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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://-/?-8/4/2019 An+Extended+DEME28093CFD+Model+for+Char+Combustion+in+a+Bubbling+Fluidized+Bed+Combustor+of+I
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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.
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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
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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
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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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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.
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(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.
Fig. 8. Graphite particle temperature vs. the particle residence time in the bed at
different oxygen concentrations in the fluidizing air.
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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.
Fig. 9. Graphite particle diameter vs. the particle residence time in the bed at
different oxygen concentrations in the fluidizing air.
Fig. 10. Graphite particle temperature vs. the particle residence time in the bed at
different superficial velocities.
Fig. 11. Graphite particle diameter vs. the particle residence time in the bed at
different superficial velocities.
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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).
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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.
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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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