies of the bedand total combustion e>ciency of the combustor (underthe assumption that volatile matter burnout is completebefore leaving the cyclone);

5. Splashing region temperature;


C

F

F0

FCP, bed

FFP, bed

FCF, bed

FP, bed

E

F0C

F0F

c, bed

= 1

= 0.511

= 0.0005

= 1

= 0.489

= 0.489fc

= 0

= 1

Fig. 4. Balance on 3xed carbon in the bed. Numerical values are relativeto base case computations, referred to unit 3xed carbon feed rate.

Burning intensity, molO2 s-1m-3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Dis

tan

ce f

rom

th

e d

istr

ibu

tor,

m

0.0

1.0

2.0

3.0

4.0

5.0

FLUIDIZED BED

FREEBOARD

SPLASHING ZONE

CoarsesFines Volatiles

Fig. 5. Axial burning pro3le in the combustor. Base case computations.

6. Heat generation rates in the three regions of the combus-tor;

7. Fraction of heat generated in the splashing region re-turned to the bed (thermal feedback e>ciency).

Results of base-case computations are summarized in Ta-ble 6. The analysis is complemented by the graphs reportedin Figs. 4 and 5. Fig. 4 reports the 3xed carbon balance inthe bed, referred to unit 3xed carbon feed rate. Fig. 5 re-ports the axial pro3le of the speci3c burning intensity, ex-pressed as the rate of oxygen consumption per unit volumein the various sections of the reactor highlighting terms rel-ative to the combustion of coarse and 3ne char phases andof volatile matter, respectively.Calculations indicate that char from Robinia yields a large

amount of elutriable 3ne particles by percolative fragmenta-tion. Char 3nes, however, quickly burn over their residencetime in the bed due to their large intrinsic reactivity, so that3xed carbon combustion e>ciency is close to unity (Fig. 4).The two pathways responsible for 3xed carbon conversion,namely:

Pathway 1: direct coarse char burningPathway 2: generation of 3ne particles by attrition of

coarse char, followed by char 3nes postcombustion, are char-

acterized by a profound di<erence in the time-temperaturehistory of char along burn-o<. In particular, Scala et al.(2000) outlined that carbon conversion along pathway1 yields peak combustion temperatures only moderatelyhigher than bed temperature, whereas more complex is thesituation as regards the time-temperature history of charburnt along pathway 2. The same authors highlighted theimportance of a better characterization of the interactionbetween burning char 3nes and bed inert solids and of itsimpact on heat transfer and fate of ash residues.In all conditions char combustion took place under con-

trol of boundary layer di<usion of oxygen. Notably, coarsecarbon loading in the bed is orders of magnitude smallerthan loadings correspondingly observed in the !uidized bedcombustion of coal. Several reasons concur to this result:the small 3xed carbon content of the biomass, the largecontribution to coarse char combustion associated with car-bon attrition=postcombustion (about 50%), the large oxy-gen concentration in the bed due to extensive bypass ofvolatile matter, the large intrinsic reactivity of biomass char.The 3ne carbon loading in the bed for the biomass fuel ismuch smaller than that corresponding to coarse carbon, be-cause of the much larger burning rates of the former. Charloadings in the splashing region and in the freeboard arenegligible.It is interesting to consider axial burning pro3les reported

in Fig. 5 for the various phases in the di<erent sectionsof the combustor. The bed section represents the main lo-cation for 3xed carbon conversion. Most volatile matter isconverted in the splashing region of the combustor. Despitesubmerged fuel feeding is considered in the computations,in-bed volatile matter burning is rather limited (f = 0:09)and only marginally larger than if over-bed feeding wereconsidered (f = 0). About 25% of the volatile matter es-capes the splashing region. It must be underlined that evenlarger fractional volatile matter would escape the splashingzone if, contrary to model assumption, lateral fuel spreadingacross the combustor cross-section upon feeding would notbe e<ective. Fixed carbon conversion in the bed is equallyshared between the coarse and the 3ne phases, in spite ofthe much larger loading of the former.On the whole results can be summarized into the follow-

ing statements:

1. Combustion of the high-volatile biomass fuel takes placeto comparable extents in the bed and in the splashing re-gion of the combustor. Fixed carbon is mostly convertedin the bed.

2. A signi3cant role of the pathway coarse–char–attrition=3nes–postcombustion is observed, in parallel to the usualcoarse–char–combustion pathway.

3. In spite of the submerged fuel feeding considered in thecomputations, extensive volatile matter segregation withrespect to the bed occurs, bringing a signi3cant portionof the heat release into the splashing region of the com-bustor.


4. A non-negligible fraction of the volatile matter burns inthe freeboard and=or in the cyclone.

5. Char concentrations in the dilute regions of the combus-tor, and associated burning rates, are rather limited. Inspite of this, they might be relevant to the emission issues,by determining the existence of locally reducing zones.

Table 6 reports heat generation rates in the three combus-tor sections. On the basis of the above considerations and ofthe results reported in Table 6, one can estimate that about45% of the heat release takes place within the bed duringcombustion of the biomass under the simulated conditions,the remainder being released in the splashing region (40%)and in the freeboard=cyclone (15%), because of extensivevolatile matter postcombustion.It is interesting to assess, at this point, the magnitude of

thermal !uxes that are established at steady state betweenthe di<erent sections of the combustor. The main goal isthat of determining the extent to which heat released inthe splashing region is fed back to the bed and the relatedtemperature of the splashing region. It is recalled here thatbed and freeboard temperatures were 3xed in the base-casecomputations at 850◦C and 700◦C, respectively.Results of computations are summarized in

Table 6. The importance of volatile matter afterburningbrings about a pronounced overheating of the splashingregion (about 40◦C). However, large thermal feedback tothe bed prevents overheating from being even larger. About80% of the heat released in the splashing zone is fed backto the bed. The contribution from solids convection asso-ciated with particles ejection=fall-back is by far dominant.Heat transfer between gas and ejected solids in the splash-ing region takes place along parallel pathways associatedwith convection (about 94% of the heat !ux) and radiation(about 6%).On the whole, results indicate that overheating of the

splashing region with respect to the bed may be signi3cantwhen volatile matter segregation=afterburning take place.These phenomena are clearly enhanced in the presence ofhigh-volatile solid fuels, as proven in a number of exper-imental studies (Peel & Santos, 1980; Hampartsoumian &Gibbs, 1980; Gulyurtlu & Cabrita, 1984; Achara et al., 1984;Jovanovic & Oka, 1984; Leckner et al., 1984; Andersson etal., 1985; Irusta et al., 1995). However, thermal feedbackfrom the splashing region to the bed turns out to be ex-tremely e<ective and keeps overheating within about 40◦C,under the operating conditions simulated in the base case.The e<ectiveness of thermal feedback is critically relatedto the fact that volatile matter afterburning be completedwithin the splashing region, i.e. within the zone where signif-icant particle recirculation is established by bubble bursting.Should homogeneous volatiles combustion be ine<ective tothe point of delaying most of the heat release beyond thesplashing region, much lesser thermal feedback should beexpected. It is important to note, under this respect, that noair staging was considered in the simulations which might

Q, W

0.0

1.0e+6

8.0e+5

6.0e+5

4.0e+5

2.0e+5

1.2e+6

frac

tio

nal

vo

lati

le m

atte

r b

urn

ing

, -

0.8

0.6

0.4

0.2

0.0

1.0

BED

SPLASHING - PREMIXED

SPLASHING - NON PREMIXED

FREEBOARD/CYCLONE

BED - COARSE CHAR

BED - FINES

BED - VOLATILESSPLASHING - VOLATILES

FREEBOARD/CYCLONE - VOLATILES

U, m/s

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Q, W

HEAT EXTRACTED - BED

HEAT EXTRACTED - FREEBOARD

0.0

1.0e+6

8.0e+5

6.0e+5

4.0e+5

2.0e+5

1.2e+6

Fig. 6. In!uence of super3cial velocity on combustor performance.

signi3cantly a<ect gas phase mixing and volatile matterafterburning.

3.3. Assessment of the in6uence of selected operatingvariables

The following operating variables have been varied oneat a time (all the other variables being kept at the base-casevalues) in order to assess their in!uence on the combustorperformance:

1. Initial fuel size;2. bed material size;3. gas super3cial velocity;4. bed temperature;5. excess air factor;6. submerged versus over-bed fuel feeding.

Results are reported in Table 6 and in Figs. 6 and 7.

1188 F. Scala, P. Salatino / Chemical Engineering Science 57 (2002) 1175–1196fr

acti

on

al v

ola

tile

mat

ter

bu

rnin

g, -

0.8

0.6

0.4

0.2

0.0

1.0

SPLASHING - PREMIXED

SPLASHING - NON PREMIXED

FREEBOARD/CYCLONEE

BED

Q, W

0.0

1.2e+6

1.0e+6

8.0e+5

6.0e+5

4.0e+5

2.0e+5

BED - COARSE CHAR

BED - FINES

BED - VOLATILES

SPLASHING - VOLATILES

FREEBOARD/CYCLONE - VOLATILES

dS, mm

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Q, W

0.0

HEAT EXTRACTED - BED

HEAT EXTRACTED - FREEBOARD

1.2e+6

1.0e+6

8.0e+5

6.0e+5

4.0e+5

2.0e+5

Fig. 7. In!uence of bed inert particle size on combustor performance.

Computations demonstrate that the freeboard temperaturebarely a<ects the combustor performance. This result, how-ever, is partly due to the assumption that volatile matter af-terburning is complete in the freeboard and in the cyclone,regardless of the extent of afterburning in the splashing zone.Issues related to unburnt gaseous species, not considered inthe present model, would emphasize the role of the free-board temperature.Fixed carbon and total combustion e>ciencies for the

biomass were both practically unity in all operating condi-tions investigated, even at bed temperatures as low as 700◦C.This result is a consequence of the large intrinsic combus-tion reactivity of the fuel and is in line with experimentalresults reported by Scala et al. (2000). The in!uence ofexcess air factor and fuel feed particle size on FBC perfor-mance is straightforward (Table 6): a decrease of the bedcarbon loading is brought about by increasing e (due to the

increase of in-bed oxygen concentration) and by decreasingd0 (as a consequence of the increased surface area per unitmass exposed to both combustion and attrition). The splash-ing zone temperature is not in!uenced signi3cantly by theexcess air factor and by the fuel feed particle size, except atvery small sizes. For small fuel feed particles volatile matteris released and burned more e<ectively in the bed leadingto a more limited volatile matter bypass: under theseconditions it appears that submerged fuel feeding is bet-ter exploited, as an alternative to over-bed feeding. Thecomparison of results obtained using base-case values ofoperating variables under the hypothesis of over-bed feed-ing con3rm how barely do model results depend on theover-bed versus submerged feeding option. Again, it mustbe underlined that sensitivity of combustor performancesupon fuel feeding location would be much emphasized withfuel feedings of smaller particle size d0.The in!uence of the gas super3cial velocity and of the

bed inert particle size on the combustor performance is moreintriguing and is reported in Figs. 6 and 7. The 3gures re-port, as functions of U and dS , respectively, the fractionsof the volatile matter burned in the di<erent combustor sec-tions, the fraction of heat released in the di<erent combustorsections associated with coarse char, 3ne char and volatilematter combustion and the total fractions of heat extractedin the bed and in the freeboard.The in!uence of the gas super3cial velocity is signi3cant

(Fig. 6). Low values of U lead to a low fraction of oxygengoing into the bubble phase, enhancing the nearly-premixedcombustion of volatile matter above the bed. High super-3cial velocities lead to enhanced mixing between oxygenissuing from bubbles and volatile matter. High values ofU are also associated to large bed particle ejection veloc-ities and long residence times in the splashing region thatenhance thermal feedback to the bed. Intermediate valuesof U apparently correspond to the worst operating condi-tions: a signi3cant fraction of volatile matter escapes thesplashing region. At values of U between 0.5 and 1:0m=sa signi3cant fraction of the total heat release must be ex-tracted in the freeboard in order to keep it at the pre-settemperature.A strong in!uence on the combustor performance is ex-

erted also by the bed inert particle size (Fig. 7). This isthe result of two con!icting trends: on the one hand, thecoarser the particle size, the smaller the particle ejectionrate and residence time in the splashing region, the smallerthe thermal feedback to the bed. On the other hand coarserbed solids imply larger incipient !uidization velocities andsmaller fraction of oxygen going into the bubble phase.The worst operating conditions correspond to intermediatevalues of dS (0.6–0:9mm), but also to bed particle sizeslarger than about 1:2mm. Too large dS values should beavoided because of the decreased e<ectiveness of the ther-mal feedback mechanism in the splashing region and be-cause larger heat extraction has to be accomplished in thefreeboard.


4. Conclusions

An one-dimensional model of an atmospheric bubbling!uidized bed combustor of high-volatile solid fuels is pre-sented. A speci3c feature of the model is that it takes into ac-count the important processes of fuel particle fragmentationand attrition and of volatile matter segregation with respectto the bed followed by afterburning in the splashing regionand=or in the freeboard. Despite the simple modelling ap-proach, results con3rm the criticality of these aspects, oftendisregarded in previous models, with respect to axial burn-ing pro3les along the reactor and associated performanceand operability of the reactor.The model has been applied to the prediction of the per-

formance of a combustor operated with either under-bed orover-bed feeding of a high-volatile biomass fuel. Resultsindicate that volatile matter segregation with respect to thebed and subsequent postcombustion in the splashing regionare extensive in either case. Signi3cant heat release occursin this region, comparable to that relative to the bed section.However, extensive bed solids recirculation associated tobubble bursting=solids ejection at the bed surface togetherwith e<ective gas–solids heat transfer promote thermal feed-back from this region to the bed. These phenomena keepthe temperature in the splashing region within typically40–50◦C above bed temperature. Parameters like bedtemperature, excess air, fuel feed size a<ect combustorperformance in a predictable way. More intriguing, gassuper3cial velocity and bed solids particle size a<ect thecombustor performance in a non-monotonic fashion, es-sentially through the way they a<ect the balance betweenin-bed versus splashing region volatile matter burnout.Depending on the operating conditions, a signi3cant frac-tion of the volatile matter may escape the splashing regionunburnt.Altogether the issues of strati3ed combustion, of volatile

matter mixing=segregation with the !uidizing gas and of fuelfragmentation=attrition emerge as key features in combus-tor modelling. Axial non-uniformities of burning intensityand temperature are simply and e<ectively addressed in thepresent model in the framework of an one-dimensionalapproach. The model represents a 3rst step toward con-sideration of lateral, in addition to axial, non-uniformities,like those associated with uneven fuel spreading across thecombustor, that call for a multi-dimensional description ofthe combustor.

Appendix A. Fixed carbon combustion kinetics

The issue of the CO2=CO ratio as primary products of charcombustion has been the subject of several papers, mostlyaddressing coals or low-volatile fuels. Little is known aboutthe CO2=CO ratio for high-volatile fuel char oxidation. Inthe present paper, focused on the combustion of biomass,and consistently with results of experiments using lignocel-

lulosic materials (Masi et al., 1997), CO2 has been assumedas the sole primary product of carbon combustion, formedeither directly at the particle surface, or by oxidation of pri-mary CO in the particle boundary layer.The overall combustion rate constant of the I th char phase

(either C=coarse or F=3ne) in the K th combustor sectionis evaluated considering the contributions of both bound-ary layer and intraparticle oxygen di<usion and of intrinsiccombustion kinetics with the general relationship:

kIP; K =6KgI; K12dI�I

fc(CK

O2− C I; K

O2 ; S) =�I; KkvI; K12

�Ifc

(C I; KO2 ; S)

n;

(A.1)

where CKO2

is the bulk oxygen concentration, C I; KO2 ; S is oxygen

concentration at the char particle external surface, KgI; K isthe mass transfer coe>cient between the bulk of the gasand the particle, �I; K is the e<ectiveness factor, kvI; K isthe constant of the intrinsic combustion rate referred to theapparent volume of the particle, all relative to the I th charphase in theK th combustor section. n is the apparent reactionorder.The kinetic constant of the intrinsic combustion rate re-

ferred to the apparent volume of the particle is

kvI; K = k0�Ifc(RTI; K)

n

12exp(− EaRTI; K

); (A.2)

where k0 is the pre-exponential factor, Ea is the activationenergy and TI; K is the particle temperature (assumed to beuniform within the particle) of the I th char phase in the K thcombustor section.The e<ectiveness factor is given by

�I; K =3

>I; K

(1

tanh(>I; K)− 1

>I; K

)(A.3)

as a function of the particle Thiele modulus >I; K of the I thchar phase in the K th combustor section:

>I; K =dI

2

√√√√ (n+ 1)kvI; K (CI; KO2 ; S)

n−1

2DI; KO2 ; e<

: (A.4)

DI; KO2 ; e<

is the oxygen e<ective intraparticle di<usivity of theI th char phase in the K th combustor section:

DI; KO2 ; e<

=

(1

DI; KO2

+1

DI; KO2 ; Kn

)−1

# 2; (A.5)

where # is the particle average porosity and DI; KO2 ; Kn is the

oxygen Knudsen di<usivity, function of the average porediameter dpore.The boundary layer mass transfer coe>cient can be writ-

ten as

KgI; K =DI; K

O2ShI; KdI

; (A.6)


where oxygen di<usivity is evaluated at the mean temper-ature between the particle and the bulk and ShI; K is theparticle Sherwood number of the I th char phase in the K thcombustor section. The particle Sherwood number of thecoarse char phase in the bed section is evaluated using thecorrelation by Prins, Casteleijn, Draijer, and Van Swaaij(1985) that 3ts satisfactorily experimental data obtained bySalatino et al. (1998).The 3nes Sherwood number in the bed, splashing zone

and freeboard sections is assumed equal to 2, consistentlywith the assumption that the slip velocity of 3ne char isapproximately zero.Coarse char particle temperature at the steady state is as-

sumed to be uniform. This assumption is based on an orderof magnitude evaluation of the Prater number, which re-sulted much lower than 0.1 for both coarse and 3ne particlesin the di<erent combustor sections. The temperature of char3nes in the bed (TF; bed) has been assumed equal to the bedtemperature. This corresponds to assuming that, while per-colating through the bed, char 3nes experience contact timeswith inert bed solids that exceed those required to equalizechar and bed temperatures (Chirone, Russo, Serpi, Salatino,Scala, 2000). In all the other cases the char particle temper-ature of the I th char phase in the K th combustor section iscalculated by solving the steady-state energy balance arounda burning char particle:

kIP; K |VHfc|�IfcdI

6

=hI; K; C(TI; K − TK) + 81e< (T 4I; K − T 4

K): (A.7)

The e<ective emissivity for coarse char particles in the bedis calculated as

1e< =(

11char

+11B

− 1)−1

: (A.8)

For 3nes in the splashing zone and in the freeboard thee<ective emissivity is 1e< = 1char.Evaluation of the convective heat transfer coe>cient be-

tween coarse char particles and the bed is carried out usinga correlation by Prins, Draijer, and Van Swaaij (1986). Asfor the evaluation of Sherwood numbers for 3ne particles inthe splashing zone and in the freeboard, the convective heattransfer coe>cient in these regions is calculated by assum-ing a particle Nusselt number of 2.

Appendix B. Calculation of the oxygen concentration inthe dense phase of the bed

The oxygen concentration in the dense phase of the bedhas been calculated according to the two-phase theory of!uidization and considering gas well mixed in the densephase and in plug !ow in the bubble phase. Fixed carbon isassumed to burn only in the dense phase. Volatiles released

in the bed during uprise of the devolatilizing fuel particlesare assumed to burn uniformly along the bed height in thebubble phase. This assumption is based on the argumentsthat endogenous volatile bubbles generated during fuel de-volatilization are likely to experience extensive coalescencewith exogenous air bubbles and that volatile matter com-bustion in the emulsion phase should be quenched (van derVaart, 1988; Hayhurst, 1991).The oxygen balance on the dense phase reads as

AUmf(C inO2

− CbedO2

) + ? = F0Yfc; (B.1)

where ? is the total oxygen in!ow from the bubble phase.The oxygen balance on the bubble phase reads as

−A(Ubed − Umf)dCbub

O2

dz=

(Ubed − Umf)Ubub

×AKbe(CbedO2

− CbubO2

) +F0Yvolfhbed

; (B.2)

where CbubO2

is oxygen concentration in the bubble phase.Integration of Eq. (B.2) with the initial condition Cbub

O2(0)=

C inO2

gives

CbubO2

(z) =CbedO2

− F0YvolfUbub

Ahbed(Ubed − Umf)Kbe

+[C inO2

− CbedO2

+F0YvolfUbub


]

×exp(− Kbe

Ububz): (B.3)

The total oxygen !ow rate from the bubble to the emulsionphase is given by

? = A(Ubed − Umf)

UbubKbe

∫ hbed

0[Cbed

O2− Cbub

O2(z)] dz: (B.4)

Solution of Eq. (B.4) gives

?= A(Ubed − Umf)[C inO2

− CbedO2

+F0YvolfUbub


]

×[1− exp(−X )]− F0Yvolf; (B.5)

where X =hbedKbe=Ubub is the bubble–emulsion phase masstransfer index. Substituting Eq. (B.5) in Eq. (B.1) and rear-ranging gives

CbedO2

= C inO2

−F0(Yfc + Yvolf)− F0YvolfUbub[1− exp(−X )]=hbedKbe

A{Umf + (Ubed − Umf)[1− exp(−X )]} :

(B.6)


Further rearrangement and introduction of the excess airfactor in the bed 3nally gives

CbedO2

=C inO2

{1− Ubed

ebed[Ubed − (Ubed − Umf) exp(−X )]

}

+F0Yvolf[1− exp(−X )]

AX [Ubed − (Ubed − Umf) exp(−X )]: (B.7)

On the RHS of Eq. (B.7) there are two terms: the 3rst oneis equal to the oxygen concentration that would establish inthe dense phase if the released volatiles burned only in thisphase. The second term accounts for the increase of the oxy-gen concentration in the dense phase due to the assumptionthat volatiles burn only in the bubble phase. It is interestingto note that for large oxygen exchange rates between thetwo phases, i.e. for large values of X , the second term van-ishes and the oxygen concentration in the dense phase doesnot depend on the location of volatiles combustion in thebed.

Appendix C. Calculation of the global view factors for thesplashing zone energy balance

Radiative !uxes are calculated by treating the bed and thefreeboard as two parallel in3nite gray planes separated bya zone containing the absorbing=emitting gas and the grayejected bed particles.The geometrical view factors of the system are evaluated

as follows. The geometrical mean beam length in the splash-ing zone (i.e. the reciprocal of the extinction coe>cient dueto the presence of ejected particles) is given by

Tlsp =4

nS; sp3d2S; (C.1)

where the number of bed particles per unit volume of splash-ing zone is

nS; sp =6"S; sp3d3

S: (C.2)

On the other hand the mean beam length between two in3niteplanes separated by a distance hsp is

TLsp = 1:76hsp: (C.3)

The geometrical view factor between the bed and the free-board results

7GBF = 7G

FB = exp

(−

TLspTlsp

); (C.4)

where the symmetry of the system has been considered.As no part of a plane can see another part of the sameplane:

7GBB = 7G

FF = 0: (C.5)

The sum of the geometrical view factors relative to a surfacemust equal one, so we can write

7GFP = 7G

BP = (1− 7GFB) = (1− 7G

BF): (C.6)

From the property that the IJ th geometrical view factor mul-tiplied by the I th exposed surface area must be equal to theJI th geometrical view factor multiplied by the J th exposedsurface area we obtain

7GPF = 7G

PB =7G

FP

6=

7GBP

6: (C.7)

Finally, the particle–particle geometrical view factor is ob-tained as

7GPP = (1− 7G

PF − 7GPB) = (1− 27G

PF) = (1− 27GPB):

(C.8)

Once all the geometrical view factors and all the surfaceand gas emissivities are calculated, the zone method (Hottel& Saro3m, 1967) can be used to evaluate the global viewfactors needed in the energy balance on the splashing zone.The global view factors, all referred to the cross-sectionalarea of the bed, relative to the three surfaces (bed, freeboardand inert bed particles) are given by

7BF = 7FB =1B1F

(1− 1B)(1− 1F)

(−D′

BF

D

); (C.9)

7BP = 7PB =61B1P

(1− 1B)(1− 1P)

(−D′

BP

D

); (C.10)

7FP = 7PF =61F1P

(1− 1F)(1− 1P)

(−D′

FP

D

); (C.11)

7BB =1B

(1− 1B)

[1B

(1− 1B)

(−D′

BB

D

)− 1B

]; (C.12)

7FF =1F

(1− 1F)

[1F

(1− 1F)

(−D′

FF

D

)− 1F

]; (C.13)

7PP =61P

(1− 1P)

[61P

(1− 1P)

(−D′

PP

D

)− 1P

]; (C.14)

where

D =

∣∣∣∣∣∣∣∣∣∣∣

7GBB(1− 1S)− 1

(1− 1B)7G

BF(1− 1S) 7GBP(1− 1S)

7GBF(1− 1S) 7G

FF(1− 1S)− 1(1− 1F)

7GFP(1− 1S)

7GBP(1− 1S) 7G

FP(1− 1S) 6[7G

PP(1− 1S)− 1(1− 1P)

]

∣∣∣∣∣∣∣∣∣∣∣(C:15)


and D′ij are the cofactors of D, given by

D′BF =−

∣∣∣∣∣∣∣7G

BF(1− 1S) 7GFP(1− 1S)

7GBP(1− 1S) 6

[7G

PP(1− 1S)− 1(1− 1P)

]∣∣∣∣∣∣∣ ;

(C.16)

D′BP =

∣∣∣∣∣∣7G

BF(1− 1S) 7GFF(1− 1S)− 1

(1− 1F)7G

BP(1− 1S) 7GFP(1− 1S)

∣∣∣∣∣∣ ;(C.17)

D′FP =−

∣∣∣∣∣∣7G

BB(1− 1S)− 1(1− 1B)

7GBF(1− 1S)

7GBP(1− 1S) 7G

FP(1− 1S)

∣∣∣∣∣∣ ;(C.18)

D′BB

=

∣∣∣∣∣∣∣∣7G

FF(1−1S)− 1(1−1F)

7GFP(1−1S)

7GFP(1−1S) 6

[7G

PP(1−1S)− 1(1−1P)

]∣∣∣∣∣∣∣∣;

(C.19)

D′FF

=

∣∣∣∣∣∣∣∣7G

BB(1−1S)− 1(1−1B)

7GBP(1−1S)

7GBP(1−1S) 6

[7G

PP(1−1S)− 1(1−1P)

]∣∣∣∣∣∣∣∣

(C.20)

D′PP

=

∣∣∣∣∣∣∣7G

BB(1− 1S)− 1(1− 1B)

7GBF(1− 1S)

7GBF(1− 1S) 7G

FF(1− 1S)− 1(1− 1F)

∣∣∣∣∣∣∣ :(C.21)

The global view factors, referred to the cross-sectional areaof the bed, relative to heat !uxes between the three sur-faces and the gas in the splashing zone can be calculatedas

7BS = 1B − 7BB − 7BF − 7BP; (C.22)

7FS = 1F − 7FB − 7FF − 7FP; (C.23)

7PS = 61P − 7PB − 7PF − 7PP: (C.24)

Notation

A cross-sectional area of the bed, m2

cJ speci3c heat of the J th phase, kJ=kgK

CKJ concentration of the J th gaseous species (O2,

volatile matter) in the K th section of the reactor,kmol=m3

C I; KO2 ; S oxygen concentration in the K th section of the

reactor at the I th phase char particle externalsurface, kmol=m3

d0 initial average size of fuel feed particles, mdbed bed diameter, mdI average size of particles belonging to the I th

phase, mdpore average pore diameter, mDbub; s bubble size at the bed surface, mD matrix in Eq. (C.14), dimensionless numbersD′

ij cofactors of matrix D, dimensionless numbersDI; K

O2oxygen molecular di<usivity of the I th charphase in the K th combustor section, m2=s

DI; KO2 ; e<

oxygen e<ective di<usivity of the I th char phasein the K th combustor section, m2=s

DI; KO2 ; Kn oxygen Knudsen di<usivity of the I th char phase

in the K th combustor section, m2=se excess air factor, dimensionless numberseK excess air factor referred to the K th section of

the reactor, dimensionless numbersEa activation energy, kJ=kmolEc; K unburned 3xed carbon escaping the K th section

of the reactor, kg=sf fractional volatile matter burning in the bed, di-

mensionless numbersF0 fuel feed mass !ow rate, kg=sF0J mass !ow rate of 3xed carbon to coarse (J =C)

or 3ne (J = F) phase, kg=sFIJ; K 3xed carbon mass !ow rate from the I th phase

to the J th phase in the K th section of the reactor,kg=s

FJ; K mass !ow rate of gas (J=G) or volatiles (J=V )in the K th section of the reactor, kg=s

FS mass !ux of ejected inert bed particles at the bedsurface, kg=sm2

g fractional volatile matter burning in the splash-ing region (premixed), dimensionless numbers

h fractional volatile matter burning in the splash-ing region (non-premixed), dimensionless num-bers

hK height of the K th section of the reactor, mhtot total reactor height, mhI; K; C particle heat transfer coe>cient of the I th char

phase in the K th combustor section, kW=Km2

hS; C heat transfer coe>cient of ejected bed particlesin the splashing region, kW=Km2

HK heat generation rate in the K th combustor sec-tion, kW

VHfc heat of combustion of 3xed carbon, kJ=kgVHvol heat of combustion of volatile matter, kJ=kgk0 pre-exponential factor, s−1 kPa−n

kab char particle attrition constant, dimensionlessnumbers


kCF; bed 3nes generation constant by abrasion and=or per-colative fragmentation in the bed, s−1

kd devolatilization constant, s=m2

kel 3nes elutriation constant, s−1

kIP; K overall combustion kinetic constant of I th phasein K th section of the reactor, s−1

kJ thermal conductivity of the J th phase, kW=KmkvI; K constant of the intrinsic combustion rate referred

to the apparent volume of the particle relative tothe I th char phase in the K th combustor section,s−1 (kmol=m3)1−n

Kbe bubble-emulsion phase mass transfer coe>cient,s−1

KgI; K mass transfer coe>cient of the I th char phase inthe K th section of the reactor, m=s

Tlsp geometrical mean beam length in the splashingzone, m

TLsp mean beam length, mm parameter in Eq. (10), dimensionless numbersn apparent reaction order, dimensionless numbersn1 particle multiplication factor due to primary

fragmentation, dimensionless numbersn2 particle multiplication factor due to secondary

fragmentation, dimensionless numbersnS; sp number of bed particles per unit volume of

splashing zone, m−3

qSJ; H convective (H = C) or radiative (H = R) heat!ux from splashing region to J th section of thereactor, kW=m2

qPPJ; H convective (H = C) or radiative (H = R) heat!ux from an ejected bed particle to J th sectionof the reactor, kW=m2

Qent total gas entrainment rate in the splashing re-gion, m3=s

Qent1bub gas entrainment rate at a single “ghost bubble”,

m3=sR universal gas constant, kJ/kmol KShI; K particle Sherwood number of the I th char phase

in the K th combustor section, dimensionlessnumbers

TK temperature of the K th section of the reactor, KTI; K particle temperature of the I th char phase in the

K th combustor section, KTTP mean ejected particles temperature in the splash-

ing region, KUmf bed solids minimum !uidization velocity, m=sUK super3cial gas velocity in the K th section of the

reactor, m=sUbub average bubble rise velocity in the bed, m=sUbub; s bubble velocity at the bed surface, m=svr particle rise velocity in the bed during de-

volatilization, m=sv∞r particle rise velocity during devolatilization in

the bed at incipient !uidization, m=svS;0 initial ejection velocity of bed particles at the

surface of the bed, m=s

Vash volume fraction of ash in the char particle, di-mensionless numbers

WI; K loading of the I th char phase in the K th section,kg

xcoarse fraction of 3xed carbon as coarse char after de-volatilization, dimensionless numbers

xJ mass fraction of 3xed carbon (J = fc), of ash(J = ash), of volatile matter (J = vol), in theraw fuel, dimensionless numbers

X bubble-emulsion phase mass transfer index, di-mensionless numbers

Yfc stoichiometric oxygen demand for completecombustion of 3xed carbon, kmol=kg

Yvol stoichiometric oxygen demand for completecombustion of volatile matter, kmol=kg

z height above the distributor, m

Greek letters

" parameter in Eq. (3), dimensionless numbers"S; sp volumetric fraction of ejected bed solids in the

splashing zone, dimensionless numbers5 parameter in Eq. (15), m−1

. parameter in Eq. (11), dimensionless numbers0 parameter in Eq. (12), dimensionless numbers1e< e<ective emissivity, dimensionless numbers1J emissivity of the J th phase or section of the

reactor, dimensionless numbers1mf bed voidage at incipient !uidization, dimension-

less numbers� global 3xed carbon combustion e>ciency of the

reactor, dimensionless numbers�K total combustion e>ciency in the K th section of

the reactor, dimensionless numbers�I; K e<ectiveness factor relative to the I th char phase

in the K th combustor section, dimensionlessnumbers

# particle average porosity, dimensionless num-bers

#0 char initial porosity, dimensionless numbers#cr char porosity at the percolation threshold, di-

mensionless numbers*F; K 3nes postcombustion degree in the K th section

of the reactor, dimensionless numbers�J density of the J th phase, kg=m3

�Ifc density of coarse (I = coarse) or 3ne (I = 3ne)

char particles referred to 3xed carbon, kg=m3

8 Stefan–Boltzmann constant, kW=m2 K4

'd fuel devolatilization time, s'i particle induction time during devolatilization, s'r time for particle rise (segregation) to the bed

surface during devolatilization, s'S; sp average residence time of the ejected bed parti-

cles in the splashing region, s'gb residence time of “ghost bubbles” in the splash-

ing region, s


>I; K particle Thiele modulus of the I th char phase inthe K th combustor section, dimensionless num-bers

7IJ global view factor relative to the I th and J thsections of the combustor, referred to the crosssection of the bed, dimensionless numbers

7GIJ geometrical view factor relative to the I th and

J th sections of the combustor, dimensionlessnumbers

6 ratio between the total exposed surface area ofthe ejected particles in the splashing zone andthe cross section of the bed, dimensionless num-bers

? total oxygen !ow rate exchanged between denseand bubble phase in the bed, kmol=s

Subscripts or superscripts

bed !uidized bedbub bubbleB !uidized bedC coarse particles, convectiveE elutriated carbon 3nesF 3ne particles, freeboardfc 3xed carbonfb freeboardG gas, geometricalin inletP combustion products, inert ejected particlesR radiativeS inert bed particles, splashing regionsp splashing regionvol volatile matterV volatile matter

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Modelling fluidized bed combustion of high-volatile solid fuels

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