An+Extended+DEME28093CFD+Model+for+Char+Combustion+in+a+Bubbling+Fluidized+Bed+Combustor+of+Inert+Sand...

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An extended DEMCFD model for char combustion in a bubbling fluidized bed

combustor of inert sand

Yongming Geng, Defu Che n

State Key Laboratory of Multiphase Flow in Power Engineering, Xian Jiaotong University, Xian 710049, China

a r t i c l e i n f o

Article history:

Received 8 June 2010

Received in revised form30 August 2010

Accepted 6 October 2010Available online 15 October 2010

Keywords:

Multiphase flow

Combustion

Fluidization

Inhibitory effect

Mathematical modeling

DEMCFD

a b s t r a c t

This paper proposes a transient three-phase numerical model forthe simulation of multiphase flow, heat

and mass transfer and combustion in a bubbling fluidized bed of inert sand. The gas phase is treated as a

continuum and solved using the computational fluid dynamics (CFD) approach; the solid particles aretreated as two discrete phases with different reactivity characteristics and solved on the individual

particle scale using an extended discrete element model (DEM). A new char combustion submodel

considering sandinhibitoryeffects is also developed to describe char particle combustion behavior in the

fluidized bed.Two conditions, i.e.a single larger graphite particle anda batchof smaller graphite particles,

areused to test theprediction capability of themodel. Themodel is validatedby comparingthe predicted

results with the previous measured results and conclusions in the literature in terms of bed

hydrodynamics, individual particle temperature, char residence time and concentrationsof the products.

The effects of bed temperature, oxygen concentration and superficial velocity on char combustion

behavior are also examined through model simulation. The results indicate that the proposed model

provides a proximal approach to elucidate multiphase flow and combustion mechanisms in fluidized bed

combustors.

Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Fluidized bed combustors which involve multiphase flow and

combustion are particularly attractive and widely used in many

chemical processes due to their proper mixing, high combustion

efficiency, low combustion temperature and low pollutants emis-

sion. However, the mechanism of multiphase flowand combustion

in fluidized beds is extremelycomplex andhas been, andcontinues

to be, a challenge to the scientist and practicing engineer (Crowe

et al., 1998).

Numerical simulation which can get more information than

experimental research has become a popular methodin the field of

gassolid two-phase flow in recent years. As well known to all,

there are two kinds of mathematical models for studying thehydrodynamics in gassolid fluidized beds. One is the two fluid

model (TFM) in which the solid phase is treated as a continuous

fluid like the gas phase based on the Eulerian method (Anderson

and Jackson,1967; Gidaspow, 1994); the other is EulerianLagrangian

model in which the motion of the particle is calculated at the

particle level by using a trajectory model. Discrete element model

originating from molecular dynamics is one of the trajectory

models (Cundall and Strack, 1979; Tsuji et al., 1992). With the

advances in computing power and numerical algorithms for

nearest neighbor sorting, DEM has become an attractive method

for studying the hydrodynamics of particulate flows and heat and

mass transfer on the particle scale (Tsuji et al., 1993; Xu and Yu,

1997; Zhu et al., 2007, 2008; Zhou et al., 2009).

Although an impressive amount of papers employing the

DEMCFD model (i.e. a DEM for particle motion combined with

a CFD model for gas-phase flow) to simulate gassolid systems

have been presented over the past two decades, the DEM simula-

tion of char combustion in fluidized beds has significantly lagged

behindowingto thecomplex mathematicalmodeland thelack of a

comprehensive understanding of the char combustionmechanism.

There are only very few papers using this method to study char

combustion behavior in fluidized beds so far (Rong and Horio,1999; Zhou et al., 2004). In these limited studies, the char

combustion model is described by using the conventional

pulverized coal combustion models (Field et al., 1967; Smoot,

1993). However, the fluidized bed combustor is a binary particle

system which only contains a small amount of reactive particles.

The char particle combustion behavior in this system is essentially

different fromthe all-particles-activesystem due to the presence of

inert particles. The char particle temperature tends to be over

predicted and is close to the temperature in pulverized coal-fired

furnace by using these conventional models (Zhou et al., 2004;

Ravelli et al., 2008). Therefore, these models cannot be directly

employed to deal with the combustion process of char in fluidized

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ces

Chemical Engineering Science

0009-2509/$- see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2010.10.011

n Corresponding author: Tel.: +86 029 82665185; fax: +86 029 82668703.

E-mail address: [email protected] (D. Che).

Chemical Engineering Science 66 (2011) 207219
http://-/?-http://www.elsevier.com/locate/ceshttp://dx.doi.org/10.1016/j.ces.2010.10.011mailto:[email protected]://dx.doi.org/10.1016/j.ces.2010.10.011http://dx.doi.org/10.1016/j.ces.2010.10.011mailto:[email protected]://dx.doi.org/10.1016/j.ces.2010.10.011http://www.elsevier.com/locate/ceshttp://-/?-


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bed combustors with inert particles. In addition, they also cannot

be employed to accurately predict the information of char burnout

time or particle size, which are very important since they

determine the residence time of the char particle in fluidized beds.

In this paper, a transient three-phase model is developed to study

the complete combustion process of char in a bubbling fluidized bed

with inert sand by meansof an extended DEMCFD model. In orderto

obviate those complex effects (e.g. gas turbulence combustion, gas

radiation, particleparticle radiation, ash content, char fragmentationand attrition), a special fluidized bed with standard conditions is

chosen for investigation, which is available in Hayhurst and Parmar

(1998, 2002). As the combustion proceeds, the char particle diameter

will shrinkand this shrinkingeffect on thewholecombustionprocess

is taken intoaccount through a kinetic/diffusion-limited ratemodel.A

new char combustion submodel considering sand inhibitory effects

(Hayhurst, 1991; Hayhurst and Parmar, 1998; Loeffler and Hofbauer,

2002) is also developed and incorporated into the model to describe

char combustion behavior in the fluidized bed. By comparing the

predicted results with the previous experimental results and

conclusions in the literature, the model is validated.

2. Mathematical model

For the purpose of modeling the transient nature of multiphase

flowand combustion in fluidized beds with inert sand, an extended

DEMCFD model is developed in this section. In the model, the gas

phase is treated as a continuum, while the solid particles are

modeled as two discrete phases, i.e., one represents inert sand

phase and the other char phase. The sand phase is treated as an

unreactive phase whose mass andsize is kept constant allthe time.

Oppositely, the char phase is treated as a reactive phase whose

mass and size will vary with time due to its combustion.

2.1. Gas phase model

The gas phase in fluidized bed combustors is compressible and

obeys thelawsof conservationof mass,momentum andenergy.Thus,

the governing equations for the gas phase are the NavierStokes

equations in terms of the local average variables overa computational

cell with the interphase exchange terms.

The continuity equation for the gas phase is expressed as

@

@tegrg rUegrgug

Xnupi 1

Rig 1

where eg, rg, ug and n0p are the gas phase local porosity, density,velocity and the number of char particles in the cell, respectively;

Rig is the volumetric interphase mass transfer from char particle i

to gas due to char combustion. The gas porosity is given by

eg 1Xnpi 1

aViVc 2

where np, a, Vi and Vc are the number of particles in the cell, thevolume fraction of particle i in the cell, the volume of particle i and

the cell, respectively.

The momentum equation for the gas phase is described by the

following formulation:

@

@tegrgug rUegrgugug egrPgrUegsg

egrggXnpi 1

bgiVc

uiug Xnupi 1

Rigui 3

where Pg, sg, g, bgi and ui are the gas phase pressure, viscous stress

tensor, gravity acceleration, gasparticle interphase drag

coefficient and particle velocity, respectively. The last term on

the right-hand side represents the volumetric momentum transfer

from char particles to gas due to char combustion. The gas phase is

modeled as a Newtonian fluid with a linear stressstrain law:

sg 2

3mgrUugdk mg rug rug

Th i

4

where mg and dk are the shear viscosity of the gas phase andKronecker delta, respectively.

Theinternal energybalance forthe gas phase is written in terms

of the gas temperature:

@

@tegrgCp,gTg rUegrgCp,gugTg rUCp,gGgrTg

Xnpi 1

QugiQugw Qug,reac 5

where Cp,g, Tg and Gg are the gas phase specific heat, temperature

and thermal diffusivity, respectively; Q0g i and Q0gw are the

volumetric heat transfer rate dueto convection from gas to particle

and convection from gas to wall, respectively; Q0g,reac is the

volumetric heat release rate of gas combustion.

The species conservation equation for the gas phase can be

written as

@

@tegrgXgn rUegrgugXgn rUDgnrXgn Rgn 6

where Xgn, Dgn and Rgn are the mass fraction, diffusivity and the

volumetric formation rate of gas species n, respectively.

2.2. Discrete element model

DEM simulation used in this work is based on the soft sphere

model originally proposed by Cundall and Strack (1979) and then

gradually modified by Tsuji et al. (1993) and Xu and Yu (1997), etc.

The governing equations for the translational and rotational

motions of particle i can be written as

miduidt

Xnc

j 1

Fc,ij Fd,ij Fd,gi Fp,gi mig 7

where mi, nc, Fc,ij, Fd,ij, Fd,gi and Fp,g i represent particle mass, the

number of the particles in contact with particle i, inter-particle

elastic contact force and viscous damping force, gasparticle drag

force and pressure force, respectively

Iidxidt

Xnc

j 1

Tt,ij Tr,ij 8

where Ii andxi representmoment of inertia and rotational velocity,

respectively; Tt,ij and Tr,ij represent the torque generated by

tangential forces and the rolling friction torque, respectively.

Details of calculation methods can be found in Zhu et al. (2007).

The energy equation for char particle is based on the heat

balance on the particle scale and can be written as

miCp,idTp,i

dtXnc

j 1

Qij Qiw QigQi,radi Qi,reac 9

where Cp,i and Tp,i arethe specific heat andtemperature of particle i,

respectively; Qij, Qiw, Qig and Qi,radi represent the rate of heat

transfer due to conduction between particle i and particle j,

conduction between particle i and wall, convection between

particle i and gas and radiation between particle i and its

surrounding environment, respectively; Qi,reac is the heat release

rate of char combustion. The energy equation for inert particle is

similar to Eq. (9) but without considering the particle combustion.

Y. Geng, D. Che / Chemical Engineering Science 66 (2011) 207219208


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2.3. Force models

2.3.1. Inter-particle forces

The inter-particle forces including the forces due to direct and

non-direct contacts between particles result from particleparticle

interactions. In this study, the direct contact forces which include

the elastic contact force and viscous damping force are calculated

basedon the spring-dashpot model proposedby Cundall and Strack

(1979). As the particles are relatively larger, the non-direct contactforces, such as the Van der Waals force, electrostatic force and

capillary force, are not considered.

The inter-particle normal and tangential elastic contact forces

implicated in Eqs. (7) and (8) are, respectively, calculated by

Fcn,ij kn,ijdn,ijni and Fct,ij kt,ijdt,ijti 10

where subscripts, n and t, represent normal and tangential

directions, respectively; kij and dij are the spring constant and

displacement between particles i and j, respectively; ni and ti are

the unit vectors along the normal and tangential directions for

particle i, respectively. If the tangential contact force exceeds a

critical value, i.e.

9Fct,

ij94

gij9Fcn,

ij9 11then sliding occurs between particle i and particle j and the

Coulomb friction law is used to calculate the magnitude of the

tangential force with the sign inherited from Eq. (10)

9Fct,ij9 gij9Fcn,ij9 12

where gij represents the coefficient of friction between particles iandj. Thenormal andtangential displacements involved in Eq.(10)

are determined from the motion history of particles. The detailed

solving methods can be found elsewhere (Tsuji et al., 1993; Xu and

Yu, 1997).

The inter-particlenormal and tangentialviscous damping forces

implicated in Eqs. (7) and (8) are, respectively, calculated by

Fdn,ij Zn,ivrUnini and Fdt,ij Zt,ivrUtiti xi rixj rj

13

where Z and vr are the viscous damping coefficient and velocityvector of particle i relative to particle j, respectively; r is a vector

which runs from themass centerof theparticleto thecontact point

with a magnitudeequalto theparticleradius. If sliding occurs, then

only friction damping is considered and viscous damping is

vanished (Xu and Yu, 1997).

2.3.2. Gasparticle forces

The gasparticle drag force Fd is determined on the individual

particle basics depending on the gas voidage and on the relative

velocity between gas and particle. Many correlations have beenwell established (Ergun, 1952; Wen and Yu, 1966; Di Felice, 1994;

Duet al., 2006). In thepresent study,Di Felices correction equation

is adopted to calculatethe gas drag force acting on a singleparticle:

Fd Fdoej

g 14

whereFdo andj arethe gasdrag force on theparticle in theabsenceof other particles and empirical coefficient, respectively

Fdo 0:5Cdoegrgpr29ugup9ugup 15

and

j 3:70:65exp 1:5log10 Rep

2

2" # 16

where Cdo and Rep are the gas drag coefficient for a single

unhindered particle and particle Reynolds number, respectively.

The gas drag coefficient is expressed as

Cdo 0:634:8

Re0:5p

!217

and the particle Reynolds number is defined as

Rep egrgdp9ugup9mg18

where dp is the particle diameter.

The pressure force acting on the particle is defined as

Fp 1

6pd3prPg 19

2.4. Heat transfer models

In the fluidized bed combustor, heat transfer can occur by three

modes: conduction, convection and radiation as described in the

following sections.

2.4.1. Conductive heat transfer

Only the thermal conduction through the area in contact

between two particles is considered in the present study. Such

conductive heat transfer involves two mechanisms: one is the

conduction due to particleparticle static contact with a zero

relative velocity, which is first proposed by Batchelor and

OBrien (1977) and then modified by Cheng et al. (1999); the

other is the conduction due to particleparticle collision with a

nonzero relative velocity, which is first proposedby Sun and Chen

(1988) and then modified by Zhou et al. (2008).

For the first one, the rate of heat transfer through the contact

area between particles i and j can be written as

Qij 4rcTjTi

1=lpi 1=lpj

20

and for the second one, the rate of conductive heat transfer is

determined as

Qij cTjTipr

2ct

1=2c

rpicp,ilpi1=2 rpjcp,jlpj

1=221

where lp, rc and tc are the particle thermal conductivity, particle

particle real contact radius and collision duration, respectively; cis

a correction coefficient and can be found in Zhou et al. (2008); rc is

obtained from the Hertz elastic contact theory. In order to

accurately calculate the conduction heat transfer, the real

Youngs modulus instead of the artificial modification of Youngs

modulus is used to restore the real deformation of the particle.

Details of calculation methods have been reported by Zhou et al.

(2010).

2.4.2. Convective heat transfer

Therate of convective heat transfer between gas andparticle i is

calculated by

Qgi hi,convAiTg,iTi 22

where hi,conv, Ai and Tg,i are the convective heat transfer coefficient

between gas and particle,particle surface area and gas temperature

in the computational cell where particle i is located, respectively.

Theconvective heat transfer coefficient between gasand particle in

fluidized beds is based on the following equations proposed by

Gunn (1978):

hi,

conv Nulg=di 23

Y. Geng, D. Che / Chemical Engineering Science 66 (2011) 207219 209


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Nu 7:010eg5e2g1 0:7Re

0:2i Pr

1=3 1:332:4eg1:2e2gRe

0:7i Pr

1=3 24

where Nu, lg and Pr are the Nusselt number, gas thermal

conductivity and Prandtl number, respectively.

The rate of convective heat transfer between gas and wall is

given by

Qgw hg,wAg,wTgTw 25

where hg,wandAg,ware the convective heat transfer coefficient and

thecontact area between gasand wall, respectively. Theconvectiveheat transfer coefficient between gas and wall is determined by the

equation:

Nuw hg,wdh=lg 0:023Re0:8 Prn 26

where dh is the hydraulic diameter; the exponent n is 0.3 for

cooling, and 0.4 for heating (Holman, 1981).

2.4.3. Radiative heat transfer

Only the radiative heat transfer between the particle and the

bed is considered in the present study, which is written as

Qi,radi sepiAiT4b T

4p,i 27

where s and Tb are the StefanBoltzmann constant and bedtemperature, respectively; epi is the particle radiation emissivitywhich is assumed to be 0.7 and 1.0 for sand and graphite particles,

respectively.

2.5. Combustion models

The combustion of large char particle in fluidized beds can be

described either with the shrinking particle model or with the

shrinking core model, depending on the fuel (Winter et al., 1995).

The graphite particle used in this study has a low porosity (7%).

Therefore, the shrinking particle model which assumes particle

density staysconstantwhile the particle diameterdecreases during

the combustion process, is adopted to describe char combustion

process.

2.5.1. Sand inhibitory effects

Up to now, the following two problems are still unsolved for

char combustion. One is the identification of the product or

products of the oxidation of the solid carbon; the other is the

position where CO oxidizes to CO2 nearby or far away from the

carbon particle. In fluidized beds, each char particle is burnt among

abundant moving inert particles. This is a crucial distinction

between fluidized bed combustion and pulverized coal flame

combustion, which leads to different answers to the above

problems.

In order to accurately simulate the char combustion process in

fluidized beds of inert sand, the following model proposed by

Hayhurst and Parmar is recommended as shown in Fig. 1. It isassumed that CO is the only product of oxidation for char particles

burning in fluidized bed and the oxidation of the resulting CO is

inhibited by the proximity of sand (Hayhurst, 1991; Hayhurst and

Parmar, 1998; Dennis et al., 2005, 2006). At lower temperaturesCO

mainly diffuses away from the original carbon particle before

burning, butat highertemperatures sand inhibitory effects seem to

be negligible and CO does burn to CO2 close to the carbon

(Hayhurst, 1991; Hayhurst and Parmar, 1998; Loeffler and

Hofbauer, 2002). This model is contrary to the one where the

primary CO/CO2 ratio is related to the char particle temperature by

an Arrhenius expression: [CO]/[CO2]A exp( B/Tp), which was

widely employed in the simulation of pulverized coal combustion

before (Arthur, 1951; Phillips et al., 1970; Rajan and Wen, 1980;

Smoot, 1993; Linjewile and Agarwal, 1995).

In addition,the presence of inert particles will also influence the

mass transfer process by decreasing the volume available and

altering the gas fluid dynamics around the char particle. Anextensive list of empirical expressions for the Sherwood number

applied to a burning particle has been established to take into

account these effects (La Nauze et al., 1984; Hayhurst and Parmar,

2002; Dennis et al., 2006; Fabrizio Scala, 2007). In the present

study, the following expression proposed by Fabrizio Scala is

adopted to calculate the Sherwood number:

Sh 2:0emf 0:70Remf=emf1=2Sc1=3 28

where emf and Remf are the gas voidage and particle Reynoldsnumber at the minimum fluidization condition, respectively; Scis

the Schmidt number. The first term on the right-hand side

represents mass transfer in stagnant conditions, while the

second one accounts for the enhancement of mass transfer

caused by the gas flow around the particle.

2.5.2. Chemical reaction heat

As discussed in the above subsection, the rate of heat release

which is derived from char combustion andreceivedby theoriginal

char particle can be calculated by

Qi,reac dmidt

DH1 wDH2DH1 29

where DH1 and DH2 are the enthalpy changes of the reactions

(C+1/2O2-CO) and (C+O2-CO2), respectively;w is the fraction ofthe resulting CO, which is oxidized to CO2 sufficiently close to the

char particle and so transfers the heat of reaction (CO+ 1/2O2-CO2) to

the carbon particle, thus it follows that a fraction (1w) of theresulting CO diffuses and burns far away from the parent carbon

particle which receives none of the heat of combustion of this CO.

Currently, there is still no general relationship to calculate the

value of w. However, Hayhurst and Parmar (1998) found that wdepends upon Tp, the temperature of the burning particle, and Umf,

the value of the minimum fluidization velocity, which indicates a

potentialpathway to resolve this problem. In thepresent study, the

following formula can be obtained for the present simulation

conditions using $ 0.5 mm bed particles based on the

experimental results of Hayhurst and Parmar (1998):

w

0 Tpr933K

2:0 103Tp1:866 933KoTpo1433K

1 TpZ1433K

8>:

30

Char

sand

sand

sand

sand

sand

sand

sand

sand

sand sand

sand

sand

sand

sandsand

sand

sand

CO combustionclose to the char

(1-) CO

combustion far

away from the char

CO

sand

Fig. 1. Char combustion model in fluidized beds with inert sand particles.



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2.5.3. Char combustion rate

As we know, char combustion can occur under three different

regimes (Basu, 2006; Winter et al., 1997). At the initial time, the

char particle fed into the bed is larger and the reaction rate is much

higher than the bulk diffusion rate. So char combustion is

controlled by bulk diffusion (Regime III). As the combustion

proceeds, the char particle diameter will shrink. Once the

diffusion rate becomes comparable to the chemical reaction rate,

thechar combustion rate is determined eitherby the kinetic rate orby the diffusion rate (Regime II), until the char particle becomes so

small that the diffusion rate is much higher than the kinetic

rate, then the combustion rate is controlled by the kinetic rate

(Regime I). In this study, all these three regimes are considered by

using the model of Baum and Street (1971) and Field et al. (1967).

The diffusion rate coefficient, Rdiff, is calculated by

Rdiff 24ShDoxy

dpRTm31

where Doxy, R and Tm are the binary diffusivity for an oxygennitrogen

mixture, the universal gas constant and the mean temperature of gas

and char particle, respectively.

Although many new mechanisms of the carbon combustion

under kinetically controlled conditions have been reported

recently (Bews et al., 2001), the char combustion reaction rate is

still simply assumed to be first order with respect to oxygen due to

its mathematical convenience for the combination of these three

regimes in the present study. The kinetic rate coefficient, Rchem, is

calculated by

Rchem A0 exp E0

RTp

32

where A0 and E0 are the pre-exponential factor and activation

energy, respectively.

Combining with the diffusion rate and the reaction kinetic rate,

the char combustion rate can be expressed as

dmi

dt

pd2p,iPox1

Rdiff

1

Rchem

1

33

where Pox is the partial pressure of oxygen in the bulk gas.

2.5.4. CO combustion rate

The oxidation of CO is another important reaction in fluidized

beds, and the rate of CO oxidation reaction is calculated by the

expression proposed by Dryer and Glassman (1973):

RCO 3:98 1014 exp

1:67 105

RTg

!CO H2O

0:5O20:25 34

3. Numerical implementation

3.1. Numerical method

The coupling methodology of DEM and CFD has been well

documented by others (Tsuji et al., 1993; Xu and Yu, 1997). This

study extends this method to integrate the hydrodynamics, heat

and mass transfer and combustion with a computer code

developed in FORTRAN language by the authors using the

submodels mentioned in Section 2. The numerical treatment

method and the main solution procedures are given below.

Thediscretizationof the gasphase governing equationsis based

on thefinitevolume methodemploying a staggeredgridand solved

by the SIMPLE algorithm (Patankar, 1980). The explicit time

integration method is used to solve instantaneous mass,

momentum and energy conservation equations of discrete

particles in the DEM. The main solution procedures of the

extended DEMCFD model in the present study are shown as

follows:

(1) Calculate the void fraction and interphase exchange terms

based on the initial values of gas phase and all particles.

(2) Calculate all physical coefficients and gas phasereactionrates.

(3) Solve gas phase momentum equation for velocities based on

the current pressure field.

(4) Solve gas phase pressure correction equation and correct gasphase pressure and velocities.

(5) Solve gas phase energy and species equations.

(6) Return to the second step and repeat calculations until

convergence.

(7) Map the mass, momentum and energy related variables to all

particles and calculate the interphase exchange terms for

particles governing equations.

(8) Execute the extended DEM for particles and get new position,

velocities, temperature, mass and diameter of each particle.

(9) Map back the particle locations to calculate a new void

fraction and calculate the interphase exchange terms which

go into gas phase continuity, momentum, energy and species

equations.

(10) Post-processing for calculating all results of interest.(11) Go to (2) for the next time step.

3.2. Simulation conditions

In order to test the prediction capability of the model, two

typical conditions are used in the present study as follows:

(1) Case 1: A single graphite particle (dp,g3.0 mm) is combusted

in theelectrically heatedfluidized bedwithsilicasand particles

(dp,s0.5 mm) as shown in Section 4.1. This condition is aimed

primarilyat studying the combustion characteristics of a single

graphite particle in fluidized beds and validating the model by

quantitative analysis and comparison with the similarexperiments in the literature.

(2) Case 2: A small batch of smaller graphite particles ( dp,g1.0

mm) are combusted in the same fluidized bed as shown in

Section 4.3. This condition is aimed primarily at extending the

model to study the combustion characteristics of a batch of

graphite particles in fluidized beds and validating themodel by

qualitative analysis and comparison withthe conclusions in the

literature.

Due to the limitations of available computers, the sand and

graphite particles are treated as spherical particles in a small scale

rectangular bedwhose dimensions arereducedto 4 cm 16cm dp,gwith its thickness equal to the graphite particle initial diameter. In

order to make sure that the simulation results can be used to becompared with the previous experimental results, the most key

parameters for a single small graphite particle combustion in the

vigorously bubbling fluidized bed (i.e. bed temperature, sand

diameter, graphite diameter, superficial velocity, gas pressure

and gas temperature as shown in Fig. 2) are inherited from the

experiment. By detailed investigation of the related literature

(Hayhurst and Parmar, 1998, 2002; Bews et al., 2001; Field et al.,

1967; Smoot, 1993; Bird et al., 2007), the experimental conditions

andmaterial properties can be determined as shown in Table 1. For

the purpose of exactly calculating the porosity, an improved

pseudo-three-dimensional model is employed to deal with this

binary particle system. It is assumed that there is only one layer of

graphite particle or n0 (n0 dp,g/dp,s) layers of sand particles in the

thin depth direction, where dp,g and dp,s are the graphite particle



6/13

initial diameter and sand particle diameter, respectively. The flow

of gas is assumed to be two-dimensional. Due to the limitation of

the DEM, the time step Dtp must be set small to capture the

displacement of the particles and to stably solve the DEM

equations. The criterion of the time step can be found in Tsuji

et al.(1992). On thebasisof thepresent simplifying approximation,

thecomputation of thesolution, carried outby means of a 2.66 GHz

Intel Core 2 Duo CPU, requires around 0.6 h per 1 s simulation, and

the computation of the solution of the graphite particle complete

combustion process (dp,g3 mm; t$600 s) requires around

15 days.

Atthe initial time,the sand particlesare randomly scatteredintothe bed and forma packedbed witha height of$ 5 cm. The gas (air)

is introduced at a uniform velocity from the bottom of the bed. The

graphite with an initial temperature of 300 K is injected into the

surface of the bed either as a single particle (case 1) or as a batch of

smaller particles (case 2) from the top of the bed. The initial

temperatures of the bed, sand particles and fluidized gas are all

1173 K (or 1073 K) in case 1 (or case 2) and the moisturecontent of

air is assumed to be 1% (mass fraction).

Forthe gasvelocity, theno-slip boundary conditionis applied to

the left and right walls (U0; V0); zero normal gradient

condition is applied to the top exit (@U/@x 0; @V/@y 0); a uniform

velocity is specified at the bottom inlet. For the gas pressure, the

pressure-outlet condition is applied to the topexit. Forother scalar

variables, F (i.e. Pg

, Tg

, Xgn

), zero normal gradient condition is

applied to thetop exit (@F/@x 0; @F/@y 0).In thediscreteelement

model, the wall is treated as an infinitely great particle with the

corresponding wall properties. The inter-particle forces and heat

transfer models are also applied to the collision and conduction

between the particle and the wall. However, it is assumed that

collision and conduction have no effect on the displacement or

temperature of the wall.

4. Results and discussion

In this section, the developed model is validated by comparing

the simulation results with the previous experimental results and

conclusions in the literature in terms of the bed hydrodynamics,individual particle temperature, char residence time and concen-

trations of the products. The effects of key operation conditions on

char particle combustion behavior are also examined.

4.1. A particle combustion in the fluidized bed

4.1.1. Bed hydrodynamics

The model is employed to simulate the bed hydrodynamics at

different gas superficial velocities and the results are shown in

Fig. 3: (a) when the fluidizing air is introduced intothe bed at a low

velocity (e.g. U0.05 m/s), no obvious movement of particles is

observedand this state is identified as a fixedbed.(b)Whenthegas

superficial velocity reaches a critical value, the heterogeneous

structure originates from the center of the bed. This will yield anincipient fluidization stage which allows the minimum fluidization

velocity to be determined. A value of $0.1 m/s is found in this

study, which is close to the value of 0.088 m/s estimated from the

well known Wen and Yus (1966) correlation at 1173 K. (c) At an

intermediate velocity (e.g. U0.2 m/s), the gas passes through the

bed as bubbles and this condition represents a bubbling fluidized

bed. (d) With still increasing gas superficial velocity, the bubbles

grow andappear more frequently until thebed becomes slugging.If

the superficial velocity is further increased (e.g. U0.80 m/s), the

particles will be carried out of the bed resulting in the phenomena

of pneumatic transport. By comparisons with previous reports

(Tsinontides and Jackson, 1993; Basu, 2006; Ravelli et al., 2008),

the present model predicts reasonable hydrodynamics results

in the fluidized bed and the successful prediction of these

Fig. 2. Calculation domain for the present simulations.

Table 1

Summary of parameters used in the present simulations.

Parameters Case 1 Case 2

Bed dimension, x y z, (mm3) 40 160 3 40 160 1

Cell size, Dx Dy Dz (mm3) 4 4 3 4 4 1

Bed temperature, Tb (K) 1173 1073Particles number, np 7200/1 7200/290

Particle initial diameter, dp (mm) 0.5/3.0 0.5/1.0

Particles density, rp (g/cm3) 2.65/2.1 2.65/2.1

Spring constant, kn (N/m) 20 20

Particles friction coefficient, g 0.3 0.3Particles restitution coefficient, e 0.8 0.8

Particles Youngs modulus, E(kg/(m s2)) 5.0 109 5.0 109

Particles Poisson ratio, n 0.3 0.3Particles initial temperature, Tp (K) 1173/300 1073/300

Particles thermal conductivity, ls(W/(m K))

0.84/150 0.84/150

Particles specific heat capacity, Cp(J/(kg K))

800/836+1.53Tp 800/836+1.53Tp

Pre-exponential factor, A0 (g/

(cm2 s atm))

8.7 103 8.7 103

Activation energy, E0 (cal/mol) 3.57 104 3.57 104

Gas initial temperature, Tg (K) 1173 1073Gas density, rg (kg/m

3) Gas state equation

Gas molecular viscosity, mg (kg/(m s)) 1.7 105(Tg/273)

1.5

(383/(Tg+110))a

Gas thermal conductivity, lg (W/(m K)) 2.52 102(Tg/300)

0.5a

Gas specific heat capacity, Cp,g (J/(kg K)) Thermochemical Databaseb

Gas superficial velocity, U (m/s) 0.308 0.308

Gas pressure at outlet, atm 1.0 1.0

Time step, Dtg, Dtp (s) 5 105/

5 1065 105/

5 106

a Bird et al. (2007).b Burcat and Ruscic (2005).

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7/13

features provides an important example to validate the present

hydrodynamics model.

4.1.2. Temperature and diameter of a graphite particle

Particle temperature is oneof themost important parameters in

fluidized beds, because it influences the gas diffusion rate around

the particle and the char chemical reaction rate. Higher charparticle temperature will lead to higher combustion rate and

shorter residence time. Based on the detailed investigation of

the related literature (Stubington, 1985; Linjewile and Agarwal,

1995; Winter et al., 1997; Ravelli et al., 2008), it can be found that

the increase of particle temperature due to char burning varies

from 10 to 500 K beyond the bed temperature.

Fig. 4 shows the variations of the graphite particle temperature

and diameter with the lifetime of the particle. The comparison

between the simulation results andthe experimentalresults is also

shown in the figure. It can be observed that the graphite particle

temperature increases from an initial value of 300 K to a relatively

steady temperature that exceeds the bed temperature by $150 K,

and its size decreases with time until it is burnt out with a time

of$580 s in the simulation results.

The prediction results are mostly in agreement with the

experimental results. However, it can be noticed that there are

somedeviations, especiallywhen the graphite particle gets smaller.

These deviations are mainly due to the fact that the model predicts

the whole combustion process of the graphite particle over a wide

range of particle sizes and operating conditions, and the mechan-

ismof this process, especially in theRegimes I andII, is still unclear.In addition, these differences also indicate that further improve-

ments of the submodels employed, especially char combustion

model, are necessary.

4.1.3. CO2 concentration

During the combustion process, CO2 was the only detectable

product in the off-gases. Due to the difference between the

simulation conditions and the experimental conditions, especially

different cross-sections of the beds with the same superficial

velocity, the CO2 concentration from the simulation divided by

the ratio of the experimental inlet gas flux to the simulation inlet

gas flux, is used to compare with the experimental results in

quantity. Because only a single smaller graphite particle is com-

busted in the bed where the concentration of the resulting CO2

Fig. 3. Snapshots of particle configurations at different superficial velocities: (a) fixed bed, (b) incipient fluidization stage, (c) bubbling fluidized bed and (d) pneumatic

transport.

Fig.4. Graphiteparticle temperatureand diametervs. theparticleresidencetime in

thebed. Thesymbols represent theexperimentalresultsfrom Hayhurstand Parmar

(1998, 2002) and the curve represents the simulation results in this study.

Fig. 5. Concentrations of CO2 in the off-gases vs. the particle residence time in the

bed. The symbols represent experimental results from Hayhurst and Parmar (1998,

2002) and the curves represent the simulation results in this study.



8/13

(range 00.0025 mol/m3) are very low at every time step, this

treatment is reasonable. Fig. 5 shows the comparison of the

simulation results of CO2 concentrations in the off-gases against

time and the experimental results. It can be seen clearly that the

CO2 concentration has an initial jump during the first several

seconds, and then a subsequent decline follows with oscillations

until the combustion is stopped. These oscillations probably result

from the graphite particle moving around the bed during the

combustion process. Different surrounding environment will leadto different char combustion rates and different concentrations of

the resulting CO2. This picture is also similar to that portrayed in

another literature (Linjewile et al., 1994), and the simulation

results can be considered to be in agreement with the

experimental results.

4.2. Effects of operational conditions

Operational conditions such as bed temperature, oxygen con-

centration and superficial velocity have important effects on char

combustion behavior in fluidized beds. A qualitative as well as

quantitative understanding of the effects of key parameters is an

important aspect in model validation and application. In order to

better understand these effects and further validate the model, aseriesof new simulations areperformed in this subsection. Thebed

temperature (from 1023 to 1173 K), the concentration of oxygen in

the fluidizing air (from 10 to 21 mol%) and the superficial gas

velocity (from U/Umf2.0 to 5.0) areall variedindependently in the

interested range to study their respective importance on char

particle temperature and combustion rate. The results are carefully

examined and discussed below.

4.2.1. Effect of bed temperature

Figs. 6 and 7 show the effects of the variations of the bed

temperature on the char particle temperature and combustion rate,

respectively. The char particle temperature in the bed is governed

by the energy balance between the heat transfer rate and heat

generation rate from combustion. It can be observed from thesetwofigures that thebed temperature hasa very significant effecton

the char particle temperature and combustion rate just as

expected. After the graphite particle is fed into the bed, the

particle temperature increases faster in the hotter bed due to the

faster heating rate. The char particle temperatures themselves all

stay at a quite constant level during combustion in these

conditions. However, the char particle temperature is$150 K

above the bed temperature in the hottest fluidized bed,

only$ 20 K above the bed temperature in the coldest one. This

phenomenon canbe explainedby theeffect ofw (inEq. (30)).Higherchar particle temperature (firstly obtained from the higher bed

temperature) increases the ratio of the resulting CO, which is

oxidized to CO2 sufficiently close to the char particle and so

transfers more heat of combustion to the carbon particle, andultimately leads to much higher particle temperature and shorter

char residence time. The simulation results correctly reflect the

effects of the variations of this parameter in the bed.

4.2.2. Effect of oxygen concentration

Figs. 8 and 9 show the effects of the variations of the oxygen

concentration in thefluidizing gason thechar particle temperature

and combustion rate, respectively. Char combustion rate is limited

either by the diffusion rate or by the chemical kinetic rate in

oxygen-containing atmospheres where oxygen concentration is

one of the most important parameters. The enhancement of the

oxygen concentration can promote combustion and raise particle

temperature. These two figures illustrate that raising oxygen

Fig. 6. Graphite particle temperature vs. the particle residence time in the bed at

different bed temperatures.

Fig. 7. Graphite particle diameter vs. the particle residence time in the bed at

different bed temperatures.


different oxygen concentrations in the fluidizing air.



9/13

concentrations in the inlet fluidizing air provides necessary

conditions for good combustion and leads to higher char

combustion rates and char combustion temperatures. These

effects are just the same as previous conclusions in the literature.

4.2.3. Effect of superficial velocity

Figs. 10 and 11 show the effects of the variations of the gas

superficial velocities on char particle temperature and combustion

rate, respectively. Superficial velocity controls the entire

hydrodynamics of the bed including its heat and mass transfer.

Higher superficial velocity can either increase the rate of heat

transfer between particle and gas or raise the char combustion rate

by increasing mass transfer rate of oxygen to the char particle

surface. It can be seen clearly from these two figures that char

combustion rate is slightly faster and the char combustion

temperature is also slightly higher at higher superficial

velocities. This leads to the conclusion that the effects of the

superficial velocity on char combustion behavior depend on a

complex non-monotonic two-way balance, i.e. the balance of heat

and mass transfer from gas to char particle and chemical reaction

heat generated at or near the char particle surface during its

combustion.

4.3. Particles combustion in the fluidized bed

For the combustion of a batch of graphite particles, there is

possibility of combustion characteristicsfrom one graphite particle

interacting with other graphite particles. In order to study these

characteristics and expand the application scope of the developed

model, a new simulation is performed in this section, i.e. a batch of

smaller graphite particles (dp,g1.0 mm) which consists of

290 particles are combusted in the fluidized bed with inert sand

particles (dp,s0.5 mm). The thermal behavior of the bed and

particles are carefully examined and qualitative analyzed by

comparing with foregone conclusions from literature.

4.3.1. Particles flow structure and temperature

The instantaneous position, size and temperature of all particles

are shown in Fig. 12. These snapshots illustrate the combustion

process of a batch of char particles in the binary fluidized bed. As

soon as the graphite particles with an initial temperature of 300 K

are fed into the hot bed, they sink into the bed and circulate with

the hot sand particles. It can be observed that although there is a

few bigger graphite particles depositing on the bottom of the bed,

mixing dominatessegregation due to the higher superficial velocity(U3.5Umf). Meanwhile, each graphite particle is heatedby the hot

bed, gas and sand particles until its temperature reaches the

ambient temperature. When the graphite particle temperature

reaches its ignition point, the particle starts to burn and release

heat. Once the graphite particle temperature exceeds the ambient

temperature, it is cooled by its surroundings. In addition, a careful

inspection of the animations reveals that the graphite particles

diameter are shrinking all the time until they are completely

burned out. Detailed information of the variations of graphite

particles temperature with time is shown in Fig. 13. It can be seen

that thetemperatures of thegraphite particlesrise very quickly due

to the intense mixing and high heat transfer rate over the first

several seconds, and then tends to stay at a quite constant level

($ 1173 K) whilst combustion proceeds.


different oxygen concentrations in the fluidizing air.


different superficial velocities.


different superficial velocities.



10/13

4.3.2. Gas temperature and species concentrations

Fig. 14 shows the distributions of the gas porosity, temperatureand the concentrations of O2, CO and CO2 in the bed at a random

time (e.g. t32 s, the corresponding particles information are also

shown in Fig. 12 for comparison). The O2 concentration is higher at

the bottomof the bed and it rapidly decreases along the bed height

due to the burning of more graphite particles and CO. The CO

concentration is high in the regions where are close to the graphite

particles due to the char combustion, and CO-rich bubbles are

formed because of the inhibitory effects. The resulting CO burns

insidethesebubbles,and then it decreasesdue to thereactionof CO

and O2. No CO is detected in the off-gasses. Oppositely, the CO 2concentration is lowat the bottom of the bedand it increases along

the bed height. The way in which combustion evolves inevitably

affects the temperature profile along the bed height. In fact, the

hottest areas of thebed canbe found right where thegreater part of

the char is converted to CO. These trends are in good agreement

with previous experimental results reported in the literature(Topal, 1999; Sotudeh et al., 2007; Gungor and Eskin, 2008).

4.4. Limitation of the present model

While the prediction capability of the extended DEMCFD

model is clear from previous sections, the char combustion model

in fluidized beds is still not completely resolved in the present

study.In fact, only a potentialand proximalpathwayis pointed out.

One of the most important factors in the char combustion model is

w (in Eq. (29)), which is still a puzzle and cannot be quantitativelydetermined by a general expression just as in the conventional

pulverized coal combustion model. This point limits the extension

of this model at the moment and still needs further study.

Fig.12. Instantaneous particles temperature,position andsize in thebed. Thecontour levels represent particles temperatureand thescatters represent particlesposition and

size (temperature unit: K).



11/13

It is worth stressingthat, Hayhurst andParmar notonlyprovidean

excellent char combustion model in fluidizedbeds but alsoprovidean

excellent experiment scheme to obviate those complex effects for the

present study. Thegas radiation heat transfer is neglectedmainly due

to the fact that only a single small graphite particle is combusted in

the bed. The tri-atom gas (i.e. CO2 and H2O) presented is only a little

and the temperature difference is also relatively smaller. However,

when theextended DEMCFDmodel presented in this studyis used to

simulate a large amount of char particles combustion, especially coalcombustion in actualbeds,not only thegas radiative heat transfer but

also the particleparticle radiative heat transfer must be considered

by suitableradiation heattransfer models.In additional, gas turbulent

reacting flow and heat transfer also must be considered by a

satisfactory turbulence model. These models can be integrated into

the models presented in this study.

5. Conclusions

In this study, a transientthree-phase model has been developed

to study the complete combustion process of char in a special

fluidized bed combustor. A new char combustion submodel con-

sidering sand inhibitory effects is also developed and incorporated

into themodel. Themodel is validatedby comparingthe simulation

results with previous experimental results and conclusions in the

literature in terms of bed hydrodynamics, individual particle

temperature, char residence time and concentrations of the

products. The main conclusions of this work can be summarized

as follows:

(1) The DEMCFD model has been successfully extended to

simulate the complete combustion process of char in a

fluidized bed combustor on the particle scale, and more

satisfactory simulation results, compared to the results by

the conventional char combustion model, have been obtained.

(2) The presence of the inert particles has significant effects on the

process of heat and mass transfer and char combustion in

fluidized beds and these effects must be considered in the

model. The recommended char combustion submodel which

considers sand inhibitory effects can be employed to exactly

predict the combustion behavior of char in fluidized beds with

inert sand.

(3) The model developed in this study shows good results of

describing the effects of the variations of key operationconditions. Higher bed temperatures, higher oxygen concen-

trations and higher gas superficial velocities, especially the

former two, promote the char combustion due to the better

heat and mass transfer to the char particle.

(4) Not only thegas phase temperature andspecies concentrations

but also the particles temperature and size in the whole

combustion process can be correctly achieved by the present

extended DEMCFD model.

Nomenclature

A surface areaA0 pre-exponential factor in Arrhenius equation

Cp specific heat

Cd fluid drag coefficientFig. 13. The temperature variations of five graphite particles selected randomly vs.

the particles residence time in the bed.

Fig. 14. The distributions of the gas phase porosity, temperature, mass fraction of O2, CO and CO2 at t32 s in the bed. (a) Gas porosity; (b) gas temperature/K; (c) O2

concentration; (d) CO concentration and (e) CO2 concentration.



12/13

D diffusivity

d particle diameter

E Youngs modulus

E0 activation energy

F force

g gravity acceleration

h convective heat transfer coefficient

I moment of inertia

m massNu Nusselt number

n number of particles

n normal unit vector

P pressure

Pr Prandtl number

Q heat transfer rate

R universal gas constant

r particle radius

Re Reynolds number

Sh Sherwood number

T temperature

T torque

t tangential unit vector

t time

u translational velocity

V volume

X the mass fraction of species

Greek letters

a volume fraction of particleb drag coefficient

g friction coefficientG thermal diffusivity

d displacement

e porosityZ damping coefficientk spring constant

l thermal conductivitym viscosityr densitys StefanBoltzmann constants viscous stress tensor

j empirical coefficientw mass fraction of carbon monoxidex rotational velocity

Subscripts

c contact

d damping

g gas phase

i particle i

ij between particles i and jj particle j

n normal component

p particle

t tangential component

Abbreviation

chem chemical reaction

cond conduction

conv convection

diff diffusion

oxy oxygen

radi radiation

reac reaction

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