Solids Back-mixing Behavior and Effect of the ... - ACS Publications

Article pubs.acs.org/IECR

Solids Back-mixing Behavior and Effect of the Mesoscale Structure in CFB Risers† Xingying Lan, Xiaogang Shi, Yinghui Zhang, Yu Wang, Chunming Xu, and Jinsen Gao* State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China ABSTRACT: Solids back-mixing significantly influences the performance of circulating fluidized bed (CFB) risers. A better understanding of the solids back-mixing behavior is greatly essential for the design and operation of CFB risers. Computational particle fluid dynamics (CPFD) modeling based on the multiphase particle-in-cell (MP-PIC) method was applied to investigate the solids back-mixing behavior and its influencing factors in CFB risers operating in dilute phase transport (DPT) and fast fluidization (FF) regimes. The present work observed extremely long residence time and wide residence time distribution (RTD) curves for particles in the FF regime, indicating an extensive back-mixing of particles in the FF regime. The overall and local backmixing behaviors of solids were further analyzed. The particles in the DPT regime have a little back-mixing in the lower part of the riser, while the particles in the FF regime experience a large-scale back-mixing throughout the riser. In addition, the factors influencing the back-mixing behavior of solids in different flow regimes were investigated. The results demonstrate that the solids back-mixing in the DPT regime is caused by the downward flow of particles near the wall region, while the severe back-mixing in the FF regime is due to the downflow particles and mesoscale structures (mainly particle clusters). The dynamic formation and dissolution of mesoscale structures could be the dominating factor, leading to the intense back-mixing for particles in the FF regime.

1. INTRODUCTION Circulating fluidized beds (CFBs) are widely used in the chemical industry because of excellent gas−solid contact and favorable heat and mass transfer. Although extensive investigations have been carried out theoretically and experimentally to understand the hydrodynamics of gas−solids flow in CFB risers, such as the velocity field, solids concentration, pressure, and core-annulus structure, it remains a challenge to understand the back-mixing behavior of solids in great depth. The reaction processes underway in CFB risers are closely related to the backmixing behavior of solids because both the reaction rate and reaction time are affected by solids back-mixing. Hence, a good understanding of the back-mixing behavior of solid particles plays a vital role in the design and operation of CFB risers. Currently, the tracer techniques are widely employed to measure the residence time distribution (RTD) of solids. A variety of tracers have been used, for instance, radioactive, colored, ferromagnetic, phosphorescent, chemical-doped, different temperature, or different-sized particles. A review of tracer techniques has been presented by Harris et al.1 Although some useful information regarding solids RTD was obtained, the tracer techniques have some inherent limitations because of the option of tracer particles, the approach of introducing and measuring tracer particles, and the definition of boundary conditions at both the inlet and outlet.2 Some novel measurement approaches were therefore proposed to surmount the limitations.2−5 Van de Velden et al.4 and Chan et al.3 used the technique of positron emission particle tracking (PEPT) to measure the particle velocity, and the residence time of particles in the riser was then calculated based on the average particle velocity. The obtained residence time was not the true residence time of some particles but rather the average residence time. Bhusarapu et al.2 tracked a single radioactive particle, which has the same size and density as bulk particles, to uniquely define its residence time in the riser. © 2013 American Chemical Society

Because the radioactive particle had multiple visits to the riser, the RTD was then obtained. These previous works have promoted the understanding of solids RTD and the back-mixing behavior in CFB risers. However, some experimental results fall into controversy over the influence of the gas velocity and solids flux on the back-mixing behavior of solids. Table 1 summarizes the results on the solids back-mixing in CFB risers obtained by different authors. Harris et al.,6 Rhodes et al.,7 Andreux et al.,8 and Van de Velden et al.4 observed that increasing the solids flux suppressed the solids back-mixing, while Smolders and Baeyens,9 Bai et al.,10 and Patience et al.11 obtained the opposite conclusion. With regard to the effect of gas velocity on solids back-mixing, Harris et al.6 found that the solids back-mixing was enhanced with the increase of gas velocity. Bai et al.10 got similar results as the gas velocity was around 3−6 m·s−1, but they pointed out that a higher gas velocity would lead to more plug flow of particles and reduce the solids back-mixing. Smolders and Baeyens9 and Van de Velden et al.4 supposed that a higher gas velocity tended to improve the portion of upward moving particles and resulted in less back-mixing of particles. The above inconsistent results on the effect of the operating conditions on the solids back-mixing are possibly due to different particles used, operating in different flow regimes, different experimental methods involved, or different riser layouts.6,9 It has been commonly believed that the solids back-mixing in CFB risers is mainly associated with the solids downflow in the annulus region and the dense bottom zone treated as a perfectly mixed dense bed.8 In fact, the solids back-mixing is the combined Received: Revised: Accepted: Published: 11888

December March 15, March 26, March 26,

14, 2012 2013 2013 2013

dx.doi.org/10.1021/ie3034448 | Ind. Eng. Chem. Res. 2013, 52, 11888−11896

Industrial & Engineering Chemistry Research

Article

Table 1. Effects of Operating Conditions on Solids Back-mixing in CFB Risers effects of operating conditions on the solids back-mixing Geldart’s classification

authors Harris et al.10

d × 10−7/m

ρp/kg·m−3

Ug/m·s−1

Gs/kg·m−2· s−1

A/C

25

1800

1.3−4.0

1.6−26.9

A

71

2160

2.8−5.0

5−80

Andreux et al.13 Smolders et al.16

A A

70 90

7 2.8−4.9

Patience et al.15 Van de Velden et al.8

B B

277 120

1400 not mentioned 2630 2260

Rhodes et al.

Bai et al.14

12

not mentioned

not mentioned

not mentioned

flow regime

increasing solids flux

increasing gas velocity

decrease

increase

decrease

not mentioned

46−133 4−35

FF and core-annular DPT FF and core-annular DPT core-annular DPT not mentioned

decrease increase

not mentioned decrease

4.1−6.3 3.6

25−166 55

core-annular DPT FF

increase decrease

not mentioned decrease

7.2 4.6 2.0−10.0

55 347 10−100

core-annular DPT FF not mentioned

increase

increase for 3 < Ug 6

result of various factors. Some other factors, probably related to heterogeneous and mesoscale structures, should also be considered to explain the back-mixing phenomena. The mesoscale structure was first proposed by Wilhelm and Kwauk12 and then demonstrated by such measurements as highspeed photography,13 capacitance probes,14 and video cameras and optical fibers.15 The mesoscale structure often takes the form of clusters and streamers. The particle clusters and streamers form at small length and time scales initially and then grow into larger scales.16 The particle clusters dynamically change either in shape, size, and motion or in space and time.17−23 Hence, the mesoscale structures have significant effects on the hydrodynamics of gas−solids systems. The back-mixing behavior of particles in the riser is closely related to its hydrodynamics, and it is therefore inferred that the mesoscale structures would influence the back-mixing behavior of particles. Unfortunately, despite the enormous efforts in describing the dynamics and characteristics of particle clusters, few works have focused on the effect of the clusters on the solids back-mixing, which is essential for designing and operating CFB risers. Now, a new simulation analytics approach, computational particle fluid dynamic (CPFD), is emerging in the modeling of fluid−solids systems. CPFD numerical methodology was proposed on the multiphase particle-in-cell (MP-PIC) method.24 In CPFD modeling, each particle has three-dimensional forces such as fluid drag, gravity, static dynamic friction, particle collision, and other possible forces. The particles move freely within the whole computational domain and are tracked in the Lagrangian approach. The large-scale systems including billions of particles can be simulated with millions of numerical particles. Hence, CPFD modeling has been successfully applied in such industrial processes as particle sedimentation,25 fluidized beds,26−29 coal gasification,30 ozone decomposition,31 downer reactors,32,33 and a FCC regenerator.34 We have successfully applied the CPFD approach to investigate the hydrodynamics of gas−solids flow in a pilot CFB riser.27 On the basis of the previous work, CPFD modeling will be applied to investigate the back-mixing behavior of particles in that riser. The back-mixing behavior of solids in dilute transport flow (DPT) regime and fast fluidization (FF) regimes will be analyzed and compared. The influence of mesoscale structures on the back-mixing behavior will also be studied. Further analysis will be performed to find the

dominating factors affecting the solids back-mixing in different gas−solid flow regimes.

2. SIMULATION SYSTEM AND APPROACH 2.1. Simulated System. The system simulated in the present study is the experimental setup of the Chemical Reaction Engineering Laboratory (CREL) at Washington University. Bhusarapu et al.2 have applied the noninvasive radioactive particle-tracking and γ-ray-computed tomography techniques to map the solids flow in the riser. Particularly, they tracked a single radioactive tracer during its multiple visits in the riser and obtained the solids RTD. These experimental data are useful for an understanding of the solid back-mixing behavior in the riser. Thus, the riser of CREL was chosen as the simulated system to investigate the effect of the mesoscale structure on the solids back-mixing behavior. The schematic diagram of simulated riser is shown in Figure 1. The CFB riser has a total height of 7.9 m, with 0.152 m internal diameter. The glass beads are fluidized with air at ambient temperature and pressure. The glass bead has a density of 2550 kg·m−3 and a mean diameter of 150 μm. 2.2. CPFD Model. The three-dimensional simulation of a CFB riser was performed using the CPFD method. The gas phase is described by the mass and momentum conservation equations with strong coupling to the particle phase. The particle momentum follows the MP-PIC numerical method of O’Rourke and Snider,35 which provides a Lagrangian description of particle motion coupled with the gas by ordinary differential equations. The governing equations of the MP-PIC formulation are provided in Table 2. The particles are implicitly coupled to the gas phase through the interphase drag. The gas−particle drag model used here is the combination of the works of Ergun36 and Wen and Yu.37 The expressions of the combined drag model are shown in Table 3. 2.3. System Setup and Simulation Parameters. The commercial CPFD software of Barracuda was employed to perform the three-dimensional simulation of the CFB riser. The geometry was based on the experimental setup described above. The operating conditions are listed in Table 4. According to the paper of Bhusarapu et al.,38 case 1 operates in the DPT regime and case 2 in the FF regime. The gas-phase inlet is at the bottom of the riser, and its velocity depends on the superficial gas velocity. The particles enter the riser through a small side entry near the bottom of the riser, and the particle flow rate is defined 11889



Article

Table 3. Combined Wen-Yu/Ergun Model Wen−Yu model: 24 −2.65 Re < 0.5Cd = θg Re 24 0.5 ≤ Re ≤ 1000Cd = (1 + 0.15Re 0.687)θg −2.65 Re

Re > 1000Cd = 0.44θg −2.65

D1 = 0.75Cd

ρg |ug − u p| ρp

dp

Ergun model: ⎛ 180θp ⎞ ρg |ug − u p| + 2⎟⎟ D2 = ⎜⎜ dp ⎝ θg Re ⎠ ρp

Re =

ρg d p|ug − u p| ug

Combination of the Wen−Yu and Ergun models: D = D1 θp < 0.75θCP

0.75θCP ≤ θp ≤ 0.85θCP

D=

θp − 0.85θCP 0.85θCP − 0.75θCP

(D2 − D1) + D1

D = D2

θp > 0.85θCP

Table 4. Operating Conditions operating condition

case 1

case 2

Ug/m·s−1 Gs/kg·m−2·s−1

4.5 36.8

3.2 26.6

Figure 1. Schematic diagram of a simulated riser.

wall boundary conditions. The related simulation parameters are provided in Table 5.

Table 2. Governing Equations of CPFD Model Gas-phase continuity equation: ∂θgρg + ∇·(θgρg ug) = 0 ∂t Gas-phase momentum equation:

Table 5. Simulation Parameters

∂(θgρg ug)

+ ∇·(θgρg ugug) = − θg∇P + θgμg ∇2 ug + θgρg g − F ∂t Momentum exchange between the gas and particle phases: ⎡ ⎤ 1 F= fVpρp ⎢D(ug − u p) − ∇p⎥ dVp dρp du p ⎢⎣ ρp ⎦⎥

∫∫∫

Liouville equation for finding the particle positions: ∂f + ∇(fu p) + ∇u p (fA) = 0 ∂t Particle acceleration equation: 1 1 A = D(ug − u p) − ∇p + g − ∇τp ρp θpρp

Psθp β max[(θcp − θp), ε(1 − θp)]

Particle volume fraction in each cell:

θp =

data 150 2550 1.225 1.84 × 10−5 0.64 0.99 0.1 2 1.17 × 1.17 × 2.63 0.001 100−600 20

3. RESULTS AND DISCUSSION 3.1. RTD of Solids. In CPFD simulation, the trajectory of each particle is minutely described. So, the residence time of an individual particle can be obtained by tracking its motion in the riser. The residence times of particles in the whole riser obtained by CPFD simulation are shown in Figure 2. To better illustrate the results, the size of particles was enlarged 8 times and the amount of particles was reduced. Different colors represent different residence times, with blue representing shorter residence time and red indicating longer residence time. Roughly, the residence time of the particles exhibits a nonuniform distribution inside the whole riser in both cases 1

Particle normal stress equation:

τp =

item particle diameter/μm particle density/kg·m−3 gas density/kg gas viscosity/kg·m−1·s−1 particle phase volume fraction at close packing particle−wall tangential retention coefficient particle−wall normal retention coefficient diffuse bounce grid size/cm time step/s simulation time/s time for average/s

∫ ∫ ∫ fVp dVp dρp dup

according to the solids mass flux. Both the gas and particles leave the riser from the top with the atmosphere pressure. No slip of the gas phase and partial slip of the particles are assumed as the 11890



Article

those in the upper part (H = 6 and 7.9 m), which exhibits the typical characteristics of a dense bottom region and dilute top region.39 As mentioned above, cases 1 and 2 operate in the DPT and FF regimes, respectively. A comparison of the particle residence times in the whole riser of cases 1 and 2 shows that the residence time of the particles in the FF regime is much longer than that in the DPT regime; moreover, more particles in the FF regime stay long, while only a small part of the particles has a long residence time in the DPT regime, which indicates a more severe back-mixing of the particles in the FF regime. By tracking the motion of the particle, the residence time of an individual particle at any location of the riser can be obtained. When the particle has arrived at the exit, its overall residence time in the riser can be determined. We took statistics on the residence time of particles at the exit and obtained the solids RTD for the entire riser, as shown in Figure 4. Obviously, particles have distinct RTD curves in case 1 (DPT regime) and case 2 (FF regime). The solids RTD is unimodal with a peak followed by a tail in the DPT regime, while the solids RTD exhibits almost multimodal characteristics along with a greatly extended tail in the FF regime. The tails of the RTD curves indicate back-mixing of the solids in the riser. The wider RTD curve with a longer tail in the FF regime implies more severe back-mixing of solids inside the riser. 3.2. Solids Back-mixing Characteristics. By mathematical analysis of the solids RTD for the entire riser, the overall backmixing degree of solids within the riser can be quantitatively evaluated by a dimensionless variance. The dimensionless variance is a measure of the spread of data around the mean, which is a characteristic of the back-mixing phenomena occurring within the riser.40 A large value of dimensionless variance means a great back-mixing. Table 6 summarizes the mean residence time and the dimensionless variance of cases 1 and 2. In contrast with case 1, the particles in case 2 have much longer mean residence time and, moreover, a larger dimensionless variance, which also implies a stronger back-mixing. The dimensionless variance of the solids RTD in case 1 is 0.23, indicating that the particle flow deviates from the plug flow to some extent, while the dimensionless variance in case 2 is 0.79, indicating that the solids flow is close to the perfect mixed flow. Bhusarapu et al.2 have mentioned that the solids flow in the FF regime is close to that of a stirred tank. It is thus inferred that, from the DFT regime to the FF regime, the RTD of solids shifts from nearly plug flow to nearly perfect mixing. The overall back-mixing of solids characterized by the mean residence time and dimensionless variance may be sufficient for the elementary reactor design. However, for the purpose of understanding the back-mixing mechanisms and incorporating it into a reactor model, it is greatly necessary to investigate the local back-mixing behavior. In the present work, the local back-mixing index is defined as the ratio of the number of downward-moving particles to the total number of particles at the specified cross section. Figure 5 illustrates the local back-mixing index at various cross sections of the riser. Overall, the local back-mixing index decreases gradually along the height of the riser. The local backmixing index at any height of case 2 is higher than that of case 1, especially in the bottom of the riser. For case 1, in the lower part of the riser, the local back-mixing index of particles has a noticeable decline, while it almost remains unchanged in the upper part of the riser. For case 2, the local back-mixing index descends all along the height. The local back-mixing index of particles could give a good explanation to the distinct difference of the mean residence time and its dimensionless variance

Figure 2. Residence time of the particles in the whole riser.

and 2. Some particles quickly pass through the riser, while some particles stay relatively long. For case 1, in the lower part of the riser, the particles just enter into the system and have relatively short residence time, and along the height of the riser, the residence time of the particles gradually increases. However, this is not the case for case 2; the particles with different residence times mix together inside the entire riser. Figure 3 illustrates that there are particles with different colors at any cross section of the riser, indicating that particles at the same cross-section experience different residence times. Parts a1 and a2 of Figure 3 show that there are some particles with long time even at the near-inlet region (H = 1 m). Clearly, these particles are of back-mixing particles. For case 1, in the bottom of the riser, the particles with long residence time mainly gather in the near-wall region, while in the upper part of the riser (H = 4, 6, and 7.9 m), the particles with different residence times disperse well. For case 2, at any cross section of the riser, the particles with different residence times disperse well, indicating the existence of severe back-mixing. Figure 3 also shows that the number of parcels in the low part of the riser (H = 1, 3, and 4 m) is more than 11891



Article

Figure 3. Residence times of the particles at various cross sections of the riser: (a1, b1, c1, d1, and e1) case 1; (a2, b2, c2, d2, and e2) case 2.

Figure 5. Local back-mixing index at various cross sections of the riser.

between the DPT and FF regimes. In the DPT regime, just smallscale back-mixing occurs in the low part of the riser, which makes the particle flow deviate a little from the plug flow, while in the FF regime, the large-scale back-mixing throughout the riser forces the particles stay fairly long and, moreover, causes the particle flow close to the perfect mixing. 3.3. Effect of the Mesoscale Structure on the Solids Back-mixing Behavior. As mentioned above, particles inside the riser experience back-mixing in both the DPT and FF regimes, however with different degrees. The solids back-mixing phenomenon is the combined result of various factors and iscaused by different factors in different flow regimes. This section will focus on an investigation of the factors influencing the solids back-mixing in the DPT and FF regimes. Figure 6 illustrates the cross-sectional views of downwardmoving particles in the riser for both case 1 and 2. In the lower part of the riser, a large number of particles flow downward, consequently resulting in the back-mixing. Along the height of the riser, the amount of downflow particles decreases and the back-mixing degree decreases. For case 1, just the particles near the wall region flow downward because of the wall effects, while for case 2, more particles in wider regions experience backflow,

Figure 4. Solids RTDs of cases 1 and 2.

Table 6. Mean Residence Time and Dimensionless Variance for Different Cases case

mean residence time/s

dimensionless variance

1 2

5.30 48.5

0.23 0.79

11892



Article

Figure 6. Cross-sectional views of downward-moving particles: (a1, b1, c1, and d1) case 1; (a2, b2, c2, and d2) case 2.

4. CONCLUSIONS CPFD modeling was performed to investigate the back-mixing behavior of particles in CFB risers operating in the DPT and FF regimes. The characteristics of solids RTD and back-mixing were compared and analyzed. The factors affecting the back-mixing behavior of solids in different flow regimes were then investigated. The following conclusions were obtained. (1) The residence time of the particles in the FF regime is much longer than that in the DPT regime. More particles in the FF regime stay long, while only a small number of particles have long residence time in the DPT regime. The solids RTD is unimodal with a peak followed by a tail in the DPT regime, while it exhibits almost multimodal characteristics along with a greatly extended tail in the FF regime. The wider RTD curve with a longer tail in the FF regime indicates more severe back-mixing of solids inside the riser. (2) In the DPT regime, a small-scale back-mixing occurs in the low part of the riser, which makes the particle flow deviates a little from the plug flow. However, in the FF regime, the large-scale back-mixing throughout the riser forces the particles to stay fairly long and causes the particle flow to be close to perfect mixing. (3) In the DPT regime, the particles undergo back-mixing mainly because of the downward flow of particles near the wall region. In the FF regime, the downward-flowing solids and the dynamic formation and dissolution of particle clusters together cause extremely severe solid back-mixing. For the catalytic gas-phase reactions or noncatalytic gas−solid reactions happening in the riser reactors, the conversion proceeding of gas or particles depends on the reaction rate and reaction time. The present work shows that the particle clusters remarkably influence the back-mixing behavior of particles and their residence time in the riser. Wang et al.43 have investigated the effects of the particle clusters on cracking reactions in a FCC riser reactor and concluded that particle clustering leads to inefficient gas−solids contact as well as heat and mass transfer and, therefore, influences the reaction rates as well as the conversion of reactants. Hence, the mesoscale structure has a remarkable impact on the performance of the riser reactors. A thorough understanding of the mesoscale structure is significantly essential for the operation and design of the riser reactors.

aggravating the back-mixing behavior. It can be concluded that one of the factors leading to solids back-mixing is due to the downward movement of particles near the wall region. It is generally agreed that mesoscale structures in the form of particle clusters often exist in the gas−solids flow system. Agrawal et al.16 thought that the mesoscale structures arose as a result of an inertial instability associated with the relative motion between the gas and particle phases and an instability due to the damping of the fluctuating motion of particles by the interstitial fluid and inelastic collisions between particles. The characterization of clusters has been extensively investigated.15,17,19,21,41,42 In different flow regimes, the particle clusters exhibit different characteristics. Case 1 operates in the DPT regime, and the particle concentration is fairly low,38 so no particle clusters can be observed in the riser except a few clusters in the bottom. Figure 7 shows the particle clusters in case 2. There are numerous clusters in the riser, especially in the low part of the riser. The particle clusters dynamically change in shape and size. The continuous formation and dissolution of particle clusters significantly affect the direction of particle movement, leading to the reverse of some upflow particles, which results in the back-mixing of particles. In addition, the particle clusters also could experience downward flow because of the fact that less gas penetrates inside the clusters and the gas cannot carry the clusters to flow upward as a whole. The downward flow of the whole clusters also would cause the back-mixing of particles. It is thus clear that the mesoscale structures have a great impact on the back-mixing behavior of solids, and the existence of particle clusters is another factor leading to solids back-mixing. According to the above discussion, it is concluded that, in the DPT regime, the particles undergo back-mixing mainly because of the downward-flowing particles near the wall region. In contrast, in the FF regime, not only the downward flow of solids but also the dynamic variation of particle clusters cause extremely severe solids back-mixing. It would be convincible that the solids back-mixing caused by the downward flow of particles near the wall makes the particle flow deviate from plug flow, while the solids back-mixing caused by particle clusters forces the solids flow close to perfect mixed flow. 11893



Article

Figure 7. Clustering phenomena in the riser for case 2.

■

■

AUTHOR INFORMATION

ACKNOWLEDGMENTS

The authors acknowledge support of the National Basic Research Program (Grants 2010CB226906, and 2012CB215000) and the Science Foundation of China University of Petroleum, Beijing (Grant KYJJ2012-03-01). The authors also thank the committee of the Fourth International Conference on Multi-Scale

Corresponding Author

*Tel: +8610-8973-3993. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 11894



Article

(10) Bai, D.; Yi, J.; Jin, Y.; Yu, Z. In Residence time distributions of gas and solids in a circulating fluidized bed; Potter, O. E., Nicklin, D. J., Eds.; Fluidization VII Engineering Foundation: New York, 1992; pp 195− 202. (11) Patience, G. S.; Chaouki, J.; Kennedy, G. Solids residence time distribution in CFB reactors. In Circulating fluidised bed technology III; Basu, P., Horio, M., Hasatani, M., Eds.; Pergamon Press: Oxford, U.K., 1990; pp 599−604. (12) Wilhelm, R. H.; Kwauk, M. Fluidization of solid particles. Chem. Eng. Prog. 1948, 44, 201−218. (13) Yerushalmi, J.; Squires, A. M. The Phenomenon of Fast Fluidization. AlChE Symp. Ser. 1977, 72, 44−47. (14) Brereton, C. M. H.; Grace, J. R. Microstructural aspects of the behaviour of circulating fluidized beds. Chem. Eng. Sci. 1993, 48 (14), 2565−2572. (15) Li, H.; Xia, Y.; Tung, Y.; Kwauk, M. Micro-visualization of clusters in a fast fluidized bed. Powder Technol. 1991, 66 (3), 231−235. (16) Agrawal, K.; Loezos, P. N.; Syamlal, M.; Sundaresan, S. The role of mesoscale structures in rapid gas−solid flows. J. Fluid Mech. 2001, 445, 151−185. (17) Xu, J.; Zhu, J.; New, A. Method for the Determination of Cluster Velocity and Size in a Circulating Fluidized Bed. Ind. Eng. Chem. Res. 2012, 51 (4), 2143−2151. (18) Wang, S.; Liu, H.; Lu, H.; Liu, W.; Jiamin, D.; Li, W. Flow behavior of clusters in a riser simulated by direct simulation Monte Carlo method. Chem. Eng. J. 2005, 106 (3), 197−211. (19) Wang, S.; Li, X.; Lu, H.; Yu, L.; Ding, J.; Yang, Z. DSMC prediction of granular temperatures of clusters and dispersed particles in a riser. Powder Technol. 2009, 192 (2), 225−233. (20) Guenther, C.; Breault, R. Wavelet analysis to characterize cluster dynamics in a circulating fluidized bed. Powder Technol. 2007, 173 (3), 163−173. (21) Chew, J. W.; Parker, D. M.; Cocco, R. A.; Hrenya, C. M. Cluster characteristics of continuous size distributions and binary mixtures of Group B particles in dilute riser flow. Chem. Eng. J. 2011, 178, 348−358. (22) Chew, J. W.; Hays, R.; Findlay, J. G.; Knowlton, T. M.; Reddy Karri, S. B.; Cocco, R. A.; Hrenya, C. M. Cluster characteristics of Geldart Group B particles in a pilot-scale CFB riser. I. Monodisperse systems. Chem. Eng. Sci. 2012, 68 (1), 72−81. (23) Chew, J. W.; Hays, R.; Findlay, J. G.; Knowlton, T. M.; Karri, S. B. R.; Cocco, R. A.; Hrenya, C. M. Cluster characteristics of Geldart group B particles in a pilot-scale CFB riser. II. Polydisperse systems. Chem. Eng. Sci. 2012, 68 (1), 82−93. (24) Snider, D. M. An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows. J. Comput. Phys 2001, 170 (2), 523−549. (25) Snider, D. M.; O’Rourke, P. J.; Andrews, M. J. Sediment flow in inclined vessels calculated using a multiphase particle-in-cell model for dense particle flows. Int. J. Multiphase Flow 1998, 24 (8), 1359−1382. (26) Zhao, P.; O’ Rourke, P. J.; Snider, D. Three-dimensional simulation of liquid injection, film formation and transport, in fluidized beds. Particuology 2009, 7 (5), 337−346. (27) Zhang, Y.; Lan, X.; Gao, J. Modeling of gas−solid flow in a CFB riser based on computational particle fluid dynamics. Pet. Sci. 2012, 9 (4), 535−543. (28) Vivacqua, V.; Vashisth, S.; Hébrard, G.; Grace, J. R.; Epstein, N. Characterization of fluidized bed layer inversion in a 191-mm-diameter column using both experimental and CPFD approaches. Chem. Eng. Sci. 2012, 80 (0), 419−428. (29) Chen, C.; Werther, J.; Heinrich, S.; Qi, H.-Y.; Hartge, E.-U. CPFD simulation of circulating fluidized bed risers. Powder Technol. 2013, 235 (0), 238−247. (30) Snider, D. M.; Clark, S. M.; O’Rourke, P. J. Eulerian−Lagrangian method for three-dimensional thermal reacting flow with application to coal gasifiers. Chem. Eng. Sci. 2011, 66 (6), 1285−1295. (31) Snider, D.; Banerjee, S. Heterogeneous gas chemistry in the CPFD Eulerian−Lagrangian numerical scheme (ozone decomposition). Powder Technol. 2010, 199 (1), 100−106.

Structures and Systems in Process Engineering. In addition, the anonymous reviewers for their comments on this manuscript are also highly appreciated.

■

NOMENCLATURE A, particle acceleration, m·s−2 Cd, drag coefficient D, drag force, kg·m−3·s−1 D1, drag force in the Wen and Yu model, kg·m−3·s−1 D2, drag force in the Ergun model, kg·m−3·s−1 dp, particle diameter, m f , particle probability distribution function F, rate of momentum exchange per unit volume, N·m−3·s−1 G, gravitational acceleration, m·s−2 Gs, solids mass flux, kg·m−2·s−1 P, gas pressure, Pa Ps, constant, Pa r, radial position, m R, radius of the riser, m Re, Reynolds number t, time, s ug, gas velocity, m·s−1 Ug, superficial gas velocity, m·s−1 up, particle velocity, m·s−1 Vp, particle volume, m3

Greek Letters

μg, gas viscosity, kg·m−1·s−1 ρg, gas density, kg·m−3 ρp, particle density, kg·m−3 τp, particle normal stress, N·m−2 θg, gas volume fraction θp, particle volume fraction θCP, particle-phase volume fraction at close packing β, constant number, 2−5 ε, small number with the order of 10−7

■

REFERENCES

(1) Harris, A. T.; Davidson, J. F.; Thorpe, R. B. A novel method for measuring the residence time distribution in short time scale particulate systems. Chem. Eng. J. 2002, 89 (1−3), 127−142. (2) Bhusarapu, S.; Al-Dahhan, M.; Duduković, M. P. Quantification of solids flow in a gas−solid riser: single radioactive particle tracking. Chem. Eng. Sci. 2004, 59 (22−23), 5381−5386. (3) Chan, C. W.; Seville, J. P. K.; Parker, D. J.; Baeyens, J. Particle velocities and their residence time distribution in the riser of a CFB. Powder Technol. 2010, 203 (2), 187−197. (4) Van de Velden, M.; Baeyens, J.; Smolders, K. Solids mixing in the riser of a circulating fluidized bed. Chem. Eng. Sci. 2007, 62 (8), 2139− 2153. (5) Mahmoudi, S.; Baeyens, J.; Seville, J. The solids flow in the CFBriser quantified by single radioactive particle tracking. Powder Technol. 2011, 211 (1), 135−143. (6) Harris, A. T.; Davidson, J. F.; Thorpe, R. B. Particle residence time distributions in circulating fluidised beds. Chem. Eng. Sci. 2003, 58 (11), 2181−2202. (7) Rhodes, M. J.; Zhou, S.; Hirama, T.; Cheng, H. Effects of operating conditions on longitudinal solids mixing in a circulating fluidized bed riser. AlChE J. 1991, 37 (10), 1450−1458. (8) Andreux, R.; Petit, G.; Hemati, M.; Simonin, O. Hydrodynamic and solid residence time distribution in a circulating fluidized bed: Experimental and 3D computational study. Chem. Eng. Process. 2008, 47 (3), 463−473. (9) Smolders, K.; Baeyens, J. Overall solids movement and solids residence time distribution in a CFB-riser. Chem. Eng. Sci. 2000, 55 (19), 4101−4116. 11895



Article

(32) Abbasi, A.; Islam, M. A.; Ege, P. E.; de Lasa, H. I. Downer reactor flow measurements using CREC-GS-Optiprobes. Powder Technol. 2012, 224 (0), 1−11. (33) Abbasi, A.; Islam, M. A.; Ege, P. E.; de Lasa, H. I. CPFD flow pattern simulation in downer reactors. AlChE J. 2012. (34) Cha, B.; Kim, J.; Son, S. R.; Park, D. S.; Il, M.; Lockhart, B. I. D.; Michael, F. CPFD simulation of fluidized bed flow in FCC regenerator. Comput.-Aided Chem. Eng. 2012, 30, 1153−1157. (35) O’Rourke, P. J.; Snider, D. M. An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets. Chem. Eng. Sci. 2010, 65 (22), 6014−6028. (36) Ergun, S. Fluid flow through packed columns. Chem. Eng. Prog. 1952, 48, 89−94. (37) Wen, C. Y.; Yu, Y. H. Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 1966, 62 (2), 100−111. (38) Bhusarapu, S.; Al-Dahhan, M. H.; Duduković, M. P. Solids flow mapping in a gas−solid riser: Mean holdup and velocity fields. Powder Technol. 2006, 163 (1−2), 98−123. (39) Bi, H. T.; Grace, J. R. Flow regime diagrams for gas−solid fluidization and upward transport. Int. J. Multiphase Flow 1995, 21 (6), 1229−1236. (40) Nauman, E. B. Residence Time Theory. Ind. Eng. Chem. Res. 2008, 47 (10), 3752−3766. (41) Sharma, A. K.; Tuzla, K.; Matsen, J.; Chen, J. C. Parametric effects of particle size and gas velocity on cluster characteristics in fast fluidized beds. Powder Technol. 2000, 111 (1−2), 114−122. (42) Noymer, P. D.; Glicksman, L. R. Cluster motion and particleconvective heat transfer at the wall of a circulating fluidized bed. Int. J. Heat Mass Transfer 1998, 41 (1), 147−158. (43) Wang, S.; Lu, H.; Gao, J.; Xu, C.; Sun, D. Numerical Predication of Cracking Reaction of Particle Clusters in Fluid Catalytic Cracking Riser Reactors. Chin. J. Chem. Eng. 2008, 16 (5), 670−678.

■

EDITOR'S NOTE This paper was originally intended to be published in the special issue, “Multiscale Structures and Systems in Process Engineering” (Ind. Eng. Chem. Res. 2013, Vol. 52, Issue No. 33). †

11896


Solids Back-mixing Behavior and Effect of the ... - ACS Publications

Recommend Documents