ef drag models fast pyrolysis
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drag models for fast pyrolsisTRANSCRIPT
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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57 , 2395 – 2410. (5) Li, J.; Kuipers, J. A. M. Chem. Eng. Sci. 2003, 58, 711 – 718. (6) Gidaspow, D. Multiphase Flow and Fluidization: Continuum and
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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.
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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.
Energy Fuels 2010, 24, 2133 – 2145 : 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
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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.
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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
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].
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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
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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.
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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.
Energy Fuels 2010, 24, 2133 – 2145 : 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
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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.
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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
Energy Fuels 2010, 24, 2133 – 2145 : DOI:10.1021/ef901497b Papadikis et al.
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