Multi-fluid Modeling Biomass Fast Pyrolysis in the Fluidized-Bed

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Multi-fluid Modeling Biomass Fast Pyrolysis in the Fluidized Bed Reactor Including Particle Shrinkage Effects Hanbin Zhong, Juntao Zhang, Yuqin Zhu, and Shengrong Liang Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b00914 • Publication Date (Web): 18 Jul 2016 Downloaded from http://pubs.acs.org on July 19, 2016

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Multi-fluid Modeling Biomass Fast Pyrolysis in the Fluidized Bed Reactor Including Particle Shrinkage Effects Hanbin Zhong*, Juntao Zhang, Yuqin Zhu, Shengrong Liang School of Chemistry and Chemical Engineering, Xi'an Shiyou University, Xi'an, Shaanxi, 710065, China

Abstract The fast pyrolysis of biomass in a bubbling fluidized bed reactor was simulated with the multi-fluid model combing the variable particle density and diameter model based on the mass conservation at the particle scale. Different particle shrinkage effects on the reactor performance were investigated through changing the apparent density of char species. The detailed distributions of particle density and diameter in the reactor and entrained out of the system were revealed. The results demonstrate that the reactor performance including the particle density and diameter distribution, entrainment behavior, biochar composition and yield, and biomass conversion are dramatically affected by the particle shrinkage effects. The average particle density increases while the average particle diameter decreases with the increase of char density which means more intense shrinkage. Weaker shrinkage effect leads to stronger entrainment behavior, larger biochar yield and mass fraction of biomass in biochar, and lower biomass conversion.

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1. INTRODUCTION With the rapid increase of global energy demand and environmental and sustainability challenges, the renewable biomass fuels have gradually been considered as an efficient option to replace conventional fossil fuels. Fast pyrolysis, which converts biomass into energy and chemical products consisting of a higher energy content transportable liquid bio-oil, solid biochar, and pyrolytic gas by heating in the absence of oxygen, has attracted increased considerable interest in recent years1. With the advantages of simple in construction and operation, good temperature control and efficient heat transfer due to the high solids density, bubbling fluid beds have become one of the major reactors for biomass fast pyrolysis2. Due to complex hydrodynamics and pyrolysis reactions and the limitation of current measurement technology, computational fluid dynamics (CFD) has been considered as an efficient and economic method to reveal the flow and reaction characteristics in the fluidized bed reactor. Typically, the CFD methods can be classified into the Eulerian-Lagrangian method and Eulerian-Eulerian method according to the different methods treating the solids. For the Eulerian-Lagrangian method, the motion and detailed forces of individual particles can be simulated by the Newton's equations of motion. However, in the Eulerian-Eulerian method, the solids are treated as fully interpenetrating continua subject to continuity and momentum equations3. Recently, the Eulerian-Eulerian method, which also known as two-fluid model (TFM) or multi-fluid model (MFM) for two or more solid phases, has been increasingly used in the CFD prediction of biomass fast pyrolysis in the gas-solid fluidized bed reactor due to the relatively lower computational cost4-15. The previous reports indicate that the effects of biomass particle size on the pyrolysis process are significant. For example, the work by Xue et al.4 shown that the predicted


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yield of unreacted biomass decreases with the increase of effective particle diameter of switchgrass; Sharma et al.5 found that the heat transfer rate decreases with the increase of the particle size, which leads to higher biochar yield in the reactor; The investigation by Ranganathan and Gu6 indicated that the percentage yield of non-condensable gas decreases with the increase of particle diameter; The results by Xue and Fox8 demonstrated that particle size distribution (PSD) may favor the mixing and transport between different size particles and bed material, and thus predict slightly higher biomass conversion than monoparticle size with higher bio-oil and char yields; Xiong et al.10 indicated that the tar, gas, and biochar yields increase with the increase of particle diameter when particle diameter is below 900 µm, while these products yields seem to be almost insensitive for the particle diameter larger than 900 µm. However, these reports only account the particle size effect of raw biomass and the variation of particle density in the simulation, which neglect the particle size change (shrinkage) due to the pyrolysis reaction with the constant particle diameter assumption. While in the CFD modeling of biomass pyrolysis and gasification process with the Eulerian-Lagrangian method, the simulation results are significantly affected by the particle shrinkage models. The constant volume (diameter) model leads to a faster devolatilization rate, higher H2, CO, and CH4 yields, lower CO2 yield, higher carbon conversion, and longer particle residence time than the constant density model, since the particle shrinkage not only has an influence on gasification but also strongly affects particle trajectory on its way out of the reactor16, 17

. Therefore, it is necessary to account the particle shrinkage during the pyrolysis reaction when

modeling the bubbling fluidized bed reactor of biomass fast pyrolysis with MFM. In the recent report by Zhong et al.18, a variable particle density and diameter model was developed based on the mass conservation at the particle scale for the biomass pyrolysis process, and it demonstrated that


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the different rules of particle shrinkage during the pyrolysis reactions could be described through tuning the apparent density of char species. With the help of the variable particle density and diameter model, the variation of particle density and diameter at the same time could be realized, which provides a more realistic treatment for the particle shrinkage caused by biomass pyrolysis reactions. However, in order to avoid the difficulty to reach the steady state when the reacted particles are not able to be totally carried out the reactor and validate the developed model comprehensively, the batch mode only with initially packed biomass particles was applied for all the simulations. Thus, the effects of particle shrinkage and the distributions of density and diameter in the actual reactor were not revealed. In the present work, the continuous biomass fast pyrolysis process in a bubbling fluidized bed reactor was simulated with the multi-fluid model (MFM) combing the variable particle density and diameter model to account the particle shrinkage effects during the pyrolysis reactions. The variable particle density and diameter model was able to describe the variation of particle density and diameter simultaneously, which overcomes the limitation of constant diameter assumption in the previous MFM. Different particle shrinkage effects on the flow and reaction behavior were revealed through changing the apparent density of char species, and the detailed density and diameter distributions of particles in the reactor and entrained out of the system were obtained.

2. MODEL DESCRIPTION A simplified one-step reaction analogous to the coal pyrolysis reaction was used to describe the mechanism of biomass pyrolysis reaction: (R1)

biomass → xc char + xt tar + xg light gas

where x is the mass fraction of pyrolysis products.


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A variable particle density and diameter model was developed based on the law of mass conservation at the particle scale. The density of bio-mixture phase is obtained by Eq. (1) as in the previous reports. ρ sm =

1 Yb

ρb

+

(1)

Yc

ρc

where ρsm is the density of bio-mixture phase. Yb and Yc are the mass fraction of biomass and char, respectively. ρb and ρc are the apparent density of pure biomass and char species, respectively. For spherical biomass particle, the particle diameter dp can be determined from the initial particle diameter dp0, mass fraction (Yb and Yc), apparent density (ρb and ρc), and mass yield of char in the pyrolysis reaction xc: 1/3

 ρ − ρb xc  1 − Yb d p = d p 0 1 − c   ρ − − 1 Y 1 x c b( c) 

1/3

 ρ − ρb xc  Yc = d p 0 1 − c   ρ − − − 1 1 Y 1 x ( c )( c )  c 

(2)

Specially, for the pyrolysis reaction with constant diameter, the particle diameter keeps constant during the pyrolysis reaction, the apparent density of char should be defined as: ρc = xc ρb

(3)

In addition, the multi-fluid model based on Eulerian-Eulerian method with the kinetic granular theory is used to simulate the biomass pyrolysis process in the fluidized bed reactor. The detailed description of these models can be found in the supporting information or related reference18. A 2-dimensional (2-D) fluidized bed reactor domain as shown in Figure 14, 5 was used for all the simulations, since Xue et al.4 have found that the time-averaged products yields and temperature of 2-D simulation at the reactor outlet were in good agreement with 3-D simulation results. The center of the biomass inlet is 170 mm above the bottom of the bed and has a height of 7.3 mm. The initial bed was 55 mm high packed with sand particles whose volume fraction is 0.59. The density and


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diameter of sand are 2649 kg/m3 and 520 µm. Most simulation conditions were determined from the reference reported by Xue et al.4. Initially, the diameter of pure biomass particles is 325 µm. The restitution coefficient is 0.97 for all the solid phase. The bed was fluidized by pure nitrogen with superficial velocity of 0.392 m/s at 773 K. The biomass was entrained through the biomass inlet with a flow rate of 100 g/h at 300 K (equated to a basis of per unit reactor volume). No-slip wall boundary conditions were applied for the gas and solid phases, and pressure-outlet boundary condition was used at the top of the fluidized reactor. In order to keep a constant temperature in the reactor, the temperature of 773 K was applied to all walls. The second order upwind differencing scheme was used for spatial discretization. The numerical convergence criteria for all the equations are 0.001. All the simulations were performed on the commercial CFD software Fluent 6.3.26 platform. The variation of particle density Eq. (1) can be realized by selecting the mixing-law on the interface of materials properties, while the variation of particle diameter Eq.(2) should be incorporated into the MFM by a user-defined function (UDF) named DEFINE PROPERTY. The properties of particle (density and diameter) will be updated after solving the mass, momentum, energy, and species equations during the iteration19. For the first 10 s, the bed was fluidized without biomass feeding, then the biomass was entrained into the reactor at a fixed flow rate, and the simulation with biomass pyrolysis reaction was performed for 120 s. The time indicated in the results starts from the simulation time including the pyrolysis reaction, which means 0 s in the following section is the simulation time of 10 s. Since the apparent density of char varies for different types of biomass mainly due to the porosity and chemical composition, and the increase of char density means more intense shrinkage during the pyrolysis reaction, four cases as shown in Table 1 were studied in the present study to


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investigate different particle shrinkage effects on the reactor performance through altering char density. Specially, case 3 and case 4 represent biomass particles with constant density (400 kg/m3) or constant diameter (325 µm) during pyrolysis, respectively. The apparent density of case 4 was determined from Eq. (3). In order to describe the particle density and diameter distributions quantitatively, the mass fraction mi for particle with density of ρi and diameter of di was determined by Eq. (4), and the average particle density and diameter in the whole fluidized bed reactor at certain simulation time can be determined from Eqs. (5) and (6). mi =

Vcell ,i × α i × ρi

∑ (V

cell ,i

(4)

× α i × ρi )

d av =

1 m ∑ ( i / di )

(5)

ρ av =

1 m ∑ ( i / ρi )

(6)

Table 1. Density of biomass and char for different cases. Case number

ρb, kg/m3

ρc, kg/m3

Case 1

400

2330

Case 2

400

1400

Case 3

400

400

Case 4

400

108

3. RESULTS AND DISCUSSION 3.1. Effect of time-step and grid size Since an automatic time-step adjustment (ranging from 0.001 s to 0.0001 s) was used in Xue et al.’s work4, the influence of time-step on the instantaneous cumulative mass fraction of particle diameter in the fluidized bed reactor for case 1 was investigated as shown in Figure 2a. Although


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the particle diameter distributions at the earlier stage of simulation (20 and 40 s) were affected by the time-step at some degree, the predicted results at the end of the simulation were almost the same for the time-step of 0.001 s and 0.0001 s. Therefore, in order to save the computation time, a time-step of 0.001 s was used in the present work. In addition, the particle diameter varies when using the variable particle density and diameter model, while finer grids are usually needed for smaller particle diameter in the simulation with TFM or MFM. In order to confirm the grid independency of the simulation results, case 2 with grid size of 3.81 mm × 3.65 mm (940 cells) and 2.5 mm × 2.5 mm (2055 cells) were performed. The instantaneous mass flow rates of bio-mixture at the outlet are shown in Figure 2b, which indicate that the mesh of 3.81 mm × 3.65 mm (940 cells) is fine enough to provide the grid-independence results. 3.2. Instantaneous flow and reaction characteristics The instantaneous distributions of volume fraction, mass fraction, and velocity for cases 1-4 at 120 s are shown in Figures 3-6. Intuitively, the instantaneous flow and reaction characteristics for all the cases are similar. The bio-mixture and sand phases are severely segregated, and most bio-mixture particles accumulate at the top of the dense bed and release tar through pyrolysis reaction. The mass fraction of biomass is high at the bottom due to the position of biomass inlet. However, some qualitative differences also can be found for different cases. The distributions of biomass mass fraction are significantly different for different shrinkage models (char density), which will affect the particle density and diameter distributions according to Eqs. (1) and (2). In addition, at the top of the reactor, the mass fraction and velocity of bio-mixture phase increases with the decrease of char density, which indicate that more bio-mixture particles are carried out of the reactor. Therefore, the particle density and diameter distributions and the entrainment behavior will


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be discussed in the following sections. 3.3 Particle density and diameter distributions With the help of variable particle density and diameter model, the particle density and diameter can be modified in real time according to the mass fraction of solid species. Therefore, the prediction of particle density and diameter distributions are realized in the CFD simulation using MFM as shown in Figure 7. Since case 3 and case 4 are specially for constant density (400 kg/m3) and constant diameter (325 µm), respectively, the density distribution for case 3 and diameter distribution for case 4 are not shown in Figure 7. It should be mentioned that the unreasonable results of particle density and diameter at the top of the reactor in Figure 7a are the the initial values of particle density (400 kg/m3) and diameter (325 µm). Since there are no bio-mixture particles at this area in case 1 which can be confirmed with the zero velocity of bio-mixture in Figure 3f, the particle density and diameter in these cells are still the initial values as at the beginning of simulation. The particle density and diameter distributions are consistent with the distributions of biomass mass fraction (Figures 3d-6d) and significantly affected by the apparent density of char according to the variable particle density and diameter model. The cumulative mass fraction of particle density and diameter are determined from Eq. (4) as shown Figure 8. The highest point at cumulative mass fraction = 1 represents the pure biomass particle with density 400 kg/m3 of and diameter of 325 µm. The more flat curve close to the highest point means the particle density and diameter in the fluidized bed are more different with the feeding pure biomass particles, which is consistent with Figure 7. The curve on the horizontal plane is the projection of cumulative mass fraction curve, which reflects the particle density and diameter explicitly. Different char density leads to dramatically different particle density and diameter


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distributions. Larger char density (more intense shrinkage effect) leads to wider particle density and diameter distributions. The density maximum increases while the diameter minimum decreases with the increase of char density. Despite the variation of particle density and diameter, the particles are the same type of particle (Gelart A) during the simulation according to the Geldart classification of particles20, and the accuracy of a gas-solid drag model is normally believed to be almost the same for the same type of particle. Therefore, it is reasonable to conclude that the different simulation results such as bed expansion or entrainment behavior in the present work are mainly caused by the particle shrinkage effect, while not caused by the probably different accuracy of drag calculation for different particle diameter and density. The average particle density and diameter in the whole fluidized bed reactor at certain simulation time are determined from Eqs. (5) and (6) as shown in Table 2, which demonstrates that the average particle density increases while the average particle diameter decreases with the increase of particle shrinkage effect during pyrolysis reaction. Table 2. The average particle density and diameter in the whole fluidized bed reactor at 120 s. Case number

case 1

case 2

case 3

case 4

Average diameter, µm

145

204

264

325

Average density, kg/m3

1342

641

400

257

The instantaneous particle density and diameter distributions in the fluidized bed reactor for different simulation times are shown in Figure 9. For cases 1-3, the instantaneous cumulative mass fraction of particle diameter are shown in Figure 9a-c, while the instantaneous cumulative mass fraction of particle density is given in Figure 9d due to the constant diameter. For all the four cases, the particle diameter/density distributions narrow down with the increase of reaction time, and the differences between 100 s and 120 s results are negligible, which indicates that the fluidized bed


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reactor reaches the steady state after 100 s reaction time. 3.4. Entrainment behavior The mass flow rate and average char mass fraction of bio-mixture at the outlet for different char density are shown in Figures 10 and 11, respectively. For case 1, bio-mixture particles are not able to be entrained out the reactor even after 120 s reaction time because of the large apparent density of char (2330 kg/m3). With the decrease of char density (shrinkage effect), the entrainment behavior becomes stronger, and the average char mass fraction decreases, which are consistent with the results in Figures 3-6. The instantaneous particle diameter/density distributions for cases 2-4 are shown in Figure 12. Normally, the diameter and density range of the entrained bio-mixture particles are about 5 µm and 12 kg/m3, respectively. With the increase of reaction time, the particle diameter/density distribution curve moves to the right side, which means the particle diameter/density becomes larger. Compared with the results in Figures 8 and 9, the bio-mixture particles carried out the reactor are the smallest diameter for cases 2-3 and smallest density for case 4, respectively, which is in accordance with the actual situation of the fluidized bed reactor. Since the instantaneous results between 100 and 120 s reaction time are almost the same as shown in Figures 9-11, it is reasonable to believe that the steady state was reached for the last 20 s. Therefore, the entrainment and reaction results over the last 20 s are shown in Table 3. The total entrainment of bio-mixture phase over the last 20 s increases with the decrease of char density (shrinkage effect), which is consistent with the instantaneous results in Figure 9. Since in the experiments the particles entrained out of the reactor and separated by high volume and high efficiency cyclones were considered as biochar products4, the biochar yield in the present work is defined as the ratio of the total entrainment of bio-mixture on the feeding pure biomass weight over


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the last 20 s. Due to the stronger entrainment of bio-mixture, the biochar yield increases with the decrease of char density (shrinkage effect). However, the average char mass fraction in the biochar products decreases for smaller char density as shown in Figure 11, which means more unreacted biomass are carried out the reactor and leads to lower conversion of biomass species. Since the present work used a simplified one-step pyrolysis mechanism, and the products yields in R1 were obtained from the pyrolysis experiments by Grønli and Melaaen21, the predicted biochar and tar yields are somewhat different with the experiments by Xue et al.4 in the fluidized bed reactor. However, the current results are sufficient to demonstrate that the shrinkage effect significantly affects the simulation results even with the same reaction kinetics, which indicate that the char density should be correctly determined for the CFD simulation, and the biochar composition should be carefully compared when validating the simulation results with experimental data. The future work which extending the shrinkage model for more complex and realistic reaction mechanism is on the progress to obtain more accurate results. Table 3. Entrainment and reaction results over the last 20 s. Total entrainment, kg

Biochar yield, wt%

Tar yield, wt%

Biomass conversion, wt%

Case 1

0

0

26.7

95.3

Case 2

0.00435

23.7

26.5

92.5

Case 3

0.00641

34.9

23.8

83.2

Case 4

0.00838

45.6

23.8

71.0

Experiment4

-

13.0 ± 1.5

71.7 ± 1.4

-

4. CONCLUSIONS The fast pyrolysis of biomass in a bubbling fluidized bed reactor was simulated with the MFM model combing the variable particle density and diameter model to account the particle shrinkage


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effects during the pyrolysis reactions. Different particle shrinkage effects on the reactor performance were investigated through altering the apparent density of char species. The detailed distributions of particle density and diameter in the reactor and entrained out of the system were revealed. The results demonstrate that the flow and reaction characteristics including the particle density and diameter distribution, entrainment behavior, biochar composition and yield, and biomass conversion are significantly affected by the particle shrinkage effect (char density). In the bubbling fluidized bed reactor, the average particle density increases while the average particle diameter decreases with the increase of char density which means more intense shrinkage. Weaker shrinkage effect (smaller char density) leads to stronger entrainment behavior, larger biochar yield and mass fraction of biomass in biochar, and lower biomass conversion. Therefore, it is reasonable to conclude that the particle shrinkage effect should be correctly described in the CFD simulation, and the biochar composition should be carefully compared when validating the simulation results with experimental data. AUTHOR INFORMATION Corresponding Author *

E-mail: [email protected].

Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The authors acknowledge the support by State Key Laboratory of Heavy Oil Processing (No. SKLHOP201506) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 16JK1610). The authors also thank the anonymous referees for their


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comments on this manuscript. NOMENCLATURE Symbols d

particle diameter, m

m

mass fraction of particles

V

cell volume, m3

x

mass fraction of products

Y

mass fraction of species

Greek symbols

α

volume fraction

ρ

density, kg m-3

Subscripts av

average

b

biomass

c

char

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Kan, T.; Strezov, V.; Evans, T. J. Renew. Sust. Energ. Rev. 2016, 57, 1126-1140.

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Bridgwater, A. V. Biomass Bioenergy 2012, 38, 68-94.

(3)

Zhong, W.; Yu, A.; Zhou, G.; Xie, J.; Zhang, H. Chem. Eng. Sci. 2016, 140, 16-43.

(4)

Xue, Q.; Dalluge, D.; Heindel, T. J.; Fox, R. O.; Brown, R. C. Fuel 2012, 97, 757-769.

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Sharma, A.; Wang, S.; Pareek, V.; Yang, H.; Zhang, D. Chem. Eng. Sci. 2015, 123,

311-321. (6)

Ranganathan, P.; Gu, S. Bioresour. Technol. 2016, 213, 333–341.

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Xiong, Q.; Xu, F.; Ramirez, E.; Pannala, S.; Daw, C. S. Fuel 2016, 164, 11-17.

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Xue, Q.; Fox, R. O. Ind. Eng. Chem. Res. 2015, 54, 4084-4094.


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Xiong, Q.; Kong, S.-C.; Passalacqua, A. Chem. Eng. Sci. 2013, 99, 305-313.

(10) Xiong, Q.; Aramideh, S.; Kong, S.-C. Energy Fuels 2013, 27, 5948-5956. (11) Xiong, Q.; Kong, S.-C. Powder Technol. 2014, 262, 96-105. (12) Xiong, Q.; Aramideh, S.; Passalacqua, A.; Kong, S.-C. Comput. Phys. Commun. 2014, 185, 1739-1746. (13) Xiong, Q.; Aramideh, S.; Kong, S.-C. Environ. Prog. Sustain. 2014, 33, 756-761. (14) Aramideh, S.; Xiong, Q.; Kong, S.-C.; Brown, R. C. Fuel 2015, 156, 234-242. (15) Xiong, Q.; Zhang, J.; Xu, F.; Wiggins, G.; Stuart Daw, C. J. Anal. Appl. Pyrolysis 2016, 117, 176-181. (16) Ku, X.; Li, T.; Løvås, T. Chem. Eng. Sci. 2015, 122, 270-283. (17) Ku, X.; Li, T.; Løvås, T. Energy Fuels 2015, 29, 5127-5135. (18) Zhong, H.; Liang, S.; Zhang, J.; Zhu, Y. Powder Technol. 2016, 294, 43-54. (19) Fluent, Inc. Fluent 6.3 UDF Manual, 2006. (20) Geldart, D. Powder Technol. 1973, 7, 285-292. (21) Grønli, M. G.; Melaaen, M. C. Energy Fuels 2000, 14, 791-800.


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Figure Captions: Figure 1. The computational domain of fluidized bed reactor. Figure 2. The effects of time-step and grid size on the simulation results. (a) Time-step; (b) Grid size. Figure 3. The instantaneous distributions of volume fraction, mass fraction, and velocity for case 1 (ρc=2330 kg/m3).

Figure 4. The instantaneous distributions of volume fraction, mass fraction, and velocity for case 2 (ρc=1400 kg/m3).



Figure 7. The instantaneous distributions of particle density and diameter at 120 s. Figure 8. The cumulative mass fraction of particle density and diameter at 120 s. Figure 9. The instantaneous cumulative mass fraction of particle density and diameter in the fluidized bed reactor. (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4.

Figure 10. The mass flow rate of bio-mixture at the outlet. Figure 11. The average char mass fraction at the outlet. Figure 12. The instantaneous cumulative mass fraction of particle density and diameter at the outlet. (a) Case 2; (b) Case 3; (c) Case 4.


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Figure 1. The computational domain of fluidized bed reactor. Figure 1 50x80mm (300 x 300 DPI)


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Figure 2. The effects of time-step and grid size on the simulation results. (a) Time-step; (b) Grid size. Figure 2 119x186mm (600 x 600 DPI)


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Energy & Fuels

Figure 3. The instantaneous distributions of volume fraction, mass fraction, and velocity for case 1 (ρc=2330 kg/m3). Figure 3 145x74mm (300 x 300 DPI)


Energy & Fuels

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Energy & Fuels



Energy & Fuels

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Energy & Fuels

Figure 7. The instantaneous distributions of particle density and diameter at 120 s. Figure 7 145x74mm (300 x 300 DPI)


Energy & Fuels

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Figure 8. The cumulative mass fraction of particle density and diameter at 120 s. Figure 8 81x71mm (600 x 600 DPI)


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Energy & Fuels

Figure 9. The instantaneous cumulative mass fraction of particle density and diameter in the fluidized bed reactor. (a) Case 1; (b) Case 2; (c) Case 3; (d) Case 4. Figure 9 119x102mm (600 x 600 DPI)


Energy & Fuels

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Figure 10. The mass flow rate of bio-mixture at the outlet. Figure 10 56x41mm (600 x 600 DPI)


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Energy & Fuels

Figure 11. The average char mass fraction at the outlet. Figure 11 56x45mm (600 x 600 DPI)


Energy & Fuels

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Figure 12. The instantaneous cumulative mass fraction of particle density and diameter at the outlet. (a) Case 2; (b) Case 3; (c) Case 4. Figure 12 180x463mm (600 x 600 DPI)


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Multi-fluid Modeling Biomass Fast Pyrolysis in the Fluidized-Bed

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