CFD Simulation of a Bubbling Fluidized Bed Gasifier Using a Bubble

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CFD simulation of a bubbling fluidized bed gasifier using a bubble-based drag model Guangbin Yu, Bing Dai, Juhui Chen, Di Liu, and Lei Zhao Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/ef501134e • Publication Date (Web): 19 Aug 2014 Downloaded from http://pubs.acs.org on August 25, 2014

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CFD simulation of a bubbling fluidized bed gasifier using a bubble-based drag model Yu Guangbin1.2.3, Dai Bing 2, Chen Juhui1.2 , Liu Di 2, Zhao Lei2 (1 The higher educational key laboratory for Measuring & Control Technology and Instrumentations of Heilongjiang Province, Harbin University of Science and Technology, Harbin, 150080, China; 2 School of Mechanical Engineering, Harbin University of Science and Technology, Harbin, 150080, China 3 Harbin Institute of Technology, Harbin, 150001, China)

ABSTRACT Wood gasification in a fluidized bed reactor is regards as a promising technique to efficiently exploit the energy from biomass, which has attracted great attentions. To further understand complex fluid mechanics and thermal behaviors of wood during the gasification process, a multiphase reactive model is presented and a CFD simulation of wood gasification in a bubbling fluidized bed gasifier is implemented. To account for the impact of bubble-structure on the gas-solid interaction, a revised bubble-based EMMS (energy minimization multi-scale) drag model is developed and incorporated into a two-fluid model. Flow behaviors and reactive characteristic in a bubbling fluidized bed gasifier are analyzed. Profiles of temperature and concentration of gas and solid phase are also obtained. By comparisons of the outlet gas species concentrations, the prediction by a revised bubble-based EMMS drag model agrees better with experimental result than that by the conventional drag model.

Keywords: Computational fluid dynamic; Bubble-based drag model; Bubbling fluidized bed; Wood gasification 1

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1. INTRODUCTION The gasification of biomass is a thermo-chemical process by partially oxidizing solid biomass at high temperatures into gaseous energy carriers. The gas produced from the gasification is upgraded into syngas, which can be applied to produce the various liquid fuels and organic chemicals[1]. Compared to combustion, gasification can produce power and heating more efficiently[2]. This technology also has the ability of supporting the base load supply and avoids the installation of elaborate electrical networks, which has attracted great attentions. Several studies have also been conducted on the development of biomass gasification applications[3-6].Matsuoka et al.[7]developed a new high-efficiency biomass gasification method using a circulating dual bubbling fluidized bed system based on the concept of separation of combustion region from gasification, which lengthened the solid residence time in both the gasification and combustion zones. Mastellone et al.[8]investigated the co-gasification of wood, coal and plastic waste in a bubbling fluidized bed reactor and evaluated the performance of the gasifier. The results indicated that the wood enhanced the formation of the solid phase including nearly pure carbon and decreased the presence of heavy hydrocarbons in the syngas. Recently, with the advancement of computer’s performance and numerical simulation method, computational fluid dynamics (CFD) is widely applied to investigate complex phenomena in multiphase flow and thermo-chemical conversion, which is helpful for optimizing the design of biomass gasifier and its operation with minimal costs [9,10]. Liu et al.[11] performed simulations of biomass gasification in a circulating fluidized bed by means of an unsteady-state three-dimensional CFD model. It was found that the char combustion product distribution coefficient had a minor impact on the outlet gas components. Xue et al.[12] presented a multi-fluid CFD model of biomass gasification in polydisperse fluidized bed gasifiers. Continuously variable particle density due to 2


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volatilization of lighter components and chemical reactions was implemented to take into account the evolution of the physical properties of reacting particles. It was shown that the residence time of char in the bed and freeboard influenced the char gasification and thus the outlet gas compositions. Papadikis et al.[13] investigated the biomass fast pyrolysis and mass, heat and momentum transport in the reactors by means of CFD model. Gerber et al.[14]simulated the wood gasification in a bubbling fluidized bed reactor using an Eulerian multiphase model and evaluated some operating parameters. The results implied that bed temperature was one of the most influential factors. Oevermann et al.[15] employed the Euler-Lagrange approach to simulate the wood gasification in a bubbling fluidized bed. It was found that the predictions for different feeding rates of wood showed qualitatively a correct change in fluidization behaviors. Bubbles in bubbling fluidized beds play a similar role as clusters in fast fluidized beds. This meso-scale structure has a great influence on the gas-solid inter-phase drag force. Wang et al.[16] revised the energy minimization multi-scale (EMMS) model using an implicit cluster diameter expression and applied it to the simulation of bubbling fluidized beds. Chalermsinsuwan et al.[17] employed a simplified EMMS model to calculate inter-phase drag coefficient and performed a simulation of Geldart A particles in a thin bubbling fluidized bed. The above models derive from the calculation of drag coefficient in a fast fluidized bed and are unsuitable for the simulations of bubbling fluidized beds. Lv et al.[18] established a bubble-based drag correlation by solving seven local structural parameters ,which were determined by seven independent equations including empirical correlation and the conservation equations of mass and momentum. Shi et al.[19] extended the multi-scale approach to the gas-solid bubbling fluidization and developed a bubble-based drag model. In this model, clusters of the original EMMS method were replaced by bubbles. This model was further 3


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verified by compassion with empirical relations and experimental data. Wang et al.[20,21] and Zhao et al.[22] applied the bubble-based EMMS model to carry out simulations of chemical looping reforming system and methanol to olefins fluidized bed reactor respectively. However, these models used the global hydrodynamic parameters to derive the correlation between drag coefficient and voidage, and neglected the effect of local velocity on the heterogeneity. Nikolopoulos et al.[23] pointed out that the heterogeneity of system depended on not only the void fraction but also local velocities. In the current study, a bubble-based EMMS drag model is revised to consider the effect of bubbles in the reactor. Meanwhile, a multiphase reactive model is incorporated to a two-fluid model to investigate wood gasification processes in a bubbling fluidized bed gasifier. Both the pyrolysis and gasification reactions are accounted for. Simulated gas compositions at the exit are validated against experimental results. The distributions of temperature and gas species concentration are also predicted.

2. MATHEMATICAL MODEL 2.1. Gas–solid hydrodynamics A two-fluid model is applied in the current study. The particle phases are assumed to be smooth and inelastic spheres. Kinetic theory of granular flow is employed for closure, as reviewed by Gidaspow[24]. Detailed governing equations and constitutive relations are listed in Table 1. The continuity equations for gas and particle phases are given by eqs.(T1-1) and (T1-2). The balance equations of momentum of the gas and particle phases are described by eqs.(T1-3) and (T1-4), where β and τ represent the inter-phase drag coefficient and the stress tensor. The energy conversion equations are expressed by eqs.(T1-5) and (T1-6). The heat exchange coefficient between gas and particles hgm is written as follows: 4


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hgm =

6 k g ε s ε g Nu d s2

(1)

where Nu takes the expression proposed by Gunn[25]: Nu = ( 7 − 10ε g + 5ε g2 )(1 + 0.7 Re0.2 Pr1 3 ) + (1.33 − 2.4ε g + 1.2ε g2 ) Re0.7 Pr1 3

(2)

To characterize the fluctuating energy of particles, granular temperature θ is introduced as θ=/3, where C denotes the solid fluctuating velocity. The conservation equation of granular temperature is given by eq.(T1-8). To close the governing equations, constitutive relations are required. The stress tensors of gas and solid phase are expressed by eqs. (T1-9) and (T1-10). At a high solid volume fraction, the closely packed particles are influenced by sustained contact with multiple neighbors. Here, the friction stress model developed by Srivastava and Sundaresan[26] is selected to consider the frictional contribution. 2.2 A revised bubble-based drag coefficient model Drag interactions between the gas and solid phase play a crucial role in the momentum conversion equation of individual phase. Shi et al.[19]proposed a bubble-based EMMS model and treated the bubble phase as the meso-scale structure. The local flow is separated into three sub-systems: bubble phase, emulsion phase and interface. A bubble-based drag coefficient consists of the contributions from bubble phase and emulsion phase, and is expressed as follows:

β bubble −EMMS =

ε g2 Fgs ε2 = g [(1 − δ b )ne Fde + δ b nb Fdb ] U slip U slip

(3)

where ne and nb denote the number of particle and bubble per unit volume. δb represnts the holdup of bubble. Fde and Fdb are the inter-phase forces in emulsion phase and acting on bubble phase. These structural parameters are obtained by solving a set of nonlinear equations in Table 2. Detailed parameters can be found in Wang et al.[21]. 5


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Here, it is emphasized that the global operating parameters (Ug, Gs) in the original bubble-based EMMS model are replaced by the local variables (ug, us, εg) in the computational cell. In the simulation of unsteady flow, local dynamic parameters are more reasonable to determine the drag coefficient in the grid. The procedure of the solution of drag coefficient is shown in Figure 1. To characterize the heterogeneous feature in a bubbling fluidized bed, a heterogeneous index Hd is introduced.

Hd =

β bubble −EMMS β Wen − Yu

(4)

where the expression of βWen-Yu is given by[27]: 3 4

β Wen-Yu = Cd

ρg (1 − ε g ) ug − us ds

ε g−2.65

(5)

The 3D surface plots of Hd with the local voidage and velocities are shown in Figure 2. It can be found that Hd shows a roughly exponential growth with the increasing voidage. At different superficial velocities, there is an obvious discrepancy in the heterogeneous index, although the change of the shape is not evident. Hence, the variation of Hd depends on not only local voidage, but also local velocities The drag coefficient model of Ergun is selected at the voidage of εg 0.8 4 d  s β = (1 − ε g ) ρg ug − us (1 − ε g ) 2 µg  ε g ≤ 0.8 150 +1.75 2  ε g ds ds 

(12)

Compared to the simulated results with consideration of bubble effects, the prediction by the Gidaspow model has a relatively obvious deviation from the measured data. The maximum relative error reaches more than 40%. As meso-scale structures, bubbles result in a reduction of gas-solid inter-phase drag and improve the gas-solid mixing and heterogeneous reactions. The concentrations of CO and H2 are promoted, which agrees better with the measured data. Hence, it is necessary to take into account the multi-scale effects on the drag in a bubbling fluidized bed. Figure 6 demonstrates the distribution of instantaneous solid volume fractions in bubbling fluidized beds. From Figure 6(a), (b) and (c), we can observe a similar distribution of solid concentration. Small bubbles form near the bed distributor. With coalescence and growth, the bubbles pass through the bed and break up at the bed surface. However, the difference among them is obvious. Compared to char 2 volume fraction, char 1 volume fraction appears higher at the bottom of bed, which is attributed to that char 1 has a bigger particle diameter. This indicates that char 1 tends to react with O2 and more char 2 involves in the C-H2O and C-CO2 reactions Figure 7 shows the instantaneous gas species concentration in the quasi-steady state at 15s. At 10


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the bottom region of reactor, the reactant O2 displays a higher concentration. With the height increased, the concentration of O2 is depleted. This indicates the combustion reaction mainly occurs at the bottom of reactor. When H2O and wood are injected into the reactor, there is the formation of local high volume fractions of CH4 and H2 near the fuel feed inlet owing to the wood pyrolysis. With the increasing height and wood gasification in progress, the CO2 concentration is reduced and the concentrations of CH4 and H2 are increased, which implies that the gasification reactions dominate at the upper section of bed. Figure 8 displays instantaneous distributions of gas and solid temperature in the quasi-steady state at 15s. It can be seen that there is a clear discrepancy of temperature between the bed regime and the freeboard area. The heat released from the combustion reaction leads to an increase of gas temperature. Near the fuel feed inlet, the temperature has a drop owing to the pyrolysis process of wood. With the oxygen consumed, the gasification reactions become dominate and the temperature is gradually reduced. The temperature of char 1 and char 2 has a similar profile. There is a low wood temperature region near the feed inlet, which is as a result of that the inlet wood temperature is set at 423K. Lateral profiles of time-averaged solid concentration and gas velocity are shown in Figure 9. It can be found that at the 0.15m height from the distributor, the lateral profile of solid volume fraction is relatively flat. The gas velocity near the fuel inlet reaches 1.2m/s, which results in a slight decrease of solid volume fraction at the location. With the height increased, the lateral discrepancy of solid volume fraction becomes significant. The internal recirculation flow of particles forms in the bed. The gas velocity appears a high value at the center zone and decreases towards the wall. Figure 10 shows the time-averaged distribution of concentration of char 1 and char 2 along the 11


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lateral direction at three different heights. Generally speaking, char 1 has a similar trend as char 2. There is a low concentration at the center region and a high value near the wall. However, for the profiles at different heights, the difference between them can be distinguished. At the height of 0.4m, the concentration of char 2 is significantly higher than that of char 1.This is due to that the particles with a small diameter are easier to be carried by gas. With the descending height, the discrepancy of lateral profiles becomes small. The concentrations of char 1 and char 2 tend to be uniform, which is related to the distribution of bubbles. The lateral distributions of molar fractions of CH4 and H2 at different heights are shown in Figure 11. It can be observed that both the concentrations of CH4 and H2 show a similar profile. At the bottom of bed, amounts of CH4 and H2 are consumed by oxidation reactions and the concentrations are very low. Due to the pyrolysis of wood near the feed inlet, CH4 and H2 at the left side appear a high concentration. With the height increased and the oxygen depleted, the fractions of CH4 and H2 are improved. The existing bubbles in the bed and the effect of fuel inlet result in the non-uniform lateral profiles of CH4 and H2 concentrations. Figure 12 shows the lateral distribution of molar fractions of CO, CO2 and H2O at different heights. The wood pyrolysis produces a lot of wood gas, which leads to a higher molar fraction of CO and H2O near the fuel inlet. The profile of CO concentration is almost consistent with those of CH4 and H2, which strongly depend on the degree of oxidation reaction. For the concentration of CO2, the discrepancy at different heights is apparent. At the bottom of reactor, it appears a clear asymmetry owing to the effect of fuel feed inlet and combustion reactions of char and CO. With the oxygen depleted, the non-uniformity of lateral profile of CO2 concentration becomes weak. The distribution of H2O concentration is greatly influenced by the feed inlet. A high volume fraction occurs near the feed inlet. At the height of 0.75m, the lateral profile of H2O becomes relatively flat. 12


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4. CONCLUSION A revised bubble-based drag coefficient model is developed to consider the impact of bubbles and incorporated into the two-fluid model. A multiphase reactive model is presented including wood pyrolysis, homogeneous reactions and heterogeneous reactions. CFD simulations of wood gasification in a bubbling fluidized bed reactor are carried out. Compared to the conventional drag model, a revised bubble-based drag model can predict better results with experimental data. Profiles of temperature and concentrations of gas components and solid phase are also obtained. It is found that oxidation reactions dominate at the bottom of gasifier and the bubbles have a great influence on the distribution of particles and gas species concentration. In the further work, the effect of bubbles on chemical reactions needs further consideration and a three-dimensional simulation is expected to reflect the real bubble behavior in the reactor.

AUTHOR INFORMATION Corresponding Author *Telephone: +0451-8639-0550. Fax: +0451-8639-0550. E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was financially supported by Program for New Century Excellent Talents of Heilongjiang No. 1252-NCET-017, the Key Program of National Natural Science Foundation of Heilongjiang No.ZD201309, and Project supported by the Major International Joint Research Program of China (Grant No. 2014DFA70400) , the Key Program of

the higher educational key

laboratory for Measuring & Control Technology and Instrumentations of Heilongjiang Province. This information is available free of charge via the Internet at http://pubs.acs.org/. 13


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NOMENCLATURE a

acceleration [m s-2]

b

stoichiometric factor

CD drag coefficient of a single particle d

particle diameter [m]

db

bubble diameter [m]

D

diffusivity [m2 s-1]

e

restitution coefficient

fb

ratio of gas in the bubble phase to that in total

E activation energy [KJ mol-1] F force acting on each particle or cluster [N] Fde the drag force in the emulsion phase per unit volume Fdb the drag force acting on the bubble per unit volume g0 radial distribution function g h

gravity [m s-2] heat-transfer coefficient [W m-2 K-1]

k0 pre-exponential factor [mol1-nm3n-2 s-1] ks conductivity of fluctuating energy [kg m-1 s-1] ne

the number of particle in the emulsion phase per unit volume

nb the number of bubble per unit volume Nu

Nusselt number

Ns energy dissipation [W kg-1] p

fluid pressure [Pa] 14


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R universal gas constant [J mol-1K-1] Re Reynolds number S

mass source term [kg m-3 s-1]

Sc

turbulent Schmidt number

T

temperature [K]

u

velocity [m/s]

U

superficial velocity [m s-1]

Umf minimum fluidizing gas velocity [m s-1] Use

superficial slip velocity in emulsion phase [m s-1]

Usb

superficial slip velocity between bubble and emulsion [m s-1]

Yi

mole fractions of gas species

Greek letters

β

drag coefficient [kg m-3 s-1]

γ

collisional energy dissipation [kg m-1 s-3]

ε

volume fraction

θ

granular temperature [m2 s-2]

λ

thermal conductivity [m2 s-2]

µ

viscosity [Pa.s]

ρ

density [kg m-3]

τ

stress tensor [Pa]

δ

bubble holdup

Subscripts b

bubble phase

e

emulsion phase 15


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g

gas phase

p

particle

s

solid phase

w

wall

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5554-5563 [12] Xue Q, Fox RO. Multi-fluid CFD modeling of biomass gasification in polydisperse fluidized-bed gasifiers. Powder Technol. 2014,254,187-198 [13] Papadikisa K, Gub S, Bridgwater AV. CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors. Part B Heat,momentum and mass transport in bubbling fluidised beds. Chem Eng Sci. 2009,64,1036-1045 [14] Gerber S, Behrendt F, Oevermann M. An Eulerian modeling approach of wood gasification in a bubbling fluidized bed reactor using char as bed material.Fuel 2010,89, 2903-2917 [15] Oevermann M, Gerber S, Behrendt F. Euler–Lagrange/DEM simulation of wood gasification in a bubbling fluidized bed reactor.Particuology 2009,7,307-316 [16] Wang JW, Liu YN. EMMS-based Eulerian simulation on the hydrodynamics of a bubbling fluidized bed with FCC particles. Powder Technol .2010. 197, 241-246 [17] Chalermsinsuwan B, Gidaspow D, Piumsomboon P. Two- and three-dimensional CFD modeling of Geldart A particles in a thin bubbling fluidized bed: Comparison of turbulence and dispersion coefficients. Chem Eng J. 2011.171, 301-313 [18] Lv XL, Li HZ, Zhu QS. Simulation of gas-solid flow in 2D/3D bubbling fluidized beds by combining the two-fluid model with structure-based drag model. Chem Eng J. 2014. 236,149-157 [19] Shi ZS, Wang W, Li JH. A bubble-based EMMS model for gas–solid bubbling fluidization. Chem Eng Sci. 2011. 66, 5541-5555 [20] Wang S, Lu HL, Li D, Tang YJ. Simulation of the Chemical Looping Reforming Process in the Fuel Reactor with a Bubble-Based Energy Minimization Multiscale Model. Energy Fuels 2013, 27, 5008−5015 [21] Wang S, Yan LM, Zhao FX, Lu HL, Sun LY, Zhang QH. Numerical simulation of hydrogen production via chemical looping reforming in interconnected fluidized bed reactor. Ind. Eng. Chem. Res. 2014, 53, 4182-4191 [22] Zhao Y, Li H, Ye M, Liu Z. 3D Numerical Simulation of a Large Scale MTO Fluidized Bed Reactor. Ind. Eng. Chem. Res. 2013, 52, 11354-11364 [23] Nikolopoulos A, Papafotiou D, Nikolopoulos N, Grammelis P, Kakaras E. An advanced EMMS scheme for the prediction of drag coefficient under a 1.2MWth CFBC isothermal flow-Part I: numerical formulation, Chem. Eng. Sci. 2010,65, 4080-4088. [24] Gidaspow D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Description, Academic 17


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Table Captions: Table 1 Governing equations and constitutive correlations used in the model Table 2 A revised bubble-based EMMS drag coefficient model Table 3 Reaction rates used in the simulation Table 4 Fixed gas composition after pyrolysis Table 5 Kinetic parameters for the heterogeneous gasification reactions Table 6 Conditions and parameters for numerical simulation

Figure Captions: Figure 1 Procedure of a revised bubble-based EMMS drag model Figure 2 The surface plots of the heterogeneity index as a function of local voidage and superficial velocity Figure 3 Structure scheme of a 2D bubbling fluidized bed gasifier Figure 4 Axial profiles of solid concentration with different grids Figure 5 Comparisons of simulation results and experimental data Figure 6 Instantaneous solid concentration in bubbling fluidized beds Figure 7 Instantaneous distributions of gas species concentration at 15.0s Figure 8 Instantaneous distributions of gas and solid temperature at 15.0s Figure 9 Lateral profiles of time-averaged solid concentration and gas velocity Figure 10 Time-averaged distributions of concentrations of char 1 and char 2 along the lateral direction Figure 11 Time-averaged distributions of molar fractions of CH4 and H2 along the lateral direction Figure 12 Time-averaged distributions of molar fractions of CO, CO2 and H2O along the lateral direction

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Table 1 Governing equations and constitutive correlations used in the model ___________________________________________________________________________________________ 1. Continuity equations (g=gas phase, gas species i=1, 2, …ng, m=particle phase, m=1, 2, …ns): n

ns g ∂ (ε g ρg ) + ∇ ⋅ (ε g ρg u g ) = ∑∑ Sim ∂t i =1 m =1

(T1-1)

n

g ∂ (ε m ρ m ) + ∇ ⋅ (ε m ρ m u m ) = ∑ Sim ∂t i =1

(T1-2)

2. Momentum conservation equations(g=gas phase, gas species i=1, 2, …ng, m=particle phase, m=1, 2, …ns): n

ns ns g ∂ (ε g ρ g u g ) + ∇ ⋅ (ε g ρ g u g u g ) = −ε g ∇p + ε g ∇ ⋅τ g + ε g ρ g g − ∑ β gm (u g − u m ) + ∑∑ Sim u i ∂t m =1 i =1 m =1

(T1-3)

n

ns g ∂ (ε m ρ m u m ) + ∇ ⋅ (ε m ρ m u m u m ) = −ε m ∇p + ε m ∇ ⋅τ m + ε m ρ m g + β gm (u g − u m ) + ∑ β sm (u s − u m ) − ∑ Sim u i ∂t s =1,s ≠ m i =1

(T1-4)

3. Energy conservation equations(g=gas phase, gas species i=1, 2, …ng, m=particle phase, m=1, 2, …ns):: n

n

n

g s s ∂ (ε g ρ g c gp Tg ) + ∇ ⋅ (ε g ρ g c gp u g Tg ) = ∇ (λg ∇ Tg ) + ∑ h gm (Tm − Tg ) − ∑ ∑ Sim ∆H gi ∂t m =1 i =1 m =1

(T1-5)

n

g ∂ (ε m ρ m c m Tm ) + ∇ ⋅ (ε m ρ m c m u m Tm ) = ∇ ( λm ∇ Tm ) + h gm (Tg − Tm ) + ∑ Sim ∆ H gi ∂t i =1

(T1-6)

4 Species transport equations: ns g µg ∂ (ε g ρ g Yg,i ) + ∇ ⋅ (ε g ρg u g Yg,i ) = ∇ ⋅ [ε g ( ρg D g,i + )∇ ⋅ Yg,i ] + ∑ Sij + ∑ Sim ∂t σY j=1,i ≠ j m =1 n

(T1-7)

5. Granular temperature conservation equations

3 ∂ [ (ε m ρ mθ m ) + ∇ ⋅ (ε m ρ mθ m u m )] = (τ m : ∇ ⋅ u m ) + ∇ ⋅ (k sm ∇θ m ) − γ m − 3β gmθ m (T1-8) 2 ∂t 6. Stress tensor

2 3

τ g = µg [∇u g + ∇u gT ] − µg∇ ⋅ u g 2 3

τ m = −p m I + µ m [∇u m + ∇u Tm ] − µm∇ ⋅ u m

(T1-9) (T1-10)

___________________________________________________________________________________________

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Energy & Fuels

Table 2 A revised bubble-based EMMS drag coefficient model ___________________________________________________________________________________________ 1. Balance equations

ε g = δ b + (1 − δ b )ε e U g = δ bU b + (1 − δ b )U ge

(T2-1) (T2-2)

U s = (1 − δ b )U pe

(T2-3)

εe 1− εe

(T2-4)

2. Superficial slip velocity U se = U ge − U pe

U sb = (U b − U e )(1 − δ b )

(T2-5)

3. Equation for particles force balance in the emulsion phase

[150

(1 − ε e )2 µg

εd

2 e s

+

7 (1 − ε e ) ρgUse Use ] 2 = (1 − ε e )( ρs − ρg )( g + ae ) ε e ds εe 4

(T2-6)

4. Equation for force balance on the bubbles phase

πd b2 1 π Cdb ρ eU sb2 = d b3 ( ρ e − ρ g )( g + ab ) 4 2 6

(T2-7)

5. Accelerations a b − ae =

δ 2 ( ρs − ρg ) g C b (1 − ε e )δ b ρ e

(T2-8)

1 + 2δ b ) 1− δb

(T2-9)

C b = 0.5(

δ2 =

(1 − ε g ) 2 ε g 4 1 + 4(1 − ε g ) + 4(1 − ε g ) 2 − 4(1 − ε g )3 + (1 − ε g ) 4

(T2-10)

6. Stability criterion by minimization of the energy dissipation by drag force ρg U se2 3 N s = Cde U + f U ( g + ab ) → min 4 ρs ds ge b g

(T2-11)

7. Number density of particles in the emulsion phase and bubbles

ne =

(1 − δ b )(1 − ε e ) π ds3 / 6 21


(T2-12)

Energy & Fuels

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nb =

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δb

(T2-13)

π d b3 / 6

8. Equations for drag force of dense phase and inter-phase

(1 − ε ) µ 1 7 1 2 1 Fde = π ds2 ρg [200 3 e g + ]U 8 ε e ds ρg U se 3 ε e3 se  0.125π d b2 ρe (1 − δ b )−0.5 38Reb−1.5 U sb U sb  Fdb =  0.125π d 2 ρ (1 − δ )−0.5 [2.7 + 24 Re−1 ] U U b e b b sb sb 

(T2-14)

Reb ≤ 1.8 (T2-15)

Reb > 1.8

___________________________________________________________________________________________

Table 3 Reaction rates used in the simulation Products

k0,i (1/s)

Ei(kJ/mol) 4

1.43×10 7.38×105 4.13×106

Wood gas Char Tar

88.6 106.5 112.7

Table 4 Fixed gas composition after pyrolysis Component

Weight fraction

CO CO2 H2 H2O CH4

0.61891 0.19787 0.02444 0.05842 0.10036

Table 5 Kinetic parameters for the heterogeneous gasification reactions Reaction rates (mol/(cm2 s))

Reaction kinetics constants

k2 = [kr−1 + kd−1 ]−1  11200  kr = 1.04 ×103 exp  −  Ts  

R2 = k2 ⋅ CO2

kd = S h Dg / d s

R3 = k3 ⋅ CCO2

k3 = 3.42 exp(

−15600 ) Ts

R4 = k4 ⋅ CH 2O

k4 = 3.42 exp(

−15600 ) Ts

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Energy & Fuels

k5 = 3.42 × 10 −3 exp(

R5 = k5 ⋅ CH 2

−15600 ) RTs

Table 6 Conditions and parameters for numerical simulation Parameter

Experiments

Simulations

Unit

Particle density(char1/char2/wood ) Particle diameter(char1/char2/wood ) Reactor height Reactor diameter

450/450/585 2.0/1.5/4.0 1.1 0.095～0.134

kg/m3 mm m m

Gas diffusivity

--

Air velocity at the bottom inlet Inlet air temperature Fuel velocity at the side wall (water/wood) Inlet temperature of fuel(water/wood) Inlet volume fraction of wood Initial solid volume fraction(char1/char2) Initial temperature Wall temperature Restitution coefficient of particle– particle Restitution coefficient of particle– wall

0.25 670

450/450/585 2.0/1.5/4.0 1.1 0.095～0.134 CH4(0.2064),H2(0.634),CO(0.18),CO2(0.138 ) H2O(0.218),O2(0.178),N2(0.15) 0.25 670

0.079/0.00035

0.079/0.00035

m/s

423/423 0.325 0.325/0.325

423/423 0.325 0.325/0.325

K /

1020 970 --

1020 970

K K

0.95

--

0.9

--

--

23


cm2/s m/s K

/

Energy & Fuels

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Figure 1 Procedure of a revised bubble-based EMMS drag model

Figure 2 The surface plots of the heterogeneity index as a function of local voidage and superficial velocity

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Energy & Fuels

Figure 3 Structure scheme of a 2D bubbling fluidized bed gasifier

Figure 4 Axial profiles of solid concentration with different grids

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Energy & Fuels

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Figure 5 Comparisons of simulation results and experimental data

21s

22s 23s 21s 22s 23s 21s 22s 23s (a)Solid phase (b)Char1 (c)Char 2 Figure 6 Instantaneous solid concentration in bubbling fluidized beds

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Energy & Fuels

Figure 7 Instantaneous distributions of gas species concentration at 15.0s

(a)Gas (b)Char1 (c)Char2 (d)Wood Figure 8 Instantaneous distributions of gas and solid temperature at 15.0s

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Energy & Fuels

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Figure 9 Lateral profiles of time-averaged solid concentration and gas velocity

Figure 10 Time-averaged distributions of concentrations of char 1 and char 2 along the lateral direction

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Energy & Fuels

Figure 11 Time-averaged distributions of molar fractions of CH4 and H2 along the lateral direction

Figure 12 Time-averaged distributions of molar fractions of CO, CO2 and H2O along the lateral direction

29


CFD Simulation of a Bubbling Fluidized Bed Gasifier Using a Bubble

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