segregation behavior of biomass and biochar particles in a bubbling fluidized bed

Chemical Engineering Science 106 (2014) 264–274

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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces

CFD modeling of mixing/segregation behavior of biomass and biochar particles in a bubbling fluidized bed Abhishek Sharma a, Shaobin Wang a, Vishnu Pareek a,n, Hong Yang b, Dongke Zhang b a b

Department of Chemical Engineering, Curtin University, Kent Street, Bentley, Perth, WA 6102, Australia Centre for Energy (M473), The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

H I G H L I G H T S







Hydrodynamic behavior of biomass in a bubbling fluidized bed has been modeled. Mixing/segregation of biomass–biochar has been investigated at different operating conditions. Effect of particle density and size on biomass distribution has been analyzed. Effect of drag, specularity and restitution coefficient has also been examined.

art ic l e i nf o

a b s t r a c t

Article history: Received 2 September 2013 Received in revised form 23 October 2013 Accepted 10 November 2013 Available online 25 November 2013

Computational Fluid Dynamics (CFD) simulations have been carried out to examine the hydrodynamics of a mixture of biomass and biochar particles in a bubbling fluidized bed. The effect of superficial gas velocity, biomass density and particle size on the mixing/segregation behavior of biomass–biochar mixture was analyzed using the Euler–Euler (EE) model. It was observed that on increasing the superficial gas velocity, the bubbles size increased which led to better mixing of both biomass and biochar particles. The biomass density had a significant impact, but particle size had a little impact on the distribution of biomass particles in the biochar bed. Simulations were conducted in both 2-dimensional (2-D) and 3-dimensional (3-D) configurations, and were validated using the available experimental data. A sensitivity analysis was also carried out for examining the effect of different gas–solid drag correlations, wall boundary conditions and particle–particle restitution coefficient. For the operating conditions considered in this study, it was determined that the choice of drag coefficient correlation, particle–wall and particle–particle interaction parameters had a considerable impact on the hydrodynamics of the biomass–biochar mixture. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Biomass Biochar Fluidized bed Computational Fluid Dynamics Eulerian–Eulerian

1. Introduction Fluidized bed reactors are important for thermo-chemical decomposition of biomass because of high rate of heat and mass transfer, and the ability to separate the solid products from the volatile components produced during the operation. Biomass particles, due to their peculiar shapes, sizes and densities, cannot be uniformly mixed without a fluidizing medium such as silica sand in a fluidized bed reactor. In addition, when the bed material also serves as a catalyst (e.g., biochar), it is important to have a uniform mixing of biomass with the catalyst particles throughout the bed. Any segregation between the biomass and catalyst particles in the bed will result into improper catalytic cracking of

n

Corresponding author. Tel.: þ 618 9266 4687; fax: þ618 9266 2681. E-mail address: [email protected] (V. Pareek).

0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.11.019

solid and gaseous products leading to incomplete conversion of biomass. Therefore, detailed computational fluid dynamics (CFD) simulations are required to understand the hydrodynamics of the system so that effect of possible segregation may be minimized. For CFD simulations of biomass in fluidized bed reactors, predominantly two different approaches, namely the Eulerian– Eulerian (EE) and Eulerian–Langragian (EL) models, have been used. However, because of its ability to handle larger-scale systems, the EE model has been more viable for conducting CFD simulations of fluidized-bed reactors. In the EE approach, both continuous and discrete phases are treated as inter-penetrating continua, and the interaction between them is accounted for using a drag force concept (Boemer et al., 1998; Hulme et al., 2005; Patil et al., 2005). In most of the previous studies, the main focus has been on understanding the hydrodynamics of a single solid phase in the presence of a carrier gas (Shah et al., 2010, 2011a, 2011b, 2011c). There have also been studies on the hydrodynamics of

A. Sharma et al. / Chemical Engineering Science 106 (2014) 264–274

fluidized bed reactors for multi-phase systems (Fan and Fox, 2008; Goldschmidt et al., 2000; Huilin et al., 2003, 2007; van Sint Annaland et al., 2009a, 2009b). The major focus of these studies has been on analyzing the segregation and mixing mechanisms of solid particles in dense gas fluidized beds. Similar to the “twofluids” model, these studies have been based on the kinetic theory of granular fluids coupled with other constitutive models. The aforementioned models mainly focus on the segregation rate of binary mixtures of different size particles. However, there have been only few studies (Chiba et al., 1980; Leaper et al., 2004) on the behavior of bi-dispersed phases having variable particle sizes and densities in bubbling fluidized beds. According to these studies (Chiba et al., 1980; Leaper et al., 2004), the particle density has a higher impact on the segregation rate as compared to the particle size. In such cases, the denser particles behave as a jetsam, while the lighter particles as a flotsam. Some experimental studies (Abdullah et al., 2003; Clarke et al., 2005; Rao and Bheemarasetti, 2001; Zhong et al., 2008) have been performed for the analysis of certain fluidization characteristics of biomass such as the minimum fluidization velocities for different mixtures in the reactor. Zhang et al. (2009) experimentally examined the mixing/segregation pattern by varying mass ratio of biomass (cotton stalk) to sand and superficial gas velocity in the bed. Qiaoqun et al. (2005) carried out an experimental as well as a modeling study of a mixture of biomass (rice husk) and sand particles. They also studied the segregation of sand and biomass particles with time, and the effect of superficial gas velocity, bed particle diameter and restitution coefficient on the mixing behavior. Zhong et al. (2012) had studied the effect of particle–wall interaction parameters such as specularity coefficient and restitution coefficient on mixing/segregation of different size and density particles in a low velocity bubbling fluidized bed. However, the modeling and experimental studies so far are not sufficient for evaluating optimum conditions for uniform mixing of the biomass particles and bed material. Furthermore, in order to enhance heat and mass transfer during biomass thermo-chemical degradation in a bubbling fluidized bed reactor, we need to focus on various operating and modeling parameters such as the effect of superficial gas velocity, biomass density, biomass particle size and wall boundary conditions in a fluidized bed reactor which can potentially affect the mixing/segregation behavior. Therefore, a multi-fluid dynamic model has been formulated here for examining the fluidization behavior of biomass with biochar particles in the bubbling fluidized bed.

2. Model description

265

! v q is the velocity of phase, q. For continuity equations of each phase, mass transfer between the phases, and the source term for mass generation or consumption have not been considered. For the gas phase ðgÞ, the momentum balance has been specified using the Navier–Stokes equation " # ! ∂ðαg ρg v g Þ ! ! ! ! n þ ∇ðαg ρg v g v g Þ ¼  αg ∇p þ ∇τg þ αg ρg g þ ∑s ¼ 1 R gs ∂t ð2Þ ! where R gs is the interaction force between gas phase and n solid phases (s ¼1, 2,_ _ _, n), τg is the stress–strain tensor for gas phase, ! g is the acceleration due to gravity and, p is the pressure shared by all phases. ! ! ! R gs ¼ K gs ð v g  v s Þ

ð3Þ

where K gs is the gas–solid momentum exchange coefficient. For the sth solid phase, the momentum balance has been defined similarly as that for gas phase " # ! ! ∂ðαs ρs v s Þ !! ! N þ ∇ðαs ρs v s v s Þ ¼  αs ∇p  ∇ps þ ∇τs þ αs ρs g þ ∑l ¼ 1 R ls ∂t

ð4Þ where ps is the pressure of sth solid phase, and τs is the stress– strain tensor for sth solid phase. ! ! ! R ls ¼ K ls ð v l  v s Þ

ð5Þ

where K ls is the momentum exchange coefficient between lth fluid (gas) or solid phase and sth solid phase and N is the total number of phases. In these equations, the contribution due to any other external force was not considered. Also, the contribution of the lift force (insignificant as compared to interaction force) and virtual mass force (only significant when secondary phase density is much smaller than primary phase density) were neglected due to negligible impact on momentum equation. The kinetic energy of fluctuating particle motion has been represented using granular temperature of the sth solid phase (θs ), which is proportional to mean square of fluctuating velocity of solid particles
 3 ∂ðαs ρs θs Þ ! ! þ ∇ðαs ρs v s θs Þ ¼  ðps I þ τs Þ : ∇ v s þ ∇ðkθs ∇θs Þ γ θs þ Φls 2 ∂t ð6Þ

The CFD model has been developed using the Euler–Euler (EE) approach, which treats the gas phase and the biomass and biochar particles as inter-penetrating continuums. The general conservation equations have been formulated for mass, momentum and fluctuating kinetic energy of solid phases by incorporating the concept of phasic volume fraction (the volume fraction representing the space occupied by each phase). The additional closure laws such as gas–solid and solid–solid drag coefficients, and solid shear and bulk viscosity have been applied in this model (ANSYS FLUENT).

here, the second term on left hand side of equation is a contribu! tion due to convective granular energy. Whereas, ðps I þ τs Þ : ∇ v s is generation of energy due to solid stress tensor, kθs ∇θs is contribution due to diffusive granular energy (here, kθs is diffusion coefficient), and γ θs is collision dissipation of energy. Φls is energy exchange between the lth fluid or solid phase and sth solid phase

2.1. Conservation equations

2.2. Additional closure equations for multi-phase flow

The overall continuity for the continuous primary and dispersed secondary phases was defined using mass conservation equation:
 ∂ðαq ρq Þ ! þ ∇ðαq ρq v q Þ ¼ 0 ð1Þ ∂t

Similar to thermal motion of gas molecules, the intensity of random motion of particles arising from particle–particle collisions determines the stresses, viscosity and pressure of the solid phase (Ding and Gidaspow, 1990). Therefore, for the solid phases, a set of constitutive relations for transport properties such as the granular temperature, pressure and viscosity were defined using kinetic theory of granular fluids. These closure equations with the drag coefficient correlations are given in the Appendix A.

where, αq is the phasic volume fraction of phase, q (gas phase and different solid phases), ρq is the physical density of phase, q and

Φls ¼  3K ls θs

ð7Þ

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2.3. Simulation scheme The coupled equations of phasic momentum, shared pressure and phasic volume fraction for a given multi-phase flow have been solved using ANSYS FLUENT version 14.0. The phase coupled SIMPLE algorithm has been utilized for solving these equations. With this, a pressure correction equation is formulated based on continuity equation. In this scheme, the coupled per phase velocities have been solved in a segregated manner. The coefficients for the pressure correction equation have been derived from the coupled per phase momentum equations. This algorithm has been integrated with an iterative time advancement scheme, where all the equations are solved iteratively for a given time step until the convergence criteria are met (ANSYS FLUENT).

2.4. Solution procedure, initial and boundary conditions The simulations were carried out in a 2-dimensional (2-D) fluidized bed reactor domain as shown in Fig. 1. The 2-D configuration is a slice of the actual reactor, which has height and width as the height and diameter of the reactor, respectively. The simulation domain was divided into fixed number of control volumes by defining grid cells in both horizontal and vertical directions. The equations were solved using a second order upwind differencing scheme for spatial discretization and second order implicit scheme for transient formulation with a time step size of 10  4 s. An initial bed height of given volume fractions of biomass and fluidizing bed material was specified at the start of each simulation. The coefficient of restitution for the biomass and

Gas Outlet

biochar particles was taken as 0.6 and 0.9 for the initial simulations, respectively. The simulations were conducted for a period of 30 s of real simulation time. The time-averaged parametric values were taken from 10 s (by which a dynamic steady state was achieved) to 30 s of simulation results. The specifications of the computational domain are given in Table 1. For the gas phase, the initial velocity was specified at the bottom of the bed. For the granular phases, the inlet velocities were assigned as zero. The pressure boundary conditions were applied at the top of the bed, which was fixed to a reference value of 1 atm. For the gas phase, a no-slip boundary condition was used on the walls. For the granular phase, the shear force at the walls was defined by the equation of Sinclair and Jackson (1989) pffiffiffi pffiffiffiffiffi!  3παs τs ¼ ϕρs g 0 θs u s ð8Þ 6αs; max ! where u s is the particle slip velocity parallel to the wall, ϕ is the specularity coefficient between the particle and the wall (assumed value of 0.5, for partial slip conditions). The granular temperature for the solid phase at the wall pffiffiffi pffiffiffi pffiffiffiffiffi! ! 3π α s 3παs 3=2 qs ¼ ϕρs g 0 θs u s u s  ð1  e2sw Þρs g 0 θs ð9Þ 6αs; max 4αs; max where esw is the coefficient of restitution at the wall ( assumed equal to particle's restitution coefficient).

3. Results and discussion In this study, a pine char was used as the bed material for analyzing fluidization of the pinewood or rice husk as the biomass. The averaged mass fraction of pinewood or rice husk was kept at 5.82 wt% in the biomass–biochar mixture for initial simulations. The biomass and biochar particles were considered mono-sized and spherical in shape for the present modeling purposes. 3.1. Effect of superficial gas velocity, biomass particle density and size

W

L

h

Uniform Gas Inlet Distribution Fig. 1. 2-D domain of the fluidized bed system.

The initial volume fraction for the pinewood and biochar particles in the bed was kept as 0.081 and 0.519, respectively. The average diameter and the density of the pinewood were 1.54 mm and 584 kg/m3 (http://www.csudh.edu/oliver/chemdata/ woods.htm), respectively; and that of biochar were 1 mm and 1470 kg/m3 (Brown et al., 2006), respectively. The calculation of the minimum fluidization velocity (umf) of the biomass–biochar mixture was performed using the relationship of Chitester et al. (1984). Due to very small amount of biomass as compared to biochar in the mixture, the umf of the biomass–biochar mixture was found to be around 0.45 m/s for both pinewood and rice husk of 1.54 mm average diameter. Fig. 2 qualitatively shows the fluidization behavior of pinewood particles in the biochar bed, which was initially patched to have a uniform volume fraction of both solid phases. It can be seen from Fig. 2(a) that the bubbles starts forming only at the minimum fluidization velocity. On increasing the gas velocity to the above minimum fluidization velocity (as shown in Fig. 2(b–d)), there was an increase in the average bubble size which led to increase in the

Table 1 Specifications of the computational domain employed in the multi-phase simulation. Reactor height, L Grid cells in vertical direction Initial bed height, h

2000 mm Reactor width, W 160 Grid cells in horizontal direction 380 mm

450 mm 75

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267

9

8

8

7

Biomass Mass fr. (%)

Pinewood Mass fr. (%)

Fig. 2. Volume fraction profile of pinewood as a function of time at different superficial gas velocities. (a) u¼ 0.45 m/s (u/umf ¼1); (b) u¼ 0.68 m/s (u/umf ¼ 1.5); (c) u¼ 1.14 m/s (u/umf ¼ 2.5); and (d) u¼ 1.59 m/s (u/umf ¼3.5).

7 6 5

u = 0.45 m/s

4 3

u= 0.54 m/s

2 1 0

u= 1.14 m/s 0

0.2

0.4

0.6

0.8

6 5 4 3

1

Fig. 3. Time averaged pinewood mass distribution at different superficial gas velocities.

movement of the pinewood particles along the bed height. This vigorous movement of particles with bubbles favours the mixing of the solid phases of different densities and sizes along the bed height. The time averaged mass distribution of the pinewood particles with respect to the dimensionless bed height at different gas velocities is shown in Fig. 3. The pinewood mass fraction is based on total solids only, without considering the gas phase. Since the pinewood particles are lighter, they behaved as flotsam, while the heavier biochar particles behaved as jetsam in the bed. The simulation results suggested that there was uniform segregation between the rice husk and char particles across the bed height at

Pinewood

2

rice husk

1 0

Dimensionless Bed Height (y/H)

u = 0.68 m/s

0

0.2

0.4

0.6

0.8

1

Dimensionless Bed Height(y/H) Fig. 4. Time averaged mass distribution of pinewood and rice husk.

the minimum fluidization velocity. On increasing the velocity just above umf (at u ¼0.54 m/s), the bubble movement from the bottom to the top of the bed leads to distribution of the pinewood particles along the bed height. But there was some segregation between the two phases as the mixing due to the formation of small bubbles was weak at this velocity. The mixing between the two solid phases was higher at velocities close to 2.5 times of the minimum fluidization velocity (at u ¼1.14 m/s). At velocities close to this value, it was considered that there was uniform mixing between the pinewood and biochar particles along the bed height. It is clear from Fig. 4 that for a fixed superficial gas velocity, on changing the density of biomass particles in the bed, there was

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Gas Outlet

Pinewood Mass fr. (%)

8 7

u = 0.68 m/s

6 5 4

diameter = 1.54 mm

3 2

diameter = 2 mm

L

1 0

0

0.2

0.4

0.6

0.8

W

1

Dimensionless Bed Height (y/H)

Pinewood Mass fr. (%)

7 6 5

h

u = 1.14 m/s

4

T

3

diameter = 1.54 mm

2

diameter = 2.5 mm

1 0

0

0.2

0.4

0.6

0.8

Uniform Gas Inlet Distribution Fig. 7. 3-D domain of the fluidized bed system.

1

Dimensionless Bed Height (y/H)

Vertical velocity (cm/s)

40 30

u = 0.54 m/s Dimensionless Bed Height = 0.5

20 10 0 -10

8

-30 -0.5

pinewood

biochar

0

0.5

u = 0.79 m/s

7 6 5 4 3

Experiment

2

2-D Model

1

3-D Model

0 0.0

-20

-40 -1

Rice Husk mass fr. (%)

9

Fig. 5. Time averaged pinewood mass distribution for different pinewood particle sizes.

0.2

0.4

0.6

0.8

1.0

Dimensionless Bed Height (y/H) 1

Fig. 8. Comparison of 2-D and 3-D simulation results with experimental data (Qiaoqun et al., 2005).

Dimensionless Radial Distance (r/R) Fig. 6. Distribution of vertical velocity of pinewood and biochar particles.

a considerable change in the biomass distribution across the bed height. For example, for gas superficial velocity of 0.68 m/s, on increasing the biomass density from 584 kg/m3 (pinewood) to 950.6 kg/m3 (rice husk) (the average particle diameter is same for both types of biomass), the segregation of biomass particles in the biochar bed decreased. This led to better distribution of rice husk particles in the bed compared to pinewood particles which had significantly lower concentration in the bottom part of the bed and higher in top section of the bed due to segregation. This was mainly because of the density difference between rice husk and biochar particles are less as compared to the difference between pinewood and biochar particles in the bed. Fig. 5(a) and (b) shows the pinewood mass distribution for different biomass (pinewood) particle sizes with respect to dimensionless bed height. According to the results, there was minor difference in the distribution of biomass particles in the biochar bed by increasing the average particle diameter. As the mass fraction of biomass was considerably less than the biochar in the bed, the effect of change of biomass particle diameter was negligible on mixing/segregation behavior of both solid phases.

The time-averaged distribution of vertical velocities of pinewood (5.82 wt%) and biochar particles at superficial gas velocity of 0.54 m/s is shown in Fig. 6. It is clear that in the centre of the bed, both pinewood and biochar particles flow upward with positive velocities, while near the walls, they flow downward with negative velocities. The velocity of pinewood particles was marginally higher than biochar particles in centre region of the bed. However, there is not much difference in their velocities in the wall region. 3.2. 2-D vs. 3-D configuration 3.2.1. Experimental validation For this study, a 3-dimensional (3-D) fluidized bed domain (shown in Fig. 7) was used. The experimental result (Qiaoqun et al., 2005) for a mixture of rice husk (5.82 wt %) and sand (94.18 wt%) was compared with the 2-D (given in Table 1) and 3-D simulations. The height (L), width (W) and length (T) for 3-D configuration were kept as 2000 mm, 450 mm and 245 mm, respectively. The number of grid cells along the height, width and length directions was 160, 36 and 20, respectively. The initial bed height (h) for the mixture was kept as 380 mm. The average diameter and density of rice husk particles were 1.54 mm and 950.6 kg/m3, respectively; and the average diameter and density of

A. Sharma et al. / Chemical Engineering Science 106 (2014) 264–274

sand particles were 0.44 mm and 2600 kg/m3, respectively. The superficial gas velocity (u) in the bed was maintained at 0.79 m/s. The initial volume fraction for the rice husk and sand particles in

269

the bed were kept as 0.0867 and 0.5133, respectively. The conservation equations were solved with additional closure laws and initial-boundary conditions given for 2-D simulations.

Fig. 9. Time-averaged volume fraction of pinewood and biochar particles for 2-D and 3-D models. (a) pinewood (2-D); (b) pinewood (3-D); (c) biochar (2-D); and (d) biochar (3-D).

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However, for the transient formulation, the time step size of 10  5 s was used for 3-D configuration. As per Fig. 8, it was found that the 2-D and 3-D simulation results were in good agreement with the experimental data for time averaged rice husk mass distribution in the mixture along the dimensionless bed height. However, there was noticeable difference in the rice husk mass fr. (%) in top section of the bed between the experimental and modeling results. This was due to the experimental error that led to the weighted average rice husk mass fraction in the bed around 6.3% compared to actual initial value of 5.82% for experimental data. 3.2.2. Pinewood–biochar mixture The simulation results for mixing/segregation behavior in 2-D and 3-D configurations were further compared. A 2-D configuration with height and width of 342.9 mm and 38.1 mm; and a 3-D configuration with height, width and length of 342.9 mm, 38.1 mm and 20.7 mm were used, respectively. The simulation domain consists of 10 grid cells in horizontal direction and 90 grid cells in vertical direction for 2-D domain. The number of grid cells along the height, width and length directions for 3-D domain was 90, 10 and 5, respectively. The initial bed height was kept as 38.1 mm for both the cases. The bed contains averaged mass fraction of 5.82 wt % of pinewood in the pinewood–biochar mixture. The initial volume fraction for the pinewood and biochar particles in the bed was kept as 0.081 and 0.519, respectively. The superficial gas velocity was maintained at 1.35 m/s. The coefficient of restitution for both the pinewood and the biochar particles was given as 0.9. The no slip boundary condition was used for the gas phase, while the free slip boundary condition (no shear) was used for both the solid phases. The time averaged volume fractions of pinewood and biochar particles for 2-D and 3-D configurations along the reactor length are shown in Fig. 9. As per the figure, it was clear that the average height of pinewood and biochar particles in the bed was higher for the 2-D model as compared to the 3-D model. It is mainly due to the difference in frequency of bubbles formation and bubbles size leading to variation in axial and lateral movements of solid phases in the bed for 2-D and 3-D cases. From the figure, it was also found that the bottom section of the bed contains mainly the biochar particles with very less amount of pinewood particles. This is due to the fact that the formation of bubbles was weak leading to the segregation of particles based on the difference in their densities in the bottom section of the bed. However, the uniform bubbles distribution at higher sections of the bed favours the movement of both the solid phases along the bed height. The pinewood mass fraction (%) in the mixture along the dimensionless bed height for 2-D and 3-D models was compared in Fig. 10. From the figure, it was clear that the pinewood distribution was in close agreement between the 2-D and 3-D models. It was also found that the mass fraction of

Pinewood Mass fr. (%)

10 8

u = 1.35 m/s

6 4

2-D Model

2

3-D Model

0 0.0

0.2

0.4

0.6

0.8

1.0

Dimensionless Bed Height (y/H) Fig. 10. Comparison of 2-D and 3-D models for time averaged pinewood mass distribution.

pinewood particles was lower in the bottom section as compared to top section of the bed due to considerable segregation between both the solid phases at this gas velocity. 3.3. Effect of drag correlations Fig. 11 shows the time averaged velocity magnitude of pinewood particles along the bed height for different drag correlations in a 2-D configuration with similar dimensions and grid cells as given in Section 3.2.2. The other conditions such as initial bed height, coefficient of restitution and volume fraction of biomass (pinewood) and biochar particles were also kept same as mentioned in Section 3.2.2. The no slip boundary condition was used for the gas phase, while partial slip boundary condition was used for the solid phases. It is clear from the figure that pinewood particles were recirculating in the bed due to the movement of gas bubbles along the bed height. However, in the top section of the bed, the pinewood particles had the tendency to move downwards due to collapsing of bubbles (not consistent for the Syamlal– Obrien model). The average particle velocity varies for different drag models due to the variation in the drag force applied by the gas phase on the solid phase in each case. Fig. 12 shows the distribution of pinewood particles in the mixture along the dimensionless bed height for different drag models. It is clear from Fig. 12 that the time averaged distribution of pinewood particles in the bed was almost similar for the Syamlal–Obrien and Gidaspow models. However, the Huilin–Gidsapow model predicted lesser segregation between the pinewood and biochar particles when compared with the Syamlal–Obrien and Gidaspow models. 3.4. Effect of wall boundary conditions The specularity coefficient for a granular flow determines the fraction of collisions transferring momentum to the walls. Its value ranges between 0 and 1. When the value is 0, the granular particles have no shear stress at the walls and they follow free slip condition. With increase in the value, the lateral momentum transfer increases at the walls. There is no slip condition for the value of 1 and the wall shear stress is maximum at this value (ANSYS FLUENT). Fig. 13 shows the distribution of time averaged velocity of pinewood particles for different values of specularity coefficient in a 2-D configuration with similar dimensions and grid cells as given in Section 3.2.2. The other conditions such as initial bed height, coefficient of restitution and volume fraction of biomass (pinewood) and biochar particles were also kept the same as mentioned in Section 3.2.2. As per this figure it is clear that for zero shear stress condition, there is no friction between particles and the wall resulting into higher particle velocity along the wall region. With increase in the specularity coefficient to 0.5, it was found that the friction increases which lowers the movement of particles in the bed. However, for no slip condition, the particle velocity was higher when compared to those using the specularity coefficient of 0.5 throughout the bed. As seen from Fig. 14, higher amount of pinewood particles were retained along the walls for the free slip and no slip conditions when compared to those using the specularity coefficient of 0.5. However, for the no slip condition, the distribution of pinewood particles near the wall region was more uniform than those with the free slip condition and the specularity coefficient of 0.5. Fig. 15 shows the time averaged mass distribution of pinewood in the pinewood–biochar mixture along the bed height for different specularity coefficient. It was found that due to higher particle velocity for free slip condition, the pinewood and biochar particles have uniform distribution along the bed height. This leads to better mixing of both the phases. With increase in

A. Sharma et al. / Chemical Engineering Science 106 (2014) 264–274

271

Fig. 11. Time averaged velocity magnitude (m/s) of pinewood particles for different drag correlations. (a) Gidaspow; (b) Syamlal–Obrien; (c) Gibilaro; and (d) Huilin– Gidaspow.

specularity coefficient to 0.5, the mixing between the solid phases was reduced and the uniform segregation was clearly observed. With further increase in specularity coefficient to 1, there was

increase in shear force along the walls leading towards no slip condition between the particles and the wall. This resulted into slightly better distribution of pinewood particles in the mixture

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12

14

specularity coefficient = 0

10

Pinewood Mass fr. (%)

Pinewood mass fr. (%)

u = 0.9 m/s 8 6

Gidaspow Syamlal-obrien Gibilaro Huilin-Gidaspow

4 2 0

0

0.2

0.4

0.6

0.8

12

specularity coefficient = 0.5

10

specularity coefficient = 1

8 6 4

u= 0.68 m/s

2 1

0

Dimensionless bed height (y/H)

0

0.2

0.4

0.6

0.8

1

Dimensionless Bed Height (y/H)

Fig. 12. Time averaged pinewood mass distribution for different drag correlations.

Fig. 15. Time averaged pinewood mass distribution for different wall boundary conditions.

20

u = 0.68 m/s Dimensionless Bed Height = 0.5

14

12 8 4 0 -1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Dimensionless Radial Distance (r/R)



0.1

u = 0.68 m/s Dimensionless Bed Height = 0.5

Volume fraction

0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

12

restitution coefficient = 0.8

10

restitution coefficient = 0.9

0.8

1

restitution coefficient = 0.99

8 6 4

u = 1.1 m/s

2 0

Fig. 13. Distribution of time averaged velocity of pinewood particles for different wall boundary conditions. ( specularity coefficient¼ 0); (– – specularity coefficient¼ 0.5); and ( specularity coefficient¼ 1).

0.09

Pinewood Mass fr. (%)

Velocity (cm/s)

16

0

0.2

0.4

0.6

0.8

1

Dimensionless Bed Height (y/H) Fig. 16. Time averaged pinewood mass distribution at different values of the restitution coefficient.

shows the effect of restitution coefficient of both pinewood and biochar particles studied for 2-D configuration given in Section 3.2.2. The other conditions such as initial bed height and volume fraction of biomass (pinewood) and biochar particles were also kept the same as mentioned in Section 3.2.2. The partial slip boundary condition was used for both pinewood and biochar particles. From the figure, it was found that with increase in restitution coefficient, there is a decrease in pinewood mass fr. (%) in lower region of the bed, while there is considerable increase in mass fr. (%) in upper region of the bed. However, there is a requirement to further study the effect of these modeling parameters with experimental data for gaining confidence in the model results.

Dimensionless Radial Distance (r/R) Fig. 14. Distribution of time averaged volume fraction of pinewood particles for different wall boundary conditions. ( specularity coefficient¼ 0); (– – specularity coefficient¼ 0.5); and ( specularity coefficient¼ 1).



along the bed height as compared to the specularity coefficient value of 0.5. However, it is required to further study the effect of specularity coefficient on mixing behavior of different solid phases at higher gas velocities and compare the simulation results with the experimental data in multi-phase systems. 3.5. Effect of restitution coefficient The coefficient of restitution of both solid phases represents the type of particle–particle interactions in the bed. This factor affects the formation of bubbles in the multi-phase systems due to elastic or inelastic collisions between the biomass and biochar particles in the bed, which causes variation in the momentum and fluctuating energy of these phases during interactions (ANSYS FLUENT). Fig. 16

4. Conclusions A multi-phase hydrodynamic model for studying the behavior of biomass (pinewood) and biochar particles in a bubbling fluidized bed has been developed. Simulations were performed to study the effect of superficial gas velocity on fluidization characteristics of the pinewood–biochar mixture. It was found that increasing the superficial gas velocities to above the minimum fluidization velocity of the mixture led to an enhanced mixing of the solid phases with bubbles in the bed. It was further analyzed that, in addition to the superficial gas velocity, the biomass particle density considerably affects the mixing/segregation of the biomass and biochar particles, whilst the biomass particle diameter had a negligible effect. It was seen that the hydrodynamics of the bed being affected due to bubbles formation in a 2-D model as compared to a 3-D model. However, the biomass distribution in the mixture was almost the same for the 2-D and 3-D models

A. Sharma et al. / Chemical Engineering Science 106 (2014) 264–274

along the bed height. It was found that the effect of different drag correlations on biomass–biochar mixing/segregation behavior is considerable for the fluidization conditions considered in this study. It was further analyzed that the value of specularity coefficient affects the segregation rate of different size and density particles at lower superficial gas velocities and there is need to study the effect of this parameter on mixing behavior at higher gas velocities. The restitution coefficient of biomass and biochar particles also affects the mixing/segregation behavior of the solid phases in the bubbling fluidized bed. However, there is a need to further analyze the effect of these modeling parameters on mixing/segregation behavior with experimental verification.

273

Whereas the equation at contact for mixtures (lth and sth solid phases) has been considered as g 0;ls ¼

dm g 0;ll þ dl g 0;ss ds þ dl

(5) Solid phase shear viscosity This is made up of kinetic, collisional and frictional viscosities of the solid phase, discussed by Syamlal et al. (1993). μs ¼ μs;kin þ μs;col þ μs;f r where μs;kin ¼

pffiffiffiffiffiffiffi
 αs ds ρs θs π 2 1 þ ð1 þ ess Þð3ess  1Þαs g 0;ss 6ð3 ess Þ 5

and Acknowledgments This research was partially supported by the Australian Research Council (ARC) under the ARC Linkage (LP100200135) and Discovery (DP110103699) schemes.

Appendix A (1) Gas phase stress–strain tensor ! !T 2 ! τg ¼ αg μg ½ ∇ v g ∇ v g   αg μg ∇ v g I 3

pffiffiffiffiffiffiffiffiffiffi 4 μs;col ¼ αs ds ρs g 0;ss θs =π ð1 þess Þαs 5 For dense flow systems, where secondary volume fraction for solid phase is close to the packing limit (considered to be around 0.61), the generation of stress is majorly because of friction between particles and the instantaneous collision between particles are less important. In such a case, frictional viscosity has to be included in the solid phase shear viscosity expression. μs;f r ¼

ps sin ϕ pffiffiffiffiffiffiffi 2 I 2D

where, μg is the gas-phase viscosity. (2) Solid phase stress–strain tensor   2 ! !T ! τs ¼ αs μs ½ ∇ v s þ ∇ v s  þ αs λs  μs ∇ v s I 3

where ps is solid phase pressure (contribution due to kinetic pressure and frictional pressure as given by Johnson and Jackson (1987)), ϕ is angle of internal friction (301), I 2D is second invariant of deviatoric stress tensor, and

where μs is the shear viscosity of the sth solid phase, and λs is the bulk viscosity of the sth solid phase. (3) Solids pressure The solid pressure consists of a kinetic term (the first term) and other term due to particle collisions (Lun et al., 1984).

P f riction ¼ Fr

ps ¼ αs ρs θs þ 2ρs ð1 þ ess Þα2s g 0;ss θs where ess is the coefficient of restitution for particle collisions, and g 0;ss is the radial distribution function. For a multi-phase system (N number of phases), this equation has been written by considering the presence of other phases as well. 3

pl ¼ αl ρl θl þ ∑N l ¼ 12

dls 3

dl

ð1 þ els Þg 0;ls αl αs ρl θl

where dls is the average diameter [(dl þ ds)/2] and els is the average value of restitution coefficient of the lth fluid (gas) or the solid phase and the sth solid phase [(el þes)/2]. (4) Radial distribution function This is a correction factor that alters the probability of collisions between grains in dense solid granular phase. Its value varies from 1 for dilute solid phase to infinity for compact solid phase. For solid phases, the function has been defined according to the relationship given by Iddir and Arastoopour (2005) as 1 3 αk g 0;ll ¼ þ d ∑M ð1  ðαs =αs; max ÞÞ 2 l k ¼ 1 dk M here, αs ¼ Σ M k ¼ 1 αk (k are solid phases only), αs; max ¼ Σ k ¼ 1 αk; max (αk; max ¼ maximum packing limit of kth solid ¼ 0.63), and M is the total number of solid phases.

ðαs  αs; min Þn ðαs; max  αsÞ p

here, Fr, n and p have the values of 0.1αs , 2 and 5, respectively. (6) Solid phase bulk viscosity The resistance of the granular particles due to compression and expansion was described by Lun et al. (1984) as pffiffiffiffiffiffiffiffiffiffi 4 λs ¼ αs ds ρs g 0;ss θs =π ð1 þ ess Þαs 5 (7) Drag coefficient between fluid (gas) and solid phase This drag coefficient, given by Gidaspow et al. (1991) is more appropriate for dense fluidized beds. When αg 40.8, the fluid–solid momentum exchange coefficient is of the form ! ! 3 αs αg ρg j v s  v g j  2:65 αg K gs ðor K ls for lth gas phaseÞ ¼ C D 4 ds where CD ¼

24 ½1 þ 0:15ð αg Res Þ0:687  αg Res

Reynold's Number ! ! ρg ds j v s  v g j Res ¼ μg and, when αg o0.8, K gs ðor K ls for llth gas phaseÞ ¼ 150

αs ð1  αg Þμg 2

αg ds

þ 1:75

ρg αs j

! ! v s  v gj ds

(8) Drag coefficient between solid and solid phases This solid–solid drag coefficient, given by Syamlal (1987), is of the following form: K ls ¼

3ð 1 þ els Þððπ=2Þ þ C f r;ls ðπ 2 =8ÞÞ αs ρs αl ρl ðdl þ ds Þ2 g0;ls ! ! j v l  v sj 3 3 2πðρl dl þ ρs ds Þ

274

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where C f r;ls is the coefficient of friction between lth and sth solid phase-particles (the value considered here is 0). (9) Diffusion coefficient of granular energy This coefficient, given by Syamlal et al. (1993), contributes to the diffusive component of granular energy. kθs ¼

pffiffiffiffiffiffiffi
 15ds ρs αs θs π 12 16 1 þ η2 ð4η  3Þαs g 0;ss þ ð41  33ηÞηαs g 0;ss 4ð41  33ηÞ 5 15π

where η ¼ ð1 þess Þ=2 (10) Collisional dissipation of energy The energy dissipation rate within the sth solid phase due to collision between particles (Lun et al., 1984) is given as γ θs ¼

12ð 1  e2ss Þg 0;ss 3=2 pffiffiffi ρs α2s θs ds π

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