Numerical Investigation of the Ability of Salt ... - ACS Publications

Article Cite This: Ind. Eng. Chem. Res. 2017, 56, 13642-13653

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Numerical Investigation of the Ability of Salt Tracers to Represent the Residence Time Distribution of Fluidized Catalytic Cracking Particles Liqiang Lu,*,† Xi Gao,† Tingwen Li,†,‡ and Sofiane Benyahia† †

National Energy Technology Laboratory, Morgantown, West Virginia 26507, United States AECOM, Morgantown, West Virginia 26505, United States

‡

ABSTRACT: For a long time, salt tracers have been used to measure the residence time distribution (RTD) of fluidized catalytic cracking (FCC) particles. However, due to limitations in experimental measurements and simulation methods, the ability of salt tracers to faithfully represent RTDs has never been directly investigated. Our current simulation results using coarse-grained computational fluid dynamic coupled with discrete element method (CFD-DEM) with filtered drag models show that the residence time of salt tracers with the same terminal velocity as FCC particles is slightly larger than that of FCC particles. This research also demonstrates the ability of filtered drag models to predict the correct RTD curve for FCC particles while the homogeneous drag model may only be used in the dilute riser flow of Geldart type B particles. Thus, the RTD of large-scale reactors can be efficiently investigated with our proposed numerical method as well as by using the old-fashioned salt tracer technology. flows such as in circulating fluidized bed (CFB) risers, the strong gas−solids and solids−solids interactions make it nontrivial to experimentally measure the true RTD. Since there are so many difficulties in experimental investigation of RTD, computer simulation of these multiphase flows offers another option to tackle this complex problem. Currently, there are mainly two types of simulations: continuum−continuum based methods like two-fluid model (TFM) 10 and continuum−discrete based methods like computational fluid dynamic coupled with discrete element method (CFD-DEM)11,12 and other variations like hard sphere13−16 and direct simulation Monte Carlo.17 In TFM, the particles are treated as a continuum, which is advantageous in terms of computational speed, but with some drawbacks including numerical diffusion,18 lack of general constitutive laws for granular flow,19,20 and additional complexities such as particle size distribution.21 The CFD-DEM approach avoids these complexities and uncertainties by simply tracking the movement of each particles, and the RTD can be directly calculated by recording the particle’s flow-in and flow-out time.22−24 The main issue with CFD-DEM is the high computational cost that makes it infeasible when simulating large CFB risers even with the help of powerful supercomputers.25,26 A practical way to circumvent this tremendous

1. INTRODUCTION Fluidized catalytic cracking (FCC) is one of the most important and oldest conversion processes used in petroleum refineries. In an FCC unit, the heavy oils are cracked into higher value light products like gasoline, olefins, and other products.1 A side effect of these catalytic cracking reactions is the deposited coke on the catalyst surface, which deactivates the catalyst and reduces the quality of the final products. Thus, the catalyst residence time distribution (RTD) is of critical importance for the design and operation of FCC reactor. Extensive experimental work has been conducted to study the RTD in chemical reactors. The tracer techniques are the most widely used experiment methods to investigate RTD in fluidized bed reactors.2 The key point of this method is to prepare tracer particles which meet the following three requirements: (a) represent the RTD of the fluidized particles, (b) are easy to detect, and (c) have little influence on the flow field. On the basis of these requirements, many kinds of tracer particles have been investigated such as chemically different tracers,3 radioactive tracers,4 magnetic tracers,5 colored tracers,6 heated tracers,7 and optical tracers.8 The reason why there are so many different kinds of tracers is that it is difficult to prepare a kind of tracer particles which can fully meet the above three requirements.9 These tracer particles usually have different physical properties from the fluidized particles, and the errors due to these differences are unknown since we do not know the real distribution of residence time. Thus, the data provided by these different techniques are usually tested only for reproducibility, but the error due to measurement technique is unknown. In complex gas−solids © 2017 American Chemical Society

Received: Revised: Accepted: Published: 13642

September 11, 2017 October 30, 2017 November 2, 2017 November 2, 2017 DOI: 10.1021/acs.iecr.7b03773 Ind. Eng. Chem. Res. 2017, 56, 13642−13653

Article

Industrial & Engineering Chemistry Research

calculated using an equivalent diameter of dpW1/3 while other forces like drag, gravity, and pressure gradient forces are calculated at real particle scale. In this section, the fluid and parcels equations of motion are briefly introduced, while the three different drag models used in this study are explained in more detail. 2.1. Fluid Governing Equations. The volume-averaged Navier−Stokes equations are used to describe the motion of fluid phase:46

cost is using coarse-grained CFD-DEM simulation in which many real particles are lumped into a numerical parcel.27,28 Previous research23 shows that the coarse-grained CFD-DEM method can predict similar RTD curves of CFB riser compared with CFD-DEM, but due to the computation limitation, that direct comparison is based on 2D simulation results and was not fully verified by comparing 3D simulation results and experiment data. Coarse CFD grids are used in coarse-grained CFD-DEM simulation of large reactors. Thus, the effect of unresolved structures in the CFD grid should be considered in the drag model.29 Currently there are three types of drag corrections to account for the subgrid flow structures. The first one is EMMS drag models30−35 based on energy minimization multiscale method.36 The second one is filtered drag models37−40 derived from fine grid TFM or CFD-DEM simulations. The last one is simply using an effective particle size for unresolved clusters.41,42 These drag models are widely used in coarse grid TFM simulations. The EMMS drag model has also been proved to be effective in coarse-grained CFD-DEM simulations of bubbling fluidized bed29 and riser.23,28 However, to the best of our knowledge, the filtered drag model has never been used in coarse-grained CFD-DEM simulation of large reactors. Recent research39,43 indicates that fine grid TFM predicts results similar to those of CFD-DEM and that the particle coarsening has little effect on the drag forces. These previous studies allow us to use with confidence filtered drag models derived from fine grid TFM in coarse-grained CFD-DEM simulation. In this research, we attempt to test the ability of coarsegrained CFD-DEM to predict RTD curves in CFB riser and investigate the ability of salt tracers to represent the RTD of FCC particles. To achieve this purpose, a riser using type A powder (FCC particles) and another one using type B material (glass beads) are simulated with coarse-grained CFD-DEM and filtered drag models. The predicted hydrodynamics and RTD curves of both FCC particles and salt tracers are compared against available experimental data to determine the ability of our numerical technique as well as that of the experimental salt tracers to correctly predict the RTD of reactors of interest to industry.

∂(εf ρf ) ∂t

+ (∇·εf ρf u f ) = 0

D(εf ρf u f ) Dt

(1)

= ∇·Sf̿ + εf ρf g − I

(2)

where εf is the volume fraction of fluid, ρf its density, uf its velocity, and I is the drag force term. Sf̿ is the fluid phase stress tensor given by Sf̿ = −Pf I ̿ + τf̿

(3)

where Pf is the fluid phase pressure and τf̿ is the fluid phase shear stress tensor: τf̿ = 2μf D̿f + λf ∇·tr(D̿f )I ̿ D̿f =

(4)

1 [∇u f + (∇u f )T ] 2

(5)

where D̿f is the fluid strain rate tensor and μf and λf are its dynamic and bulk viscosities. The interphase momentum transfer term on any fluid cell c can be calculated as Np

1 I = vc

∑ 1 πd p3 Wp(∇Pf (x i) +

c

i=1

6

βi (vf (x i) − v ip)) K 1 − εf

i

(x , x c )

(6)

where vc is the volume of cell c and Np is number of particles influencing cell c. Wp is statistic weight of particle p, The ability to use different statistic weight for different particles is important for polydisperse systems. However, in this research, the same statistic weight is used for all particles used in a simulation. βι is drag coefficient of particle i in cell c. vf(xi) is the fluid velocity interpolated at particle i, and K is the interpolation weight of particle i to cell c. 2.2. Drag Models. The momentum exchange between fluid phase and particles is closed with different drag models. The widely used drag models include empirical based correlations such as Wen−Yu drag model47 and Gidaspow drag model;48 the direct numerical simulations based drag models such as BVK drag model;49 and those including effects of unresolved mesoscale structures such as EMMS drag model30,32,34,35,39 and filtered drag model.37,38 Most of the drag models are based on standard drag coefficient for a single particle which is

2. METHOD The coarse-grained CFD-DEM has been implemented and validated in the open source code MFIX. The details can be found at.44,45 In this method, a number of Wp real particles are lumped into a computation parcel. The choice of the parcel size is important as it determines the simulation performances in terms of accuracy and speed. According to our previous research,29 the influence of computational parcel size is less than that of grid resolution and drag correlations for the range of particle coarsening used in that study. In general, small statistic weight will predict more accurate results that will converge to traditional DEM when it reduces to one. However, for large systems as in this research, it is impossible to carry out DEM simulations to exactly quantify uncertainty due to coarsening. Thus, we first select an appropriate CFD grid size to resolve the flow structures such as clusters and then select the parcel size as 2−5 times smaller than the CFD grid size (based on above reference). We are currently conducting a systematic study to quantify uncertainties due to coarsening and their possible extrapolation to larger system sizes, which will be submitted for publication soon. The collision forces are

C D0

⎧ 24 (1 + 0.15Rep0.687) Rep < 1000 ⎪ Re =⎨ p ⎪ Rep ≥ 1000 ⎩ 0.44

(7)

where 13643

DOI: 10.1021/acs.iecr.7b03773 Ind. Eng. Chem. Res. 2017, 56, 13642−13653

Article


Rep =

In filtered drag proposed by Igci et al.,37,50 the Wen−Yu drag correlation is further modified by considering the CFD grid size and local solids volume fractions and is calculated as

εf ρf |vf − vp|d p μf

(8)

In the Wen−Yu model, the drag coefficient is calculated as βWen−Yu

3 εf (1 − εf )ρf |vf − vp| = C D0εf −2.65 dp 4

βIGCI = βWen−Yu(1 − H3D) (9)

H3D =

In the Gidaspow model, the drag coefficient is calculated as

βGidaspow

⎧ (1 − εf )ρf |vf − vp| (1 − εf )2 μf ⎪150 + 1.75 , εf ≤ 0.8 2 ⎪ dp εf d p ⎪ =⎨ ⎪ 3 εf (1 − εf )ρf |vf − vp| εf > 0.8 C D0εf −2.65 , ⎪ ⎪ dp ⎩4

(Δ*filter )1.6 H2D(εp)g g (εp) (Δ*filter )1.6 + 0.4

Δ*filter =

vt =

g Δfilter vt2

(13)

18μg

(14)

⎧ 2.7ε 0.234 εp < 0.012 p ⎪ ⎪ −0.455 + 0.963 0.012 ≤ εp ⎪−0.019εp ⎪ −0.38εp − 0.176e−119.2εp 0.014 ≤ εp ⎪ 0.868e H2D(εp) = ⎨ ⎪−4.59 × 10−5e19.75εp + 0.852e−0.268εp 0.250 ≤ εp ⎪ ⎪(ε − 0.59)( −1501ε 3 + 2203ε 2 − 1054ε + 162) 0.455 ≤ ε p p p p ⎪ p ⎪0 εp ≥ 0.59 ⎩

HSakar

α=

v0 =

< 0.014 < 0.250 < 0.455 < 0.59 (15)

⎧ −α(v* − v ) p * > v0 ⎪ 0.95(1 − e slip 0 ) vslip =⎨ ⎪0 * ≤ v0 vslip ⎩

* = vslip

(17)

|vf − vp| vt

(19)

(a1 + a 2εp + a3εp2 + a4εp3 + a5εp4)(1 − e−300εp) ⎛ a 7 ⎞⎛ a6 a8 ⎞ ⎜1 + ⎟ ⎟ ⎜ 1 + + * )2 ⎟⎠ Δ*filter (Δ*filter )2 ⎠⎝⎜ (vslip ⎝ 1 + e100(εp − 0.55)

a 9 + a10εp ⎛ a13 ⎞ a12 ⎟ + a11 ⎜1 + 0.01 + εp ⎝ Δ*filter (Δ*filter )2 ⎠

(20)

2.3. Equations of Motion for Particles. The Lagrange method is used to track the motion of fewer computational parcels. The momentum equation for any real particle in a parcel takes the familiar form of Newton’s second law of motion:

(21)

⎛ a a18 ⎞ ⎟ p = (a14 + a15εp + a16εp2)⎜1 + 17 + Δ*filter (Δ*filter )2 ⎠ ⎝

mp

(22)

dvp dt

= mpg −

β(vf (x i) − vp) π 3 π 3 d p ∇Pf + d p + Fc 6 1 − εf 6 (24)

a1 − 18 = {0.75597773, 2.73931487, − 5.60196497,

where mp is the mass of the real particle and dp its diameter. On the right-hand side, the forces considered include the gravity force, pressure gradient force, drag force, and the contact force (Fc). The first three terms are calculated following the same process as that in traditional CFD-DEM (i.e., these forces are calculated on a real particle). The contact force is calculated by the discrete element method (DEM) in normal (Fn) and tangential (Ft) directions using the parcel size dCGP as collision

−1.65853820, 16.70299223, − 0.44145335, 0.18195034,− 0.01827347, 0.28441799, −1.943573770, 0.22177961, 0.31175890, −0.15971960, 0.47750002, 0.062794180, 5.13011673, 0.67680355, − 0.54535726}

(18)

(16)

In filtered model proposed by Sakar et al.,40 the drag coefficient is calculated as βSakar = βWen−Yu(1 − HSakar)

(12)

gd p2(ρp − ρg )

(10)

0.24 ⎧ (1.48 + e−18εp) εp < 0.18 ⎪ εp gg(εp) = ⎨ ⎪ εp ≥ 0.18 ⎩1

(11)

(23) 13644


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Other simulation parameters for these two risers are listed in Tables 1 and 2.

diameter, then the force is divided by the statistic weight to represent the force on a real particle: N

Fc =

∑

(Fijn + Fijt )/W

Table 1. Simulation Parameters of FCC Riser (25)

j = 1, j ≠ i

As for the rotation of particle, the moment of inertia I is calculated by mpdp2/10, and is W 5/3 times smaller than the inertia based on coarse-grained particle. Thus, the torque on each tracked particle should be calculated as N

T=

∑ j = 1, j ≠ i

(L n × Fijt )/W 5/3 (26)

where L is the distance from particle center to contact point. The details of the DEM model can be found in the MFIX-DEM documentation51 with verification and validation studies in.52,53 The first-order Eulerian integration scheme is used to update the new velocity and position. The time-step is reasonably small because it is based on spring stiffness coefficient. Subsequently, the first-order time stepping scheme is a good approximation, which is fast and has requires less memory.

3. SIMULATION PARAMETERS In this paper, two different CFB risers are simulated. The first one is operated with FCC particles54 and the second one is with glass beads.55 The detailed experimental setups are shown in Figure 1. For the FCC riser, the RTD is measured by tracing

parameters

value

FCC particle diameter, dFCC (μm) FCC particle density, ρFCC (kg/m3) FCC parcel diameter, dCGP,FCC (dFCC) NaCl particle diameter, dNaCl (μm) NaCl particle density, ρNaCl (kg/m3) NaCl parcel diameter, dCGP,NaCl (dNaCl) CGP wpring constant, kn (N/m) CGP restitution coefficient, e CGP friction coefficient, μ fluid density (kg/m3) fluid viscosity (Pa·S) superficial velocity (m/s) solid flux, Gs (kg/m2/s) CFD grid number in X direction CFD grid number in Y direction CFD grid number in Z direction gas phase time step, Δtgas (s)

70 1400 50 57.5 2160 60 1.0 × 102 0.1 0.6 1.2 1.8 × 10−5 7.0 133 22 450 22 5.0 × 10−4

Table 2. Simulation Parameters of Glass Beads Riser parameters

value

glass beads particle diameter, dgb (μm) glass beads particle density, ρgb (kg/m3) glass beads parcel diameter, dCGP,gb (dgb) CGP spring constant, kn (N/m) CGP restitution coefficient, e CGP friction coefficient, μ fluid density (kg/m3) fluid viscosity (Pa·S) superficial velocity (m/s) solid flux, Gs (kg/m2/s) CFD grid number in X direction CFD grid number in Y direction CFD grid number in Z direction gas phase time step, Δtgas (s)

150 2550 30 1.0 × 102 0.1 0.3 1.2 1.8 × 10−5 3.9, 4.5 33.3, 36.8 20 400 20 1.0 × 10−3

The three different drag models used in the simulation of FCC riser and glass beads riser are compared in Figures 2 and 3. Since the filtered models are based on the Wen−Yu drag model, the correction factors with respect to the Wen−Yu drag model are shown for comparison. For the fixed numerical grid used in this study, generally, the IGCI drag model only depends on voidage while the Sakar drag model also depend on slip velocity (i.e., Re number). The correction of Sakar model with respect to the homogeneous drag mode (Wen−Yu) is much larger (smaller values in Figure 2) than that of IGCI model in dense and high Re regions. For glass beads riser, although the CFD grid size is about 51 dp and 132 dp in radial and axial directions, the dimensionless filter size is only about 0.034584 due to the large particle terminal velocity (about 1.73637 m/s), and the calculated drag corrections are much closer to 1, especially for IGCI drag model and Sakar drag models in dilute and low Re regions.

Figure 1. Simulation domain of FCC riser (a) and glass beads riser (b).

NaCl crystals with a diameter of 57.5 μm and a density of 2160 kg/m3. The axial pressure profiles is measured with pressure probes at an acquisition frequency of 20 Hz. For the glass beads riser, the RTD and radial solids velocity profiles are measured by tracking a single radioactive particle.55 The particle-based Reynolds number is in the range of 1 to 20 for both Geldart type A and B particles used in this study. The Courant number is 0.175 for FCC riser and 0.197 for Geldart B particle riser.

4. RESULTS AND DISCUSSION 4.1. FCC Riser. Since the inlet mass flow rate of particles is set to a constant value, the solid inventory in the riser can be 13645


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Figure 2. Comparison of two filtered drag models for FCC riser with nondimension filter size of 1.8079.

Figure 3. Comparison of two filtered drag models for glass beads riser with nondimension filter size of 0.034584.

used as a metric to measure when the riser flow reaches a statistical steady-state. As shown in Figure 4, the simulation

detected at riser height of 8.5 m in accordance with experimental measurements.54 Experimentally, it is difficult to measure the solids inventory; however, the axial pressure drop can be easily measured to quantify the solids distribution in the riser because it is fair to assume that most pressure drop in the riser is due to the weight of the solids. Figure 5 compares the axial pressure gradients of

Figure 4. Predicted solid inventory in FCC riser.

with Gidaspow drag model reached a stable inventory of about 3.7 kg after about 4.0 s. However, for the filtered drag models like IGCI and Sakar it took about 10 s to reach a stable state and the inventory is about 5.1 and 4.8 kg, respectively. The different solid inventories predicted by these models indicate that with heterogeneous drag models a denser fluidized bed can be predicted. Since the inventories are stabilized after 10 s, the following time averaged results are based on the postsimulation analysis of results with a frequency of 20 Hz at 20−40 s. Also, the tracer particles are added into the riser from 20 to 23 s and

Figure 5. Axial pressure gradient profile of FCC riser. 13646


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Industrial & Engineering Chemistry Research different drag models with experiment data. It is clear that all the simulations can capture a dense phase in the bottom region and a dilute phase in the top region. In previous research,56 the CFD grid size of TFM was refined to 18 dp to capture the axial profile in FCC riser. However, in this coarse-grained CFDDEM simulation, the CFD grid size in the radial and axial directions are 71dp and 286dp. This indicates that a coarser CFD grid can be used in Euler−Lagrangian simulations. This is because the particle movements, particle−particle collisions, and interphase momentum exchange are all resolved at particle scales rather than fixed grid which needs a fine grid to reduce the errors due to discretization of convection-diffusion equations and stress models. Although the Gidaspow drag model can qualitatively capture the overall pressure profile, the predicted pressure gradient is smaller than experiment data at the bottom dense region of the riser. However, the tested two filtered drag models are in better quantitatively agree with experiment data. This indicates the filtered drag models derived from fine-grid two-fluid simulations can also be applied in Euler−Lagrangian simulations. Experimentally,54 the residence time is measured using salt (NaCl) crystals with a diameter of about 57.5 μm and a density of 2160 kg/m3. Although the terminal velocity is similar to the FCC particles, it is still not known whether these tracer particles will behave in a manner similar to that of the FCC particles especially in the dense bottom region where particle collisions dominate. Thus, in order to quantify the uncertainty due to using these tracer particles, the residence time of both FCC particles and NaCl tracers are analyzed. Figure 6

Figure 7. Cumulative NaCl tracer and FCC particles RTD in the FCC riser.

as using tracers, can benefit from our simulation tools for further validation. The void fraction (voidage) and particles Reynolds’ number (Re) statistical distribution are also analyzed in Figure 8. It clearly shows that most of the particles are either in the dense region with a voidage about 0.62 or in a dilute region with a voidage of about 0.96. This distribution is also consistent with the pressure gradient profiles in Figure 5, in which the large pressure gradient near the bottom corresponds to particles in dense region and small pressure gradient corresponds to the dilute region. For Re number distribution, most of the particles are less than 10 due to the FCC particles small terminal velocity. Also, the two tested filtered drag models predict very similar profiles for both voidage and particle Re number. Although the particle voidage and Re number distribution predictions are quite similar for these two different drag models, the drag corrections on the particles are quite different as shown in Figure 9. At the dense bottom region, the correction to the drag is more widely distributed than in the dilute region. This is because in the dense bottom region the flow is more complex and heterogeneous as indicated in Figure 9. For particles near the wall of this dense flow region, both the voidage and the slip velocity are small, resulting in a drag force close to that predicted by Wen−Yu drag correlation. However, for particles in the center region where particles are accelerating, their slip velocity and voidage are both larger implying a larger correction to the Wen−Yu drag model. It can also be observed that the IGCI drag corrections are more uniformly distributed than Sakar drag model because it only depends on local voidage, while for Sakar correction the Re number also plays an important role as seen previously in Figure 2. The normalized drag correction based on these two models is also quantitatively analyzed in Figure 10. It shows, the corrections to the IGCI model mainly lies in the range of 0.22− 0.38 while the Sakar model is more uniformly distributed in the range of 0.05 to 0.98. It is interesting that very similar pressure gradients and RTDs are observed while the drag corrections are quite different. Actually, the averaged correction to the IGCI and Sakar models is about 0.2782 and 0.3679. The averaged IGCI correction coefficient is about 24% lower than the Sakar model. This explains why the pressure drop and residence time of IGCI model is slightly greater than that predicted by Sakar model. Some previous researchers found that even with a constant drag corrections the simulation results of FCC riser or regenerator can be largely improved.57 These results indicate

Figure 6. Cumulative NaCl crystals RTD in the FCC riser.

compares the predicted RTD by cumulatively counting the transient number of NaCl tracers leaving the riser from the outlet. It shows that the filtered drag models more accurately predict the experiment data while Gidaspow drag model under predicts the residence time. Figure 7 compares the RTD calculated by counting the transient number of NaCl tracers as well as FCC particles at the outlet of the riser. It shows that the residence time of NaCl tracers slightly over predicts that of the FCC particles. This computational study proves that the NaCl tracers can represent reasonably well the RTD in this FCC riser. This is an interesting finding because even though salt tracers have been used for a long time in industry, a simulation study to further validate their use has never been conducted in the past to the best of our knowledge. It is obvious to state that our numerical CFD tools need experimental data for validation, but we can also claim that experimental data and practices, such 13647


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Figure 8. FCC particle voidage (a) and particle Reynolds’ number (b) distributions in FCC riser.

Figure 9. Normalized drag correction on FCC particles in the FCC riser (the correction ranges from 0 to 1 as color changes from blue to red).

that the drag correction distribution has minor influence on the

system geometry and operating conditions should be carried out, which is beyond the scope of this current research. 4.2. Glass Beads Riser. Similar to the FCC riser, the glass beads riser is also simulated with a constant solids inlet flux.

hydrodynamics as long as their averaged value is similar. To fully confirm this observation, more simulation in different 13648


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flow conditions. This observation is also confirmed by Figure 14 that shows more than 80% of the particles are in the region with a voidage larger than 0.8 where the Wen−Yu drag applies in the Gidaspow drag model. The Sakar drag correction predicts a larger RTD compared with those of other drag models and those measured experimentally. This can be attributed to the low drag values computed with this specific model. Recall that in the previously studied FCC riser, most of the particle Re number calculated values were less than 10. However, larger particle Re numbers can be observed for glass beads. As shown in Figure 15, for IGCI drag models there are about 20% particles with a Re number larger than 15 and about 10% particles with Re larger than 20. For the results with Sakar drag models, the predicted Re numbers are even larger. We stress that although the particle Re number of these Geldart B particles is larger than that of Geldart A FCC particles most of the calculated Re values are still less than 20. This is due to a relatively short acceleration zone in the rise and suggests that the DNS or filtered drag models should focus more on the low Re number region. The previous analysis of drag models indicates that the drag correction to the Wen−Yu correlation by the IGCI model is smaller than Sakar model and shows this effect on the RTD and Re number distribution. To confirm this observation directly in our computed results, the drag correction on each particle based on these two drag models are compared in Figure 16. It is very clear that the IGCI drag correction is close to one indicating same values as Wen−Yu model, while the calculated Sakar drag coefficient indicate drag values smaller than those preeicted with Wen−Yu model. For IGCI model, the drag predictions are more uniformly distributed from the bottom dense region to the top dilute region. For Sakar model, the drag predictions are mainly in the ranges of 0.4−0.6 and 0.95−1.0. The averaged drag correction of IGCI model is 0. 9722, while for the Sakar model, it is about 0.6042. These different drag corrections lead to different vertical velocity profiles and RTDs. Ultimately, the comparison of these predictions using different drag correlations with experimental data indicate that for the dilute transport of glass beads in a riser the traditional Gidaspow drag model shows the best performance, and the IGCI drag correction converges to Wen−Yu drag model and can also be directly used in this case. However, the currently investigated Sakar drag model overestimates the drag correction in this flow regime.

Figure 10. Drag corrections of FCC particles in the FCC riser.

Thus, the inventory is monitored as a metric to judge when a stable fluidization regime is reached. As shown in Figure 11, the inventory stabilizes after about 20 to 30 s for all the different drag models and operating conditions. In the two tested operating conditions, the IGCI drag correction predicts results similar to those with Gidaspow drag model, while the Sakar drag corrections predict a larger solids inventory. This is because the IGCI drag model is similar to Wen−Yu drag model for the glass beads case, while the Sakar model still predicts lower drag values (see Figure 3). The radial profiles of solids vertical velocity are plotted for the three drag models considered in this study and compared to experimental measurements in Figure 12. The simulations can predict the correct velocity profiles showing a higher velocity in the center and lower velocity near the wall. However, near the center of the riser the velocity is overpredicted especially for Sakar drag correction which uses the lowest values of drag coefficient. This discrepancy indicates that the current Sakar drag correction may not be directly extended to simulation of Geldart type B particles as this model was originally derived for Geldart type A particles. The RTD obtained with different drag models under different operating conditions are compared in Figure 13. As shown in previous results, similar profiles are predicted using the Gidaspow and IGCI drag models due to the fact that the values computed with IGCI drag correction are very close to those obtained with Wen−Yu drag models under the current

Figure 11. Predicted solid inventory in glass beads riser under different operating conditions. (a) Ug = 3.9 m/s, Gs = 33.3 kg/m2/s. (b) Ug = 4.5 m/s, Gs = 36.8 kg/m2/s. 13649


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Figure 12. Solids vertical velocity profiles in glass beads riser under different operating conditions. (a) Ug = 3.9 m/s, Gs = 33.3 kg/m2/s. (b) Ug = 4.5 m/s, Gs = 36.8 kg/m2/s.

Figure 13. RTD of glass beads in a riser operating under different conditions. (a) Ug = 3.9 m/s, Gs = 33.3 kg/m2/s. (b) Ug = 4.5 m/s, Gs = 36.8 kg/ m2/s.

Figure 14. Glass beads voidage distributions under different operating conditions. (a) Ug = 3.9 m/s, Gs = 33.3 kg/m2/s. (b) Ug = 4.5 m/s, Gs = 36.8 kg/m2/s.

5. CONCLUSIONS

with experimental results. Our current simulation results also confirm that salt tracers can safely be used in FCC riser to accurately represent its RTD. Through the analysis of particle Re number distribution, the results show that most of the FCC and glass beads particles in riser have Re numbers less than 10 and 20, respectively. This suggests that the DNS or filtered drag models should focus specifically on the low Re number region to provide more accurate drag models. Another interesting result is that the drag correction distribution shows only a minor effect on the flow field, while the average value is more important. This explains why previous research showed

In this research, the riser section of two fluidized beds circulating both FCC particles and glass beads are simulated with coarse-grained CFD-DEM using a homogeneous drag model as well as two filtered drag models that include the effect of unresolved flow heterogeneities, such as small clusters and streamers. By comparing our numerical results with available experimental data, we conclude that the coarse-grained CFDDEM with filtered drag models can predict the correct RTD curve for FCC particles. For the dilute riser flow of glass beads, the homogeneous drag model provides reasonable agreement 13650


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Figure 15. Particle Re number in glass beads riser under different operating conditions. (a) Ug = 3.9 m/s, Gs = 33.3 kg/m2/s. (b) Ug = 4.5 m/s, Gs = 36.8 kg/m2/s.

Figure 16. Normalized drag correction on glass beads with Ug = 3.9 m/s, Gs = 33.3 kg/m2/s (the correction ranged from 0 to 1 as color changed from blue to red).

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improved results of Geldart type A particle simulations by simply increasing the particle size in their drag models. As a summary, this study shows that the RTD of large scale reactors can be efficiently investigated with our numerical approach as well as with the old-fashioned experimental technique using salt tracers.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Liqiang Lu: 0000-0002-5101-1688 Xi Gao: 0000-0002-3305-8781 Sofiane Benyahia: 0000-0001-5193-5832 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education. This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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