Chemical Engineering and Processing 43 (2004) 971–978

Modelling of axial and radial solid segregation in a CFB boiler

Yulong Huaa,b, Gilles Flamanta,∗, Jidong Lub, Daniel Gauthiera

a Institut de Science et de Génie des Matériaux et Procédés, CNRS-IMP, 66125 Odeillo-Font-Romeu Cédex, Franceb National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China

Received 5 February 2003; received in revised form 25 September 2003; accepted 26 September 2003

Available online 19 November 2003

Abstract

Since solid exhibits a wide particle size distribution (PSD) in a circulating fluidized bed (CFB) boiler, it is difficult to predict the hydrodynamicbehavior. Therefore, a model based on the semi-empirical approach is developed to approximate the local particle size distribution in CFB. Thecore/annulus flow structure is applied to this model and the particles in the bed are discretized into several size groups. The model accountsfor the disintegration and shrinking of coal particles during the combustion process of each group of particles. It shows that coarser particlesare gathered near the walls and the average particle diameter decreases along the boiler height, and this trend is more significant in the splashregion. Moreover, coal combustion behavior affects both axial and radial segregations in a CFB boiler. All these phenomena are discussedagainst experimental data reported in literature.© 2003 Elsevier B.V. All rights reserved.

Keywords: Circulating fluidized bed; Particle size distribution; Segregation; Fragmentation; Attrition; Coal combustion

1. Introduction

A wide particle size distribution (PSD) is practical andeconomically worth in fluid bed processes, including coalcombustion in circulating fluidized bed (CFB) boiler[1,2].Since the PSD is known to have a strong influence on the hy-drodynamics, the heat transfer coefficient and the chemicalreaction extent[1–4], its variations should not be neglectedin the simulation of CFB boilers.

Solid segregation always occurs when solids exhibiting awide PSD are fluidized in a CFB. Small and light particlesthat are fluidized at low velocity tend to be elutriated bythe fluidization gas, whereas others tend to sink and remainat lower levels, which is known as the axial solid segrega-tion. The hydrodynamic behavior of systems with wide PSDcannot be described by the mathematical analysis of parti-cle size[5]. Therefore, some investigations were carried outon different CFB pilots. Johnsson et al.[6] experimented aCFB boiler furnace with representative amount of coal ofmaximum size 10 mm, and they found that coarser particlesdecrease in upward flux with height. Na et al.[7] mixed finesand with large particles in the same test unit and found that

∗ Corresponding author. Tel.:+33-4-68-30-7758;fax: +33-4-68-30-2940.

E-mail address: flamant@imp.cnrs.fr (G. Flamant).

most added coarse particles fluidize in the lower part of thecombustion chamber. Others researchers[8–12]also carriedout experiments on risers with different particle sizes and/ordifferent solid densities. Segregation patterns were charac-terized by the solid fraction of the heavier component, andparticle size decreased with riser height. The single-particleterminal velocity is the decisive parameter affecting the ax-ial solid segregation in CFB risers[8]. However, most stud-ies paid attention only to bottom or near bottom part insteadof all the riser height, and few works were focused on thecoal combustion process in CFB boiler.

So far, radial solid segregation was of little concern only[6–8,12–15]. Karri and Knowlton[13] carried out exper-iments on a 20 cm-diameter, 14 m-high CFB unit. Theyfound the PSD in the core is smaller than in the annuluswith the condition that annulus exists and flows downward.Since the downward flux in the annulus is the major featureof macroscopic flow structure in ordinary circulating flu-idized beds[16], the radial solid segregation should not beneglected. Johnsson et al.[6] found that big particles havemore opportunity to be back-mixed than small ones, andbig particles tend to accumulate near the walls. Mathiesenet al. [15], using Laser Doppler Anemometry and PhaseDoppler Anemometry techniques for the measurement,found a significant radial segregation in the riser. They de-veloped a multi-fluid Computational Fluid Dynamics model

0255-2701/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.cep.2003.09.005

972 Y. Hua et al. / Chemical Engineering and Processing 43 (2004) 971–978

to verify the experimental results, but it failed to predict thesignificant radial variation of solid size because the radialsolid segregation may result from external forces beyondthe considerations of this model.

A practical model based on a semi-empirical approach isdeveloped in the present work. The particle size variationis also considered in addition to the solid segregation phe-nomena since the in-bed carbonaceous particles are knownto shrink by both attrition and chemical reaction in a CFBcoal combustor[17]. A particle population balance modelis developed, which takes into account major physical andchemical processes occurring to carbonaceous particles ina boiler. Axial and radial solid segregation phenomena arepredicted from the analysis of the different solid segregationmechanisms in both directions.

2. Theory

The model considered in this work divides the verticalflow domain into three regions: a dense bed at the bottom,a vigorously mixed splash zone and a transport zone in theupper part[6,18]. The bottom bed zone is considered asuniform; the transport zone is based on the core-annulusstructure named 1.5D model. Solid travels upward in thecore zone and downward in the annulus. The thickness ofthe annulus and the solid fraction vary with the height. Thesolid concentration in the splash zone and in the transportzone is calculated from an exponential decay function. Inour model, particle size is widened due to the following:initial PSD of coal, fragmentation, attrition and shrinkageduring coal combustion.

The present model is based on the following assumptions:

1. The whole system is at steady state.2. The first and second fragmentations of coal particles oc-

cur in the bottom zone.3. Devolatilization at the bottom and mixing of volatiles

with feed air are instantaneous.4. The bed temperature is uniform.5. The secondary gas injection is neglected.

2.1. Solid mixing

For CFB boilers, the axial voidage profile is predicted bythe following expression[18], which incorporates the splashzone into the previous dilute region model:

ε(h) = [εd − ε∞ exp(−a(H − Hd))] exp(−asplash(h − Hd))

+ ε∞ exp(a(H − h)) (1)

whereε(h) is the voidage along the bed height;asplashandaare the decay exponents for the splash zone and the transportzone, respectively. They are function of the particle diameter.The particular values will be discussed later.εd andε∞ arethe particle volume fractions in the bottom zone and in the

upper zone.h is the height variable above the air distribution.H the total height of the boiler furnace,Hd the height of thebottom zone.

The annulus thickness can be defined as the distance fromthe wall where the net vertical solid flux is zero[19].

δ

Dt= 0.5

[1 − 0.4014ε(h)−0.0247

× Ret0.0585

(H − h

H

)−0.0663]

(2)

whereδ is the boundary layer thickness at heighth, Dt theequivalent hydraulic diameter of the CFB;Ret is Reynoldsnumber defined asugρgDt/µg. This correlation was obtainedby processing experimental data from both CFB boilers andcold models.

The mass transfer coefficient between the core and the an-nulus regions is a key factor for this semi-empirical model[4,20–22]. Nevertheless, the question remains whether lat-eral particle mixing is mainly due to gas-induced turbu-lent dispersion or to particle–particle collisions[20]. Currentmodels describe lateral particle exchange from the core tothe annulus as[4]:

dG

dh= −2ρsk[(1 − εc) − (1 − ε∞)]

rc(3)

k = 0.14

u0 − ut

where G is the solid flux in the core region;k the soliddispersion constant from core to annulus.

2.2. Fragmentation

The fragmentation is classified into the primary frag-mentation and the secondary fragmentation[23–25]. Theprimary fragmentation of a fuel particle occurs just after itsinjection into the hot bed, due to losses of material (moistureand volatiles) and internal stresses caused by heating, drying,and devolatilization. The secondary fragmentation occurs ascoal burning proceeds. It results from the weakening by com-bustion and breaking up by collisions of bridges that connectdifferent regions of a coal particle. So it takes place during allthe combustion process. The knowledge of the fragmentationof coal particles in fluidized beds is required for establishingthe comprehensive mathematical model of combustion andunderstanding the practical coal combustion process. It wasshown that coarser particles are much more sensitive to frag-mentation than fine particles[23]; therefore, the fragmenta-tion in the upper bed is neglected in the model because theparticles in the upper part of the bed are much smaller thanthose in the bottom zone. Finally, the following expression isadopted as the fragmentation model in the bottom bed[24]:

P(dp,new) = k0.33f P(dp,old) with dp,new = dp,oldk

0.33f

(4)

Y. Hua et al. / Chemical Engineering and Processing 43 (2004) 971–978 973

whereP(d) is the PSD function;dp,new and dp,old are theparticle diameters after fragmentation and before fragmen-tation, respectively,kf the fragmentation coefficient.

2.3. Attrition

In fluidized beds, particle attrition takes place by surfaceabrasion, i.e. particles of a much smaller size are createdfrom the original particles. The created particles are finewith a mean diameter below 0.05–0.1 mm. Previous studies[23,25–27] showed that the presence of smaller particlesincrease the attrition of bigger ones but not the contrary.Thus, the following expression is applied for calculating theattrition coefficient[25]:

kattr,i = kattr(u − umf)mwi

i∑j=1

wj (5)

wherekattr is the attrition constant,i the serial number ofthe particle group,umf the solid minimum fluidization ve-locity. It varies with particle diameter. The average particlediameter is used here to calculateumf in order to simplifythe correlation.

2.4. Combustion

The combustion of volatiles is supposed to be instan-taneous after the feed, and the devolatilization is uniformthroughout the bed bottom. Consequently, no combustion ofvolatiles is considered in the upper zone. The shrinking-coremodel is taken to describe the combustion of coal particles[28]. The following assumptions are made for this model:mixed kinetic control by chemical reaction and gas film dif-fusion. The continuation of combustion keeps the densityconstant. Therefore, the size decrease of the coal particle isdescribed by the following expression[4]:

−dri

dt= 12CO2

ρcjc(1/kc + dp/Sh Dg)(6)

The apparent kinetic constant for surface reaction,kc, isdetermined by[4]:

kc = k0T1/2p exp

(−Ea

RTp

)(7)

and Sherwood number is:

Sh = 2ε + 0.69

(Rep

ε

)1/2

Sc1/3 (8)

whereSc = µg/ρgDg.The diffusivity coefficient for oxygenin nitrogen depends on the bed temperature[29]:

Dg = 0.207× 104(

Tp

300

)1.75

(9)

In Eq. (7), Tp is the temperature of the burning coal particles.It is supposed to be 100 K over the bed temperature[30,31].

Fig. 1. Particle flux structure in the CFB boiler.

In Eq. (6), CO2 is the oxygen concentration in the bed, itvaries with the axial and radial directions, according to Zhaoet al. [32].

2.5. Numerical solution

The transport zone is divided into 100 serial cells verti-cally (Fig. 1). The equivalent hydraulic diameter is adoptedfor the 1.5D model, so the rectangular cross section of CFBboiler is simplified as a circular one. It is divided as a corepart in the center and an annulus part in the periphery. Thecore part is assumed to be uniform and the annulus is partedas 10 cells in the radial direction for investigation on the ra-dial solid segregation. The oxygen concentration, the solidvolume fraction and the particle attrition coefficient changein radial direction in the annulus. Particles are discretizedinto 12 groups totally. The maximum feed coal diameter is10 mm. The particle size distribution depends on fragmenta-tion and combustion in the furnace. It is chosen in this paperas shown inFig. 2. The Sauter mean diameter is adopted asaverage particle size. It is applied to calculate the solid vol-ume fraction in the bottom bed, the minimum fluidizationvelocity and the annulus thickness. The solid volume frac-tion in the rest of the riser is computed as the summation ofall groups.

0 2 4 6 8 10 120

5

10

15

20

5

6

7

8

9

10

11

12

Mas

s fr

actio

n [%

]

Particle size [mm]

0.0 0.2 0.40

5

10

15

4

3

2

1

Fig. 2. Initial particle size distribution of coal for simulation.

974 Y. Hua et al. / Chemical Engineering and Processing 43 (2004) 971–978

Table 1Decay constants asplash and a for each group of particles

Group 1 2 3 4 5 6 7 8 9 10 11 12

asplash 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 4.0 5.0a 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.18 0.2 0.3 0.5 0.8

Table 2Attrition coefficient of particles in different oxygen concentrations

Oxygen concentration (%) kattr

0 0.15 0.2

10 0.320 0.5

2.6. Model parameters

In Eq. (1), asplash and a are the decay exponents for thesplash zone and the transport zone, respectively. They arethe key parameters to simulate the axial solid segregation.They are valued as 2.6 and 0.125 in reference [6]. In fact,the decay factor depends significantly on the particle diam-eter and on the fluidization condition [33,34]. So a differentvalue is given to each group of particles. In the transportzone, the solid volume fraction is very low. The interactionbetween particles is then negligible [35], and the decayfactor is valued according to the terminal velocity of eachgroup of particles. In the splash zone, the solid volumefraction is greater and the interaction between the particlesis intense. So the fluidization conditions strongly affectthe coefficient. The resulting choice of values is given inTable 1.

Since the attrition of burning particles is increased fivefoldin comparison to inlet particles [23], the attrition constantkatt in oxygen-rich areas is much greater than that in theoxygen-poor ones. The particular values are given in Table 2.

Other considered parameters and computation conditionsare given in Table 3, including data from Johnsson et al. [6]that were introduced to validate the simulation.

Table 3Considered parameters and computation conditions

Properties Value

Cross-section of boiler, L × W (m2) [6] 1.7 × 1.4Boiler height, H (m) [6] 13.5Bottom bed height, Hd (m) [6] 0.45Bed temperature Tb (K) [6] 1123Excess-air ratio [6] 1.2Superficial gas velocity, Ug (m/s) [6] 3.2Fuel (Australian coal) density, ρs (kg/m3) 2250Coal density, ρc (kg/m3) 1130Carbon fraction in coal particles, jc (kg/kg) 0.6Apparent activation energy, Ea (kJ/mol) 1.113 × 105

Gas constant, R (kJ/mol K) 8.314Fragmentation coefficient, kf 3

0.1 1 100

20

40

60

80

100

Feed Fragmentation

Cum

ulat

ive

wei

ght f

ract

ion

[%]

Particle size [mm]

Fig. 3. Particle size distribution initially (feed) and after fragmentation.

3. Results and discussion

Let consider first the results concerning the basic hydro-dynamic information and initial conditions. Fig. 3 plots thecumulative weight fraction of both initial feed coal and afterfragmentation. Because of the fragmentation, the particleswith maximum diameter almost vanish, and the proportionof particles greater than 5 mm decreases a lot. Less frag-mentation happens for particles smaller than 2 mm. Fig. 4shows the simulated annulus thickness which decreases from0.12 m near the bottom to 0.05 m at height equal to 10 m.The only one experimental result that exists agrees very wellwith the theoretical result. The solid volume fraction profileunder fluidization by primary air only at 3.2 m/s is shownin Fig. 5. There is always more solid in the annulus than inthe core, and the solid volume fraction in the annulus is two

2 4 6 8 10 12 140.0

0.1

0.2

0.3

Simulation results Experimental data [6]

Ann

ulus

thic

knes

s [m

]

Height [m]

Fig. 4. Annulus thickness along the boiler furnace.

Y. Hua et al. / Chemical Engineering and Processing 43 (2004) 971–978 975

0 2 4 6 8 10 12 14

0.01

0.1

Core average Annulus average

Solid

vol

ume

frac

tion

[-]

Height [m]

Fig. 5. Particle fraction profile in CFB boiler; primary air only, u =3.2 m/s; dense bed: 0.45 m, splash bed: 1.60 m.

to three times than that in the core. It exactly agrees the ex-perimental results about 2.3 of Wirth and Seiter [36]. In theupper dilute zone, solid volume fraction is very low as 0.4%.It is near the value 0.3% from Werdermann and Werther[37].

Fig. 6 points out a significant segregation of solid accord-ing to the mean size in both vertical and horizontal directionsand shows a very good agreement between simulation re-sults and measurements. The axial segregation is explainedby the fact that smaller particles fluidize more easily andare more entrained by the gas than larger ones. Entrainmentis accomplished through two different parallel mechanisms:the prompt entrainment of very fine particles, and the en-trainment through bubble wake ejection [17]. By the secondmechanism, coarser particles can be carried up to the up-per bed although their terminal velocities are higher thanthe gas velocity. Therefore they still exist in some extent inthe splash zone. In the transport zone, there is less chancefor bubbling, and interactions between particles are weaker.Consequently, coarser particles do not follow the gas effec-tively. On the contrary, they loose momentum, start accumu-lating and then fall down near the wall, in the annulus regionwhere the gas velocity is very low. As a result, the axialsolid segregation is significant in this area and it is related

0 2 4 6 8 10 12 140.0

0.1

0.2

0.3

Core (theoretical) Annulus (theoretical) Core (experimental) [6] Annulus (experimental) [6]A

vera

ge p

arti

cle

size

[m

m]

height [m]

Fig. 6. Vertical distribution of average particle size.

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

annulus

core

(1)

(2)

(3)

h=3.8m

Cum

ulat

ive

wei

ght f

ract

ion

[-]

Particle size [mm]

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

annuluscore

h=5.5m

Cum

ulat

ive

wei

ght f

ract

ion

[-]

Particle size [mm]

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.2

0.4

0.6

0.8

1.0

annulus

core

h=7.9m

Cum

ulat

ive

wei

ght f

ract

ion

[-]

Particle size [mm]

Core: theoretical and experimental [6]Annulus: theoretical and experimental [6]

Fig. 7. (1)–(3) Cumulative particle size distribution at different heights,core: (—) theoretical; and (�) experimental [6]. Annulus: (- - -) theoret-ical; and (�) experimental [6].

to the radial segregation. Axial segregation in CFB boileris also due to another phenomenon that will be discussedlater.

Fig. 7 shows the cumulative char particle size distribu-tion at three different heights in the dilute zone in both thecore and annulus. The particle size clearly decreases withheight, in both parts of the transport zone of the CFB. Thesimulation results fit well the experimental data from Johns-son et al. [6] in the core, and in the upper part of the an-nulus. But there exists some discrepancy in the annulus at

976 Y. Hua et al. / Chemical Engineering and Processing 43 (2004) 971–978

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.20

0.25

0.30 h=2.1m h=5.0m h=8.0m

Part

icle

ave

rage

siz

e [m

m]

Radial position [m]

Fig. 8. Average size of particles along radial direction, depending on theheight in the boiler.

1 3 5 7 90.000

0.005

0.010

0.015

0.020

0.025

(1)

(2)

(3)

h=2.1m

Part

icle

siz

e de

crea

se [m

m]

Part

icle

siz

e de

crea

se [m

m]

Part

icle

siz

e de

crea

se [m

m]

Particle group

Particle group

Particle group

1st cell 5th cell 9th cell

1 3 5 7 90.000

0.005

0.010

0.015

0.020

0.025

h=5.0m 1st cell 5th cell 9th cell

1 3 5 7 90.000

0.005

0.010

0.015

0.020

0.025

h=8.0m 1st cell 5th cell 9th cell

Fig. 9. (1)–(3) Particle size decrease with height in the annulus, from thecore (first cell) to the wall (ninth cell).

h = 3.8 m for coarser particles, which may be due to com-plicated turbulence hydrodynamics in the region. In the an-nulus, one part of the solid flux comes from the upper celland the other part comes from the core by mass transfer.Eq. (3) shows that the particle diameter affects significantlythe mass transfer from the core to the annulus. Coarse parti-cles transfer much more from the core to the annulus than thefine ones. Thus, the mean diameter in the annulus is largerthan in the core region whatever the height. Fig. 8 shows thestrong decrease of the particle mean diameter with height inthe annulus, and it points out the particle non-uniformity inthe region. One reason is the non-uniform turbulence in theCFB local position. Another reason is that the oxygen con-centration is reduced in both axial and radial directions. Asa result, more particles are burned out at the bottom and atthe center. Fig. 9 shows the diameter decrease of all groupsof char particles in different positions in the annulus, fromthe wall (first cell) to the inner border (ninth cell). Whenoxygen concentration is higher, the char combustion occursmore deeply, the mean diameter reduces and more particleattrition happens with great combustion rate, thus inducingmore axial and radial solid segregation. In the upper bed,char disintegrated is the main cause of axial segregation.

So, Eq. (1) simulates mostly the axial solid segregation,whereas from Eq. (3), it can be concluded that the masstransfer from the core to the annulus is the main reason forradial segregation. Attrition and combustion, Eqs. (5) and (6)respectively, also affect the axial and radial solid segregationin some extent.

4. Conclusions

1. The model shows that both axial and radial solid segre-gations are significant in CFB boiler with wide particlesize distribution. The mean diameter of coal decreasessignificantly with the height in the bed, and it is larger inthe annulus than in the core region.

2. The axial solid segregation is more significant in thesplash zone than in the upper bed. The hydrodynamic be-havior of coarser particles plays an important role on theaxial segregation in this part. The segregation decreasesalong the height but it still exits because the char disin-tegration also affects the axial segregation.

3. Solid segregation exists everywhere radially, but it ismore significant between the core and the annulus region.The radial solid segregation is characteristic of CFB withcore-annulus solid structure. However, radial solid seg-regation is also due to the non-uniform char combustionand attrition.

Acknowledgements

The authors are grateful to the French Minister of For-eign Affairs (Ministère des Affaires Etrangères) for the grant

Y. Hua et al. / Chemical Engineering and Processing 43 (2004) 971–978 977

allocated to Y. Hua permitting a Sino-French co-advisedthesis, and AFCRST (Association Franco-Chinoise pour laRecherche Scientifique et Technique) and Key Program forInternational Cooperation of Science and Technology ofChina (2001CB711203) for financial assistance.

Appendix A

Physical properties of air [38]:

µg = 0.42 × 10−6Tb2/3

ρg = 351/Tb

Particle volume fraction in bottom zone [34]:

(εd − εmf)/(1 − εmf) = 0.19Re0.77p Ar−0.31

A.1. Nomenclature

a decay constant in the upper zone (m−1)aspleash decay constant in the splash zone (m−1)Ar Archimedes number defined as

d3pρg(ρs − ρg)g/µ2

gCO2 oxygen concentration in the bed (mol m−3)dp particle diameter (mm)dp,new particle diameter after fragmentation (mm)dp,old particle diameter before fragmentation (mm)Dg diffusivity coefficient for oxygen in nitrogen

(m2 s−1)Dt bed diameter defined as L × W /(L + W) (m)Ea apparent activation energy (kJ mol−1)G solid flux in the core region (kg m−2 s−1)h height variable above the air distribution (m)H height of the boiler furnace (m)Hd limit height of the bottom zone (m)jc carbon fraction in coal particles (kg kg−1)k solid dispersion constant from core to annulus

(m s−1)kattr attrition coefficient (−)kc apparent kinetic constant for surface reaction

(m s−1)kf fragmentation coefficient (−)ko pre-exponential factor (m s−1 K−1/2)m solid mass fractionP(d) particle size distribution function (−)rc radius of the core region (m)ri radius of the coal particleR gas constant (kJ mol−1 K−1)Ret Reynolds number defined as ugρgDt/µgRep Reynolds number defined as ugρgDt/µgSc Schmidt number defined as µg/ρgDg

Sh Sherwood number defined as2ε + 0.69(Rep/ε)1/2Sc1/3

Tb bed temperature (K)Tp coal particle temperature (K)

umf solid minimum fluidization velocity (m s−1)ug superficial gas velocity (m s−1)ut particle terminal velocity (m s−1)wi solid mass fraction of each group of particles

Greek lettersδ thickness of the annulus (m)εc mean voidage in the coreεd particle volume fraction in bottom zoneε(h) particle volume fraction at height hε∞ particle volume fraction in the upper dilute zoneµg gas viscosity (kg m−1 s−1)ρc average density of char (kg m−3)ρg average density of gas (kg m−3)ρs average density of solid (kg m−3)

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