Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b
Published on Web 02/22/2010
Numerical Comparison of the Drag Models of Granular Flows Applied
to the Fast Pyrolysis of Biomass
K. Papadikis,† S. Gu,*,† A. Fivga,‡ and A. V. Bridgwater‡
†School of Engineering Sciences, University of Southampton,
Highfield, Southampton, SO17 1BJ, United Kingdom, and ‡School
of Engineering and Applied Science, Aston University, Aston
Triangle, Birmingham B4 7ET, United Kingdom
Received December 8, 2009. Revised Manuscript Received February 9,
2010
The paper presents a comparison between the different drag models
for granular flows developed in the literature and the effect of
each one of them on the fast pyrolysis of wood. The process takes
place on an 100 g/h lab scale bubbling fluidized bed reactor
located at Aston University. FLUENT 6.3 is used as the modeling
framework of the fluidized bed hydrodynamics, while the fast
pyrolysis of the discrete wood particles is incorporated as an
external user defined function (UDF) hooked to FLUENT’s main code
structure. Three different drag models for granular flows are
compared, namely the Gidaspow, Syamlal O’Brien, and Wen-Yu, already
incorporated in FLUENT’s main code, and their impact on particle
trajectory, heat transfer, degradation rate, product yields, and
char residence time is quantified. The Eulerian approach is used to
model the bubbling behavior of the sand, which is treated as a
continuum. Biomass reaction kinetics is modeled according to the
literature using a two-stage, semiglobal model that takes into
account secondary reactions.
1. Introduction
Fluidized beds have been the center of modeling attention for many
years, and various simulation approaches have been developed,
ranging from Lattice-Boltzmann methods (LBM)1 to discrete particle
(DPMs, Eulerian-Lagrangian)2-5
and two-fluid models (TFMs, Eulerian-Eulerian).6,7 More recently,
discrete bubble models (DBMs)8 have been deve- loped and been
applied to fluidized beds, increasing the potential of industrial
scale simulations beyond the capabi- lities of TFMs.
The Eulerian formulation of the granular medium, using the kinetic
theory of granular flows, has made the realization of fluidized bed
simulations, less computationally intensive. The particulate phase
is treated as a continuum with an effective viscosity, thus the
method is also called a two-fluid approach. The calculation of the
momentum exchange coeffi- cient of gas-solid systems is very
different in comparison of a single sphere surrounded by a fluid.
When a single particle moves in a dispersed two-phase flow,the drag
forceis affected by the surrounding particles. Several correlations
have been
reported in the literature6,9-14 to account for the momentum
exchange between the gas and solid phases and have been applied to
dispersed two-phase flow simulations with great success. Most of
these models have been studied and compared with experimental data
in several cases, such as the studies of Kafui et al.,4 Li
and Kuipers,5 and Taghipour et al.15 The work of Kafui et al.,4
concerned the simulation of pressure drop-gas superficial velocity
using two models (pressure gradient force model, fluid density
based buoyancy model) in an Eulerian- Lagrangian framework, using
the continuous single-function correlation of Di Felice13 to
account for thedragforces in dense and dilute regimes. The study
showed significant differences in the pressure drop-superficial gas
velocity profiles in the fixed bed regime and corresponding
significant differences in the prediction of minimum fluidization
velocity. The work of Li and Kuipers5 examined the occurrence
of heterogeneous flowstructures in gas-particle flows and theimpact
of nonlinear drag force for both ideal particles (elastic
collision, without interparticle friction) and nonideal particles
(inelastic collision, with interparticle friction). Several drag
models were com- pared,10,13,14,16 and the study showed that
heterogeneous flow structures exist in systems with both nonideal
and ideal particle-particle interaction. For the ideal particle
interac- tion it was shown that heterogeneous flow structures are
caused purelyby thenonlinearity of thegas drag andthat the stronger
the dependence of drag to voidage, the more heterogeneous flow
structures develop. The weak depen- dence of voidage to drag causes
more homogeneous flow
*To whomcorrespondence should be addressed.Telephone: 0238059 8520.
Fax: 023 8059 3230. E-mail:
[email protected].
(1) Ladd, A. J. C.; Veberg, R. J. Stat. Phys.
2001, 104, 1191. (2) Feng, Y.Q.; Xu, B. H.; Zhang,S. J.;
Yu, A. B.; Zulli, P. AIChE. J.
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(2-3), 166 – 177. (4) Kafui, K. D.; Thornton, C.;
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Chem. Eng. Sci. 2003, 58, 711 – 718. (6)
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Dissertation; Cornell University: 2001 .
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
structures. The simulations were also carried out in an
Eulerian-Lagrangian framework. The work of Taghipour et al.15
concerned the Eulerian-Eulerian simulation of a fluidized bed
comparing the effect of the drag correlations of Gidaspow,6
Syamlal-O’Brien,9 and Wen and Yu10 at the pressure drop and sand
bed expansion. All studies showed good qualitative gas-solid flow
patterns.
Fluidized beds are the most widely used type of reactor for fast
pyrolysis, as they offer a number of advantages, such as highheat
transfer rates and good temperature control. Several models have
been developed and applied to biomass pyro- lysis.17-30 Most of the
models apply numerical analysis to determine heat, mass, and
momentum transport effects in a single biomass particle varying the
pyrolysis conditions. Usually, the influence of parameters such as,
size, shape, moisture, reaction mechanisms, heat transfer rates,
and parti- cle shrinkage is the main objective of study. The
numerical investigations of di Blasi.17-22 are typical examples of
single particle models that study the heat, mass, and momentum
transport through biomass particles by varying the pyrolysis
conditions, feedstock properties (implementing different che- mical
kinetics mechanisms), particle sizes, effect of shrinkage,
etc.Themodels provideveryuseful informationabout different
conditions of pyrolysis and product yields and canbe an excel- lent
guide for every researcher on the field. Saastamoinen,23
and Saastamoinen and Richard24 studied the effect of drying to
devolatilization stating that the surface temperature of the
particles after drying can exceed those of the initiation of
devolatilization, meaning that drying and pyrolysis may over- lap.
The models of Babu and Chaurasia25-30 treat the pyro- lysis process
in a similar way as the one of di Blasi and focus more on the heat
transfer effects and estimation of optimum parameters for biomass
pyrolysis. They also study the effect of the enthalpy of reaction
on product yields and vary the shrinkage parameters of biomass
close to the complete degradation of the particles. They found that
their approach gave better validation with experimental data
compared to those of di Blasi.
The main research of the authors has been focused on the
incorporation of the single particle models presented in the
literature into a unified computational model that simulates the
complete process of fast pyrolysis inside a bubbling fluidized
bed.31-37 In this way, several important parameters, such as heat
transfer coefficients from the bubbling bed, char and pyrolysis
vapor residence times, biomass particle trajec- tories, and effect
of particle size and shape, can be monitored and quantified,
something that is impossible by single particle models alone. This
unified CFD model can greatly aid the design and optimization of
pyrolysis equipment by specifying the operation limits of the
fluidized bed reactor regarding the type, the size, and the shape
of biomass particles, as well as the high heat transfer regimes for
more efficient biomass degrada- tion and consequently efficient
char elutriation at the freeboard.
The scope of the current paper is to quantify the effect of
the various drag models for granular flows that have been presented
in the literature, to the fast pyrolysis of biomass. The different
flow pattern and bubble distribution that will be created by these
models will have a certain impact on the heat transfer coefficient,
the momentum transport from the bed to the biomass particle, the
final product yields, and more importantly the char and vapor
residence times in the reactor. The reaction kinetics is based on a
two-stage, semiglobal mechanism, withkinetic constants suitable for
wood pyrolysis according to Chan et al.,38 for the primary stage
and Liden et al.,39and di Blasi17 for the secondary reactions.This
scheme has been chosen for this study because it can predict the
correct behavior of wood pyrolysis including the dependence of the
product yields on temperature.18,22,38 The simulation results are
compared with experimental data, whenever it is possible, that
comes from the pyrolysis of spruce in the same reactor.
2. Model Description
2.1. Experiment. The biomass fast pyrolysis experiment was
carried out in Aston University’s fluidized bed reactor. The
reactor has a capacity of 100 g/h, is constructed of
stainless steel, and is 40 mm in diameter and 260 mm high. The
fluidizing gas was nitrogen, whereas sand was used as a fluidizing
and heat transfer medium with an average particle diameter of 440
μm. The flow rate of nitrogen used was sufficient to provide
3 times the minimum fluidizing velocity (MFV) to the bed. The
residence time of the pyrolysis vapors in the reactor was
approximately 0.93s at a reaction tem- perature of 538 C. The
main apparatus of the fast pyrolysis unit consists of thefeeder,
thereactor, andthe liquid product collection system and is shown in
Figure 1.
2.2. Numerical Model. The dimensions of the 100 g/h fast
pyrolysis reactor are illustrated in Figure 2. Nitrogen flows
(17) Di Blasi, C. Combust. Sci. Technol.
1993a, 90, 315 – 339. (18) Di Blasi, C.
Chem. Eng. Sci. 1996, 51, 1121 – 1132.
(19) Di Blasi, C. Chem. Eng. Sci. 2000, 55,
5999 – 6013. (20) Di Blasi, C. Biomass Bioenerg.
1994, 7 , 87 – 98. (21) Di Blasi, C.
Ind. Eng. Chem. Res. 1996b, 35, 37 – 46.
(22) Di Blasi, C. J. Anal. Appl. Pyrol.
1998, 47 , 43 – 64. (23) Saastamoinen, J.
Model for drying and pyrolysis in an updraft
gasifier.In Advancesin ThermochemicalBiomassConversion; Bridgwater,
A. V. Ed.; Blackie: London, 1993; pp 186 -200.
(24) Saastamoinen, J.; Richard, J.-R. Combust. Flame 1996, 106,
288 –
300. (25) Babu, B. V.; Chaurasia, A. S. Modelling and
Simulation of
Pyrolysis: Influence of Particle Size and Temperature . Proceedings
of the International Conference on Multimedia and Design,
2002a, 4, Mumbai, India; pp 103-128.
(26) Babu, B. V.; Chaurasia, A. S. Modelling and Simulation
of Pyrolysis: Effect of Convective Heat Transfer and Orders
of Reactions . Proceedings of International Symposium and 55th
Annual Session of IIChE (CHEMCON-2002), 2002b, OU, Hyderabad,
India; pp 105 -106.
(27) Babu, B. V.;Chaurasia,A. S. Energ. Convers. Manage. 2003a, 44,
2251 – 2275.
(28) Babu, B. V.;Chaurasia,A. S. Energ. Convers. Manage. 2003b, 44,
2135 – 2158.
(29) Babu, B. V.; Chaurasia, A. S. Modelling and Simulation
of Pyrolysis of Biomass: Effect of Heat of Reaction .
Proceedings of Inter- national Symposium on Process Systems
Engineering and Control (ISPSEC 03) for Productivity
Enhancement Through Design and Optimisation 2003c, IIT-Bombay,
Mumbai, India; pp 181-186.
(30) Babu, B. V.;Chaurasia, A. S. Energ. Convers. Manage. 2004c,
45, 1297 – 1327.
(31) Papadikis, K.;Bridgwater,A. V.;Gu, S. Chem.Eng. Sci. 2008, 63
(16), 4218-4227.
(32) Papadikis, K.;Gu, S.;Bridgwater,A. V. Chem.Eng. Sci. 2009, 64
(5), 1036-1045.
(33) Papadikis, K.; Gerhauser, H.; Bridgwater, A. V.; Gu,S. Biomass
Bioenerg. 2009, 33 (1), 97-107.
(34) Papadikis, K.; Gu, S.; Bridgwater, A. V.; Gerhauser, H.
Fuel Process. Technol. 2009, 90 (4),
504-512.
(35) Papadikis, K.; Gu, S.;Bridgwater, A. V. Chem. Eng.
J. 2009, 149 (1-3), 417 – 427.
(36) Papadikis, K.;Gu, S.;Bridgwater, A. V. Biomass Bioenerg. 2010,
34 (1), 21 – 29.
(37) Papadikis, K.; Gu, S.; Bridgwater, A. V. Fuel Process.
Technol. 2010, 91 (1), 68 – 79.
(38) Chan, W. R.; Kelbon, M.; Krieger, B. B. Fuel
1985, 64, 1505 –
1513. (39) Liden, A. G.;Berruti,F.; Scott,D. S. Chem. Eng. Commun.
1988,
65, 207 – 221.
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
through a porous plate at the bottom of the reactor at a velocity
of U 0 = 0.6 m/s and temperature of 303 K.
The superficial velocity is approximately 3 times greater than the
minimum fluidizing velocity U mf of the
reactor, which is typically around 0.2 m/s using a sand bed with
average particle diameter of 440 μm.40 The sand bed has been
preheated to 815 K as it was also performed in the experi- mental
procedure.
The biomass particle of density of 700 kg/m3 is injected at the
center of the sand bed, which has been previously fluidized for1 s.
Momentum is transferred from thebubbling bed to the biomass
particle as well as from the formed bubbles inside the bed. The
studied biomass particle was chosen to be 350 μm in diameter,
which is more-or-less the
size of the particles used in the experiments. Bigger rigs and
commercial plants use much larger particles in the range of
2-5 mm.
The different bubble distribution that will occur due to the
different granular flow drag models will have an impact on the heat
transfer conditions and consequently will affect the degradation
rate of the particles and subsequently the final product yields and
theresidence time of char and vapors. The numerical model will try
to identify any significant differ- ences between the models and
compare the results with real- life experiments. The simulations
last until the particles are entrained from the reactor
independently of the simulation time needed to achieve that.
3. Mathematical Model
3.1. Multiphase Flow Governing Equations. The simula- tions
of the bubbling behavior of the fluidized bed were performed by
solving the equations of motion of a multifluid system. An Eulerian
model for the mass and momentum for the gas (nitrogen) and fluid
phases, was applied, while the kinetic theory of granular flow was
applied for the conserva- tion of the solid’s fluctuation energy.
The Eulerian model is already incorporated in the main code of
FLUENT, and its governing equations are expressed in the following
form.
Mass Conservation. Eulerian-Eulerian continuum model- ing is
the most commonly used approach for fluidized bed simulations. The
accumulation of mass in each phase is balanced by the convective
mass fluxes. The phases are able to interpenetrate, and the sum of
all volume fractions in each computational cell is unity.
Gas Phase.
∂ðεgFgÞ ∂t
Solid Phase.
∂ðεsFsÞ ∂t
þr 3 ðεsFsυsÞ ¼ 0 ð2Þ
Momentum Conservation. Newton’s second law of motion states that
the change in momentum equals the sum of forces on the domain. In
gas-solid fluidized beds the sum of forces consists of the viscous
force r 3 τ Cs , the solids pressure force
r ps, the body force εsFs g, the static pressure force εs
3r p and the interphase
force K gs(ug - us) for the coupling of gas and
solid momentum equations by drag forces.
Gas Phase.
∂ðεgFgυgÞ ∂t
g þ εgFg g þ K gsðug -usÞ ð3Þ
Solid Phase.
∂ðεsFsυsÞ ∂t
þr 3 ðεsFsvsXυsÞ ¼ -εs 3r p-r ps þr 3
τ ¼
s
τ ¼
2
s ð5Þ
Figure 1. Experimental apparatus. Adapted from Coulson M, EC
Project Bioenergy Chains Final Report, Aston University,
ENK6-2001-00524.
Figure 2. Fluidized bed reactor geometry used in the
simulation.
(40) Geldart, D. Powder Technol. 1973, 7 ,
285.
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
The Gidaspow interphase exchange coefficient is,
K gs ¼ 3
K gs ¼ 150 ε2
s μg
where the drag coefficient is given by
C d ¼ 24
and
μg
ð9Þ
K gs ¼ 3
Res=ur, s
g , for εg e 0:85 ð13Þ
or
g , for εg > 0:85 ð14Þ
The Wen-Yu interphase exchange coefficient is,
K gs ¼ 3
½1 þ 0:15ðεgResÞ0:687 ð16Þ
The bulk viscosity λs is a measure of the resistance of
a fluid to compression, which is described with the help of the
kinetic theory of granular flows
λs ¼ 4
ffiffiffiffiffiffi
Θs
π
r
ð17Þ
The tangential forces due to particle interactions are summar- ized
in the term called solids shear viscosity, and it is defined
as
μs ¼ μs, col þ μs, kin þ μs, fr
ð18Þ
where the collision viscosity of the
solids μs,col is
μs, col ¼ 4
ffiffiffiffiffiffi
Θs
π
r
ð19Þ
At the packed state of the bed, the stresses are dominated by
interparticle friction rather than collisions and fluctuating
motion. This phenomenon is quantified by the term called frictional
viscosity
μs, fr ¼ ps sinðφÞ
2 ffiffiffiffiffiffiffi
I 2D
p ð20Þ
which contains the angle of internal friction φ. This expres-
sion of frictional viscosity is valid if the volume fraction
of solids is constant, which is reasonable in the dense
packed bed state of particles. The Gidaspow6 kinetic viscosity
is
μs, kin ¼ 10Fsd s
ffiffiffiffiffiffiffiffiffi
5 εs g 0, ssð1þessÞ
2
ð21Þ
μs, kin ¼ εsFsd s
ffiffiffiffiffiffiffiffiffi
ð22Þ
The solids pressure ps, which represents the normal force due
to particle interactions is given by
ps ¼ εsFsΘs þ 2Fsð1 þ essÞε2 s g0, ssΘs
ð23Þ
Fluctuation Energy Conservation of Solid Particles.
The solid phase models discussed above are based on two crucial
properties, namely the radial distribution func-
tion g0,ss and granular temperature Θs. The radial
distribu- tion function is a measure for the probability of
interparticle contact. The granular temperature represents the
energy associated with the fluctuating velocity of particles.
3
2
s þ τ ¼
sÞ : r 3 us þr 3 ðkΘs 3r 3ΘsÞ-γ Θs þφgs
ð24Þ
where τ Cs is defined in eq 5. The diffusion
coefficient of granular temperature kΘs according
to eq 6 is given by:
kΘs ¼ 150Fsd s
1þ 6
2
ffiffiffiffiffiffi
Θs
π
r
ð25Þ
g0, ss ¼ 1- εs
εs, max
γ Θs ¼
jgs ¼ -3K gsΘs ð28Þ
(41) Ranz, W. E.; Marshall, W. R. Chem. Eng. Prog.
1952a, 48, 141 –
146. (42) Ranz, W. E.; Marshall, W. R. Chem. Eng. Prog.
1952a, 48, 173 –
180.
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
An analytical discussion of the solid-phase properties can be found
in ref 43.
3 2. Forces on Discrete Particles. The coupling between the
continuous and discrete phases hasbeen developedin a UDF to take
into account the bubbling behavior of thebed. For an analytical
discussion of this section the reader is referred to the previous
work done by the authors in this aspect.31
Assuming a spherical droplet with material density of Fd
inside a fluid, the rate of change of its velocity can be expressed
as44
dud
Fcon
Fd
þ F υm ð29Þ
where f is the drag factor and τ u is the
velocity response time
τ u ¼ Fdd d
2
ð30Þ
There are several correlations for the drag factor
f in the literature.45-47 The one usedin thisstudy
is the correlation of Putnam47
f ¼ 1 þ Rer ð2=3Þ
6 for Rer < 1000 ð31Þ
f ¼ 0:0183Rer for 1000 e Rer <
3 105 ð32Þ
The second term on the right-hand side of the equation represents
the gravity and boyancy force, while the third term represents the
unsteady force of virtual mass, which is expressed as
F υm ¼ FconV d
2
ducon
dt -
dud
dt
ð33Þ
According to Kolev,48 if bubble three-phase flow (i.e., solid
particles in bubbly flow) is defined, two subcases are distin-
guished. If the volume fraction of the space among the solid
particles, if they were closely packed, is smaller than the liquid
fraction (in this case the Eulerian sand)
ε s < εs ð34Þ
εd ð35Þ
then the theoretical possibility exists that the particles are
carried only by the liquid. The hypothesis is supported if we
consider the ratio of the free setting velocity in gas and
liquid
wdg
wds
. 1 ð36Þ
Due to great differences between gas and liquid densities, the
particles sink much faster in gas than in a liquid. There- fore,
the drag force between gas and solid particles is zero,
and the dragforce between solid and liquid is computed for a
modified particle volume fraction εp
εp ¼ εd
εs þ εd
μeff , con ¼ 1- εp
εdm
-1:55
ð38Þ
If the volume fraction of the space among the solid particles, if
they were closely packed, is larger than the liquid fraction
ε s > εs ð39Þ
εdg ¼ εdð1-εs=ε s Þ ð40Þ
are surrounded by gas and the drag force can be calculated between
one single solid particle and gas as for a mixture
εp ¼ εdg
εg þ εdg
ð41Þ
3.3. Reaction Kinetics. The reaction kinetics of biomass
pyrolysis is modeled using a two-stage, semiglobal model.49
The mechanism is illustrated in Figure 3. The mechanism utilizes
the Arrhenius equation which is
defined as
K i ¼ Ai expð-E i =RT Þ
ð42Þ
The values of the kinetic parameters were obtained by Chan et al.38
for the primary pyrolysis products, while the fourth and fifth
reactions were obtained from Liden et al.39 and Di Blasi,17
respectively. The choice of a different set of para- meters used in
the simulation was mainly done to predict as correctly as possible
the fast pyrolysis of wood. The kinetic parameters of the
three-step model of Chan et al.38 were used for the primary
products because, when coupled with sec- ondary reaction kinetics,
they can predict, at least qualita- tively, the correct behavior of
wood pyrolysis.22 However, the secondaryreaction kinetic constants
were taken from the work of Liden et al.39 and di Blasi17 because
these studies included secondary reaction effects that depend on
the con- centration of tar vapors from flash pyrolysis in the
porous matrix of the solid, something that is more suitable for the
current study. The elemental analysis of the pine wood used in the
experiments of Chan et al. can be found in refs 38 and 50.
The model associates, via a UDF, the reaction kinetics mechanism
with the discrete biomass particle injected in the fluidized bed.
The particle’s properties change according to the reaction
mechanism due to the phase transition pheno- mena. Momentum and
heat transfer on the particle are
Figure 3. Two-stage, semiglobal model.49
(43) Boemer, A.;Qi, H.; Renz, U. Int. J. Multiphas.
Flow 1997, 23 (5), 927 – 944.
(44) Crowe, C. T.; Sommerfeld, M.; Tsuji, Y. Multiphase Flows
with Droplets and Particles; CRC Press LLC: 1998.
(45) Schiller, L.; Naumann, A. Ver. Deut. Ing.
1933, 77 , 318. (46) Clift, R.; Gauvin, W. H.
Proc. Chemeca 1970, 1, 14. (47) Putnam, A.
ARS JNl. 1961, 31, 1467. (48) Kolev, N. I.
Multiphase Flow Dynamics 2. Thermal and Mecha-
nical Interactions, 2nd ed.; Springer: 2005.
(49) Shafizadeh, F.; Chin, P. P. S. ACS Symp. Ser.
1977, 43, 57-81. (50) Chan, W. R.; Kelbon, M.; Krieger,
B. B. Ind. Eng. Chem. Res.
1988, 27 , 2261 – 2275.
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
calculated according to the new condition in the UDF, and the
variables associated with it are updated in each time-step.
Intraparticle secondary reactions due to the catalytic effect of
char are taken into account, resulting in secondary vapor
cracking.
∂
ð43Þ
The boundary condition at the surface of the particle is given
by
hðT ¥ -T sÞ ¼ -keff
∂T
∂r
∂T
∂r
r ¼0
¼ 0 ð45Þ
The effective thermal conductivity keff and
effective speci- fic heat capacity
C p,eff are given by
keff ¼ kc þ jkw -kcjψw ð46Þ
C peff ¼ C pc
þ jC pw -C pc
jψw ð47Þ
The heat transfer coefficient is evaluated from the well- known
Ranz-Marshall41,42 correlation, when the particle is carried only
by the fluidizing gas
Nu ¼ hd p
¼ 2:0 þ 0:6Rep 1=2Pr1=3 ð48Þ
However, since the diameter of the biomass particle is smaller than
the diameter of the sand particles, a modi- fied Nusselt number is
used to calculate the heat transfer
coefficient according to the findings of Collier et al.,51
Nu ¼ 2 þ 0:9Rep, mf 0:62ðd p=d bÞ0:2
ð49Þ
where
μg
ð50Þ
4. Model Parameters
For the implementation of the model, certain parameters have been
quantified and assumptions have been made in order to provide, as
much as possible, an insight to the fast pyrolysis process in
bubbling beds.
(1) The particles used in the simulation were assumed to be totally
spherical, whereas theparticles usedin experiments can be found on
all sorts of shapes. The actual sphericity of the particles greatly
differs from 1. This would have an impact on the drag and virtual
mass forces and consequently on the trajectory of the particle
inside the reactor.
(2) The model assumes a plugflow profile at the inlet of the
reactor.
(3) The geometry of the reactor has been discretized using a
structured grid. The average side length of the computational cells
is about 1 mm, resulting in a total number of 10440 cells.
(4) The time-step used for the simulation was on the order of 10-5
s. The reason for this small time advancements was that the
computational algorithms in the UDF had to con- verge
simultaneously with the algorithms of FLUENT. The explicit central
difference scheme used for the discretization of the
heatdiffusionequation demands very small time-steps due to the
small radial discretization resulting from particles of
350 μm in diameter. For further analysis of the CFD code
structure together with the flow-chart and advantages and drawbacks
of the model, the reader is referred to the pre- viously published
work of the authors in this aspect.32
The simulation parameters are shown in Table 1.
5. Results
Table 1. Simulation Parameters
property value comment
biomass density, Fw 700 kg/m3 wood biomass particle
diameter, d p 350 μm fixed biomass specific
heat capacity, C pw 1500 J/(kg K) wood char
specific heat capacity, C pc 1100 J/kg K
char biomass thermal conductivity, kw 0.105 W/(m K)
wood char thermal conductivity, kc 0.071 W/(m K) char
superficial velocity, U 0 0.6 m/s
≈3U mf
gas density, Fg 1.138 kg/m3 nitrogen (303 K) gas
viscosity, μg 1.663 10
-5 kg/(m s) nitrogen (303 K) gas specific heat capacity,
C p,g 1040.67 J/(kg K) nitrogen (303 K) gas
thermal conductivity, kg 0.0242 W/(m K) nitrogen (303
K) solids particle density, Fs 2500 kg/m3 sand sand
specific heat capacity, C p,s 835 J/(kg K)
fixed sand thermal conductivity, ks 0.35 W/(m K) fixed
mean solids particle diameter, d s 440 μm
uniform distribution restitution coefficient, ess 0.9
value in literature initial solids packing, εs 0.6
fixed value static bed height 0.08 m fixed value bed width 0.04 m
fixed value heat of reaction ΔH = -255 kJ/kg
Koufopanos et al.52
(51) Collier, A. P.; Hayhurst, A. N.; Richardson, J. L.; Scott, S.
A. Chem. Eng. Sci. 2009, 59,
4613 – 4620.
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
together with the instantaneous position of the biomass particle
indicated by the black spot. The snapshots were taken for 1 s time
intervals, from the time of injection at 1 s until close to the
entrainment time of approximately 4 s. Figure 7 illustrates
thecomplete trajectory of theparticles for the three different drag
models. The residence time of the particles was finally determined
as 2.92, 3.3, and 2.6 s for the Gidaspow, Syamlal-O’Brien, and
Wen-Yu drag models, respectively.
One can observe that the residence time of the particles is
somewhat higher, though not unreasonable, compared to what the fast
pyrolysis process suggests, i.e., < 2 s. This is
mainly caused by the tendency of the particles to move toward the
wall of the reactor as it is shown in Figure 7 where gas velocities
tend to be much lower than at the central axis of the reactor. This
is valid for all the drag models compared in this study, however
the bubble distribution created from the Gidaspow drag model moved
the particle to the right-hand side of the reactor in contrast to
the Syamlal-O’Brien and Wen-Yu drag models, which moved the
particle on the left-hand side. The 2D nature of the simulation
excludes the mixing of the biomass particles in the z-direction of
thereactor,however thesamebehaviorwas also observed in the previous
papers by the authors,35,37
where 3D geometry was considered. The inclusion of the pyrolysis
vapors mass source in the simulation greatly dis- courage the use
of a 3D geometry since the simulation times approach the order of
months even with the use of 16 processors. Another phenomenon
thatis of great importance is the transverse mixing of the
particles. Despite the dom- inance of the motion in
the y-direction of the reactor, we can easily notice that the
particles have moved across the whole width of the bed
(x-direction) before their entrainment. This comes in great
agreement with the experimental study of Hoomans et al.,3
where they showed the validity of this phenomenon using the
positron emission particle tracking (PEPT) technique, and the
numerical study of Xu and Yu.53
Despite the fact that these studies were performed using 2D
geometries, the same phenomenon was also observed in the previous
numerical investigations performed by the authors31,35,37 where a
3D geometry was used.
5.2. Heat Transfer. Figure 8 shows the temperature rise
of the particles for the different drag models. The
temperature rise in the Gidaspow and Syamlal-O’Brien model appears
to be relatively similar, however a higher temperature rate is
observed for the Wen-Yu drag model, represented by a steeper
surface temperature profile at the first 0.1 s after the
Figure 4. Volume fraction of sand with instantaneous position
of the biomass particle, Gidaspow drag model.
Figure 5. Volume fraction of sand with instantaneous position
of the biomass particle, Syamlal-O’Brien drag model.
Figure 6. Volume fraction of sand with instantaneous position
of the biomass particle, Wen-Yu drag model.
Energy Fuels 2010, 24, 2133 – 2145 :
DOI:10.1021/ef901497b Papadikis et al.
particle injection. In thecase of theWen-Yu drag model, the
particle reaches the splash zone of the reactor much faster than in
the Gidaspow and Syamlal-O’Brien drag models. In this region, high
velocity gradients are dominant due to the eruption of bubbles, and
the slip velocity between the fluidizing gas and the particles is
high, resulting in a very high convective heat transfer
coefficient. This can be easily seen in Figure 9, where the heat
transfer coefficient becomes very large for the case of the Wen-Yu
model almost instantly. In the other two cases a certain amount of
time (≈0.3 s) is needed for the particles to experience the same
high heat transfer rates.
The constant value of the heat transfer coefficients, which is
close to 320 W/(m2 K), comes from the correlation of Collier
et al. in eq 49, which is appropriate for the heat
transfer between a fluidized bed of particles larger than the
injected particles. In our case the bed consists of particles of
440 μm in diameter, whereas the biomass particles are 350
μm in diameter. Collier et al.51 showed that when a particle
finds itself among fluidized particles of larger dia- meter, the
heat transfer coefficient appears to have a con- stant value
depending on the ratio of the diameter of the particles and the
minimum fluidization velocity of the bed. This is because the
conductive effect of the larger particles to the smaller ones is
negligible and convective effects are dominant. This approach is
used in the current study. There- fore, whenever the heat transfer
coefficient appears to have this constant value, it means that the
particle finds itself in a densely packedzone of sand particles.
Theothervalues of the heat transfer coefficient represent the
motion of the particle inside a bubble, or the splash zone, or the
freeboard of the reactor. This gives a good indication of the
region that the particle is instantly located.
The high heat transfer values, close to 700-750 W/(m2 K), that are
observed in all of the three diagrams clearly indicate the motion
of the particle close to the wall of the reactor, where the wall
heat transfer effects become more noticeable. In the current
simulation only theconvective effects from the wall were taken into
account andthe collision of the particles with the wall were
neglected, since the actual contact time of the particles
with the wall is extremely small. However, Figure 9 in conjunction
with Figure 7 clearly show the wall effect on the rise of the heat
transfer coefficient. This becomes even more noticeable when the
particle flies toward the outlet of the reactor and the heat
transfer coefficient drops significantly in all cases, only to rise
again in the actual outletof thereactor where thex-velocityof
thegasesincrease significantly due to the small diameter of the
outlet.
Figure 7. Particle trajectories inside the fluidized bed
reactor.
Figure 8. Surface and center temperatures of the
particles.
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The effect of the heating rates can be seen in Figure 10, where the
density drop due to the reaction mechanism is illustrated. The
Gidaspow and the Syamlal-O’Brien models appear to have the same
effect on the density drop of the particle, whereas the Wen-Yu
model has a more rapid effect due to the higher heat transfer rates
that appear during the simulation. From Figure 10 one canalso
observe theonset of pyrolysis, which comes close to 0.2 s,
where, according to Figure 8, the temperature is close to 750 K.
The density drop of the particles has a major effect on their
trajectory inside thereactor since their motion is heavily
dependentupon their density and consequently their mass that is
involved on the particle motion equations given in Section
3.2.
5.3. Particle Dynamics. Figure 11 shows the instantaneous velocity
components of the particles inside the reactor until their
entrainment time. All the drag models appear to have a similar
effect on the average velocity magnitude of the particles with some
exceptions regarding their instantaneous positions. For example,
the particle on the Wen-Yu case
appears to have more intense y-velocityfluctuations, and
this
is because, as it was discussed earlier, it reaches the
splash
zone of thereactor almost0.2 s fasterthan theotherparticles.
This high y-velocity fluctuation gave rise to the very
high
heat transfer coefficients that were observed earlier and
consequently the more rapid density drop of the particle.
Comparing Figures 8, 9, and 11. one can conclude that the
unstable splash zone of the reactor is the most desirable
region for fast pyrolysis. In other words, the violent
velocity
gradients that occur due to bubble eruption and sand
recirculation have a higher impact on the particles that
float
on the top of the bed, in contrast with the particles that
are
immersed deeply inside it. Also, the high velocity gradients
give rise to the virtual mass force that can greatly
contribute
to theviolent ejection of theparticles from thesand bedto the
freeboard of the reactor, thus making the elutriation pheno-
menon easier, when the density drop of the particles has
reached the desirable level. It has to be noted that for the
current simulation the
particles were considered to be totally spherical, something
that differs from reality. Also, shrinking and attrition
effects
were assumed not to play an important role and therefore
were neglected in the simulation. For the complete analysis
of the momentum transport model, the reader is referred to
the previous study of the authors,31 and for the modeling
of
the impact of shrinkage to ref 35. 5.4. Product Yields.
Figure 12 shows the final product
yields (vapors, gases, char) percentage by weight of original
wood. We canobserve that thedifferent drag models actually
have an impact on the final product yield of condensable
volatiles (vapors), char, and gases, while there is still a
small
percentage of wood that has not yet reacted. The final
product yields for the three cases are given in Table 2, and
the experimental data is given in Table 3. In general terms, we can
observe that there is a similarity
between the final vapors and the gases in the experiment and the
simulation. However there is a significant difference on
Figure 9. Heat transfer coefficient.
Figure 10. Density drop of the particles.
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DOI:10.1021/ef901497b Papadikis et al.
the final char content, and differences of up to 7.5% can be
observed. This is mainly due to the reaction kinetics mecha- nism
and not to the fluidized bed operation. Due to the lack
of analytic kinetic data regarding spruce fast pyrolysis, the
selection of kinetic data that would as closely as possible
Figure 11. Particle velocities inside the fluidized bed
reactor.
Figure 12. Product yields.
wood vapors char gases pyrolysis
temperature C
Gidaspow 3.5% 62% 20.5% 14.0% ≈525 Syamlal-O’Brien 2.0% 63%
20.8% 14.2% ≈525 Wen-Yu 6.4% 60% 20.0% 13.6%
≈528
Table 3. Experimental data and product yields
feedstock spruce
pyrolysis temperature 538 C
vapor residence time <0.93s
char 12.72
gases 15.58
vapors 68.65
organics 56.22
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match the behavior of a softwood like this was a necessity. The
kinetic data of Chan et al.38 refer to the pyrolysis of pine
wood, which belongs to the same softwood family. The
simulation results highly agree with data published in the
literature that make use the same reaction mechanism such
as the work of di Blasi.22 It has to be also noted that the
specific chemical kinetics represent the degradation of large
pine wood particles where differences on the percentages
of
Figure 13. Volume fraction of pyrolysis vapors, Gidaspow drag
model.
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cellulose, hemicellulose, and lignin as well as the different
amount and composition of inorganic matter lead to differ-
ent primary yields.18 Also, the heating rates that are com-
monly used in the laboratory for the determination of the
reaction kinetics of biomass cannot match the high heating
rates that are provided by a fluidized bed. The impact of the
different drag is mainly noticeable on
the final amount of wood that has not reacted. For the cases of
Gidaspow and Syamlal-O’Brien drag models, the differ- ence in the
final percentage of wood is relatively minor, whereas in the case
of the Wen-Yu drag model the differ- ence can be up to almost 4%.
This is explained by the faster entrainment of the biomass
particle, which in the case of Wen-Yu and Syamlal-O’Brien
models there is a difference of approximately 0.7s. However,
thehigher residencetime of the char particle inside the
reactor is not a desirable pheno- menon for fast pyrolysis due to
the catalytic effect of char, aiding the secondary cracking of the
vapors. It has to be noted that the extraparticle
secondarycrackingof the vapors is not taken into account in the
current simulation and only the intraparticle phenomena are
considered.
Figures 13-15 illustrate the evolution of volatiles in the reactor
during the pyrolysis of the biomass particle. The actual residence
time of the vapors comes close to 0.8 s, something that is
difficult to notice from the contour plots due to scale
limitations. This phenomenon comes in perfect agreement with the
experimental data where the vapor residence time was observed to be
less than 0.93 s. The different drag models, however, have a major
effect on the flow field of the vapors due to the different bubble
distribu- tion and consequently the fluidizing gas flow field that
interacts with the produced vapors. In the cases of the Gidaspow
and Syamlal-O’Brien drag models there is still a larger amount of
vapors inside the reactor (Figures 13 and 14), whereas in the case
of the Wen-Yu drag model the
amount of vapors left is approximately 1 order of magnitude
lower. As was mentioned earlier, this is due to the faster
entrainment of the biomass particles that consequently
stopped the production of vapors inside the reactor. The
simulation of the vapor flow field inside the reactor is one
of
the most important parameters in the operation of the
fluidized bed reactors for fast pyrolysis since it greatly
influences the final bio-oil yields.
6. Conclusions
models for granular flows available in the literature and
their
effect on the fast pyrolysis of biomass.Several conclusions can be
made regarding the complete fast pyrolysis process.
One can easily state that the different drag models certainly
have an impact on the trajectory of the biomass particle, the heat
transfer coefficient, and consequently on the degrada-
tion, the char, and the vapor residence time. The results
showed that in the case of the Wen-Yu drag model, the heat
transfer coefficient reached a maximum value of approxi-
mately 780 W/(m2 K) compared to the models of Gidaspow
and Syamlal-O’Brien, where the maximum values reached
750 and 650 W/(m2 K), respectively.This wasmainly observed because
of the fast movement of the particle toward the splash
zone of the reactor in the case of the Gidaspow and Wen-Yu
model. The residence time of the particle was greatly
affected
by this effect, since in that case the residence time was
reduced
by a maximum of 0.7 s when comparing Wen-Yu(3.6 s) and
Syamlal-O’Brien (4.3 s) models. In the case of the Gidaspow
model the residence time was determined at 3.9 s. This period of
time is of great importance in fast pyrolysis, where the
optimum residence time is less than 2 s. It was also shown
that
the trajectory of the particle was different in all three
cases,
however in all of them the particle moved toward the wall
of
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the reactor due to the dominant formation of the gas bubbles at the
central axis of the reactor. This phenomenon acts as a decele-
rating factor in theentrainmentof the particle since the fluidizing
gas velocities are much smaller close to the walls of the
reactor.
In the case of the final product yields, we can see that the
residence time of the particle is the factor that mainly defines
the outcome. The differencein the final char yieldbetween the
experiments and the simulation is mainly due to the reaction
kinetics mechanism and the differences between the two types of
wood (pine wood for the reaction kinetics and spruce in the
experimental procedure). However, there is a definite similar- ity
at the final closure of the system, where in almost all cases the
total conversion exceeded 95%, something that indicates that the
simulations are quite realistic in conjunction with the very
representative residence times of char and vapors. Quan-
titatively, the Gidaspow model predicted 62% vapors, 20.5% char,
and 14.0% gas occurring at a pyrolysis temperature of 525
C; in the Syamlal-O’Brien model, 63% vapors, 20.8% char, and
14.2% gas occurring at a pyrolysis temperature of 525 C;and
inthe Wen-Yu model, 60% vapors, 20.0% char, and 13.6% gas occurring
at a pyrolysis temperatureof 528C. The results were comparable to
the experimental data, which produced 68.65% vapors, 12.72% char,
and 15.58% gas occurring at a pyrolysis temperature of 538
C.
Despite the fact that significant differences between the drag
models were observed, it is still very difficult to say which one
gave the better prediction for various reasons mainly concern- ing
the running time limitations of the model and the post- processing
of the data. However, it was shown that the drag modelhas a
definite impact in thesimulationof fast pyrolysisin fluidized beds,
which can be quantified and examined.
Nomenclature
Ai = pre-exponential factor, 1/s C d = drag
coefficient, dimensionless C p = specific heat
capacity, J/kgK d i = diameter, m E =
activation energy, J/mol ess = restitution coefficient,
dimensionless
g = gravitational acceleration, m/s2
g0,ss = radial distribution coefficient, dimensionless
h = convective heat transfer coefficient, W/m2K I =
stress tensor, dimensionless I 2D = second invariant of
the deviatoric stress tensor,
dimensionless f = drag factor, dimensionless
F i = force, N/kg k = thermal conductivity,
W/mK kΘs = diffusion coefficient for granular energy, kg/sm
K gs = gas/solid momentum exchange coefficient,
dimen-
sionless
m = mass, kg Nu = Nusselt number
p = pressure, Pa Pr = Prandtl number R = universal
gas constant, J/molK Re = Reynolds number, dimensionless t =
time, s T = temperature, K U 0 = superficial
gas velocity, m/s ui = velocity, m/s V =
volume, kg/m3
wi = free settling velocity, m/s
Greek Letters
γΘs = collision dissipation of energy, kg/s3m ΔH =
heat of reaction, J/kg εi = volume fraction,
dimensionless Θi = granular temperature, m2/s2
λi = bulk viscosity, kg/sm Fi = shear
viscosity, kg/ms Fi = density, kg/m3
τ υ
= velocity response time, s τ = stress tensor, Pa
φgs = transfer rate of kinetic energy, kg/ms3
ψ = mass fraction
Subscripts