Effect of Particle Polydispersity on Flow and Reaction Behaviors of

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Effect of Particle Polydispersity on Flow and Reaction Behaviors of Methanol to Olefins Fluidized Bed Reactors Li-Tao Zhu, Hui Pan, Yuanhai Su, and Zheng-Hong Luo Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b04026 • Publication Date (Web): 11 Jan 2017 Downloaded from http://pubs.acs.org on January 21, 2017

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Industrial & Engineering Chemistry Research

Effect of Particle Polydispersity on Flow and Reaction Behaviors of Methanol to Olefins Fluidized Bed Reactors

Li-Tao Zhu, Hui Pan, Yuan-Hai Su, Zheng-Hong Luo* Department of Chemical Engineering, College of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

* Correspondence to: Z.H. Luo; e-mail: [email protected] Tel.: +86-21-54745602 Fax: +86-21-54745602

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ACS Paragon Plus Environment


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ABSTRACT: In this contribution, a reactor model has been first developed with the objective to fundamentally comprehend the qualitative influence of the solid polydispersity on the features of a methanol-to-olefins (MTO) fluidised bed reactor. Regarding that coke deposition on the MTO catalyst significantly affects the reaction rate with its formation usually taking dozens of minutes to achieve the desired coke content, the optimum average coke content was firstly obtained based on a filtered computational fluid dynamic (CFD) model. Furthermore, comparison of predictions through a CFD method and a reaction engineering approach (REA) was conducted. Predictions basically match the experimental data. Subsequently, the influence of the solid PSD on reactor characteristics was comprehensively explored through a filtered CFD method coupled with the population balance model (PBM). Results suggested that the particle breakage performed a significant function in MTO FBRs, causing particle size evidently decreased.

Keywords: Fluidization; Particle polydispersity; Multiphase flow; CFD–PBM coupled model; Filtered model; MTO lumped kinetics.

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1. INTRODUCTION Recently, a CFD method has been applied to feature the fluid-particle two-phase flow behavior in methanol-to-olefin (MTO) fluidized bed reactors (FBRs).1-4 Zhu et al.4 first developed a filtered two-fluid model (FTFM) using coarse grids to explore performance of a large-scale MTO FBR, whose efforts mainly focused on the monodisperse gas–solid ﬂows. In recent years, more and more contributions5-17 have been focused on comprehending the polydisperse gas-particle flows in FBRs. There is considerable literature showing interest involving the particle size distributions (PSDs) that used population balance model (PBM)18 in polydisperse FBRs,19-33 and thus some CFD-PBM incorporated model11,12,26-28,30-33 have been developed to characterize the fluid-particle features in flow fields of the fluid–particle two-phase flow reactors. To solve the PBM numerically, the method of moments (MOMs)34 was introduced. Yet, at its early stage this method has suffered from the issue of closure, inevitably limiting its applicability. Subsequently, the quadrature approximation to PSDs was proposed to solve this closure problem.35 Since then, several improved MOMs, such as quadrature method of moments (QMOM) and direct quadrature method of moments (DQMOM), have been reported by different researchers.36-39 For details, the relevant literature to which the readers can refer to.35, 38, 39 Up to now, most of significant developments regarding the PSD, however, have been applied to fluidized-bed polymerization reactors or fluid catalytic cracking (FCC) riser reactors, whereas currently no open studies are devoted to studying the effect of the catalyst particle polydispersity in MTO FBRs.

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So far, a challenging issue in simulating the hydrodynamics of FBRs is that the state of heterogeneous gas-solid flows is frequently fluctuating, thereby causing solid concentration and velocities fluctuate across a wide range of spatial and time scales.40-43 Commonly, Gidaspow model,44 is used in considerable numerical simulation studies, in which Wen and Yu drag45 and Ergun drag46 closures for dilute and dense systems respectively. However, this empirical drag approach didn’t consider the effect of small-scale heterogeneous flow structures, accordingly leading to failed flow predictions.40,43 Classic empirical laws provided a routine to capture these small scales in gas-solid flows, whereas these laws usually suffered from the high cost of computing abilities since mesh element sizes demanded should be no more than a few solid particle diameters.40,43,47 Notably, even for a laboratory-scale FBR, simulation using the TFM with the classic closures would be unrealistic, since the small time step and the fine grid size required will still make such a CFD simulation rather time-consumption.48,49 Correspondingly, coarse-grid simulation procedures through a sub-grid closure are preferable, especially for industrial-scale devices.43,48,50,51 To address this challenging issue, in recent decades constructive contributions41,50,52,53 have been made to driving the development of the sub-grid methods, among which sub-grid filtered closure bases on appropriate simulation data extracted from simulation with highly fine-grid resolution while energy-minimization multiscale (EMMS) model is on the basis of the energy minimization approach. Moreover, Sundaresan et al.10,41,54-57 has systemically studied the filtered methods for both the monodisperse non-reactive conditions and the polydisperse reactive gas-solid

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two-phase flows. However, no efforts have been paid to the application of the filtered model coupled with PBM for a polydisperse MTO reaction system. In fact, PSD of MTO catalyst is similar to that FCC catalyst that belongs to typically Geldart type A solid particles. The PSD of this type of solid particles like FCC particles has been focus of studies for many years, whereas the explorations on PSD of MTO solid catalyst on reactor behavior are still rather scarce. Moreover, because of the existence of the forces such as intermolecular force, static electricity and other relevant forces between solid particles, the solid particles will unavoidably agglomerate. At the same time, because of the collision consumption, catalyst particles also show a certain degree of breakage. Thus, the PSD evolution performs an important function in reactor behavior in gas-solid reaction flow systems. With this in mind, a reactor model, namely, the filtered CFD model coupling of MTO lumped kinetics with PBM, was applied to understand the effect of the solid phase polydispersity on features of a laboratory-scale MTO FBR fundamentally. Firstly, the simulation results were compared with the numerical predictions computed through a classic reaction engineering approach (REA) (i.e. continuous stirred tank reactor (CSTR) model) together with the experimental data. Meanwhile, the optimum average coke content along the bed was obtained by means of simulation without considering the solid phase PSD. Finally, the effect of the solid phase PSD in the PBM was integrated with the previously obtained optimum average coke content in order to closely approach the realistic industrial operation conditions.

2. MODEL DESCRIPTION 5



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Given that governing equations, filtered drag model, species and energy conversation equations and kinetic model are available in the fluent code user guide58 or the open reports4,55,59,60, herein the above equations have been briefly summarized in Tables 1 and 2. The kinetic scheme is shown in Figure 1. In addition, the thermodynamic parameters for gaseous species and the kinetic data are listed in the Supporting Information. 2.1. Descriptions of the PBE and QMOM. Based on the contribution conducted by Hulburt et al.34, the common form of the PBE is defined as follows:

r ∂n( L; x, t ) ∂ + ∇⋅[un( L; x, t )] = − [G(L)n( L; x, t )] + Bag ( L; x, t ) ∂t ∂L −Dag ( L; x, t ) + Bbr (L; x, t ) − Dbr ( L; x, t )

(1)

In the left part of the eq 1, n( L; x, t ) represents the number density function; On the right-hand side of the eq 1, G ( L) n( L; x, t ) is the solid flux resulted from component growth rate. Bag ( L; x, t ) and Dag ( L; x, t ) represent the birth and death rates of the solid particle diameter resulted from particles aggregation. Bbr ( L; x, t ) and Dbr ( L; x, t ) represent the birth and death rates of the solid particles diameter

resulted from particles breakup, respectively. The moments of PSD are: ∞

mkk (t ) = ∫ n( L; x, t ) Lkk dL

kk = 0,1, ⋅⋅⋅, 2 N − 1

(2)

0

Where, N represents the quadrature approximation order (in this work, N=3) and kk represents the specified number of moments. These moments are given special meanings:

m0 , m1 , m2 , m3 are determined by the total number, length, area and volume of solid particles per unit volume of mixture suspension, namely, N total =m0 , Ltotal =m1 ,

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Atotal =K a m2 , Vtotal = K v m3 . In addition, the volume-average particle diameter, namely, L32 , is commonly regarded as the volume-average solid particle diameter, which is written as follows:

L32 =

m3 m2

(3)

The moment transformation is described as follows: ∞ r ∂mkk + ∇ ⋅ (u s mkk ) = − ∫ kLkk −1G ( L)n( L; x, t )dL + B ag (t ) − D ag (t ) ∂t 0

(4)

+ Bbr (t ) − Dbr (t ) where, ∞

B ag (t ) =

∞

1 n(λ ; x, t ) ∫ β (u , λ )(u 3 + λ 3 )kk /3 n(u; x, t )dud λ ∫ 20 0 ∞

∞

0

0

D ag (t ) = ∫ Lk n( L; t ) ∫ β ( L, λ )n(λ ; t )d λ dL ∞

∞

0

0

(5)

(6)

B br (t ) = ∫ Lk ∫ a(λ )b( L | λ )n(λ ; t )d λ dL

(7)

∞

D br (t ) = ∫ Lk a ( L)n( L; t )dL

(8)

0

For MTO reaction systems, because of the existence of the forces such as intermolecular force, static electricity and other relevant forces between solid particles, the solid particles will unavoidably agglomerate. Meanwhile, because of the collision consumption, solid particles also exhibit a certain degree of breakage; however, this process does not involve the particles growth. The moment transformation mechanism can be further described as follows:

r ∂mkk + ∇ ⋅ (u s mkk ) = B ag (t ) − D ag (t )+ B br (t ) − Dbr (t ) ∂t In QMOM, a quadrature approximation is utilized as follows:

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(9)


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∞

N

0

i =1

mkk = ∫ n( L; x, t ) Lkk dL ≈ ∑ wi Lkki

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(10)

McGraw proposed a product-difference method based on lower-order moments35 and the weights ( wi ) and the abscissas ( Li ) can be hence calculated through this approach.

Bag =

N 1 N 3 3 kk /3 w a( Li , L j ) ∑ i ∑ w j ( Li + L j ) 2 i =1 j =4

N

N

i =1

i =1

N

∞

i =1

0

(11)

Bag = ∑ wi ∑ w j a( Li L j )

(12)

Bbr = ∑ wi ∫ Lkk g ( Li ) β ( L)dL

(13)

N

Dbr = ∑ Lkki wi g ( Li )

(14)

i =1

The Ghadiri model61 is employed to simulation only the breakage frequency of solid particles:

f = Kb v 2 L5/3

(15)

Where, Kb is the breakage constant, about 1.1326×10−8 in this work. The parabolic breakage probability density function (PDF) is expressed to specify the daughter distribution:

β ( Li | L j ) =

3CL2i C 72 L8i 72 L5i 18L2i + (1 − )( − 6 + 3 ) L3j 2 L9j Lj Lj

(16)

Where, C is set to 1, meaning that unequally-sized fragments would be more likely to obtain. The solid particle aggregation kernel should consist two parts: Brownian and hydrodynamic kernels62,63 suggested by the literature36,64: 2 2k BT ( Li + L j ) 4 3π 1/2 ε 1/ 2 a ( Li , L j ) = + ( ) ( ) ( Li + L j )3 υ 3µ Li L j 3 10

8


(17)

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Where, kB, ν and ε represent Boltzmann’s constant, the turbulent dissipation rate and the kinematic viscosity, respectively. The moment transport equation is given as follows: N N N r ∂mkk 1 N + ∇ ⋅ (u s mkk ) = ∑ wi ∑ w j ( L3i + L3j )kk /3 β ( Li , L j ) − ∑ Lkki wi ∑ w j β ( Li L j ) + ∂t 2 i =1 j = 4 i =1 i =1 N

∞

N

(18)

+∑ wi ∫ Lkk a( Li )b( L Li )dL − ∑ L wi a( Li ) kk i

i =1

i =1

0

2.2. CFD simulation method and conditions. A common FBR studied by Wang B.65 was selected in this work, as shown in Figure 2. The 2-D geometry and the mesh were generated through GAMBIT 2.3.16 (Ansys Inc., US). Three different resolved grids (i.e. 120 × 10, 240 × 10, 240 × 15 ) were generated to study the grid sensitivity. And then the simulation was performed by means of FLUENT (Ansys Inc., USA) and discretization for continuity and momentum equations employs a finite volume solution. The double precision mode was selected. To incorporate the pressure and velocity fields, a SIMPLE algorithm was used. The volume fraction was discretized through a Quick method and the discretization of momentum and each component term in the incorporated model was a second-order upwind procedure. An unsteady implicit time was discretized through a first-order approach. The boundary condition of the wall is no slip for the two phases. Additionally, an under-relaxation iteration approach was adopted to ensure the simulation convergence. Numerical simulations with 1.0×10−3 s time step and 1.0×10−3 convergence criteria were accomplished on a 2.6 GHz Intel®, 1 CPU (8 cores) with 16 GB of RAM. It should be noted that the convergence criteria for energy terms was set 1.0×10−4. The simulation using medium grids ( 240 × 10 ) took about 20 min of 1 CPU (8 cores) time to calculate a 9



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one-second physical process and thus it will take about 56-days wall-clock time to compute a 4000-seconds physical coke deposition process. Note that the case with medium grids ( 240 × 10 ) was executed about 4000-seconds physical time, whereas the cases employing fine grids ( 240 ×15 ) and coarse grids ( 120 ×10 ) were both about 1000-seconds physical time. The main physical properties of the MTO catalyst and −1 −1 experimental data (1 atm; 723 K ; 2.1 g MeOH g cat h ; X w 0 = 0.2 ) were obtained from Ying et

al.60 Further detailed model parameters are available in Table 3. Herein, the current procedure uses TFM to obtain basic description of hydrodynamic behavior of fluidized bed, solid particle velocity and concentration obtained from TFM is utilized to solve the PBE. Once the PBE relating to the particle aggregation and breakage is solved, the Sauter average particle diameter can be gotten through the moments of PSD and utilized in the filtered drag closure to compute the filtered closure coefficient. Then the predicted filtered drag coefficient is fed back to TFM and the information of solid concentration and velocity updates. This loop will end at a desired flow time. Therefore, an integrated incorporation between filtered-CFD method and PBM is accomplished.

3. SIMULATION RESULTS AND DISCUSSION 3.1. Model verification and validation. Figure 3 illustrates the predictions through three different grid resolutions and Figure 4 compares the simulation results based on the medium grids ( 240 × 10 ) with experimental data.

Figure 3a plots similar bed expansion height computed with medium grids ( 240 × 10 ) and fine grids ( 240 ×15 ) but the simulation predicted with coarse grids

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( 120 ×10 ) produced a slightly higher bed expansion height. Nevertheless, qualitatively similar mass fraction of gaseous products without a water present basis predicted with different resolved grids can be observed in Figure 3b. Meanwhile, with the reaction proceeding shown in Figure 3c, similar trends of the inlet coke content through three sets of different grids were obtained, although a certain degree of the deviation predicted by coarse grids (120 × 10 ) still existed at the early stage of the reaction process. Form Figure 4, one can see that simulation results match the experimental data as the reaction goes on, showing the effectiveness of the reactor model employed in this work. Furthermore, comparing the difference between Figures 3c and 4, it can be concluded that, with the coke content increasing in the bed, the ethylene concentration without a water present basis shows a positive growth, whereas the mass fraction of propylene, C4 and C5 lumps exhibit an opposite trend. These results show that coke deposition performs a key function in the reaction rate. Actually, such an interesting phenomenon accords with the kinetic model. Specifically, to achieve a higher ethylene-to-propylene ratio, it is rationalized to realize through a relatively higher coke deposition on the MTO catalyst in the bed. In addition, the Courant number ( N c = U ∆t / ∆y , where U , ∆t , ∆y are the gas velocity, time step and mesh size along the flow direction) with mediums grids ( 240 × 10 ) was about 0.044, essentially satisfying range of 0.03-0.30 suggested by the literature.66-68 The value of Courant number shows that the numerical results were independent of convergence criterion, mesh size and time step.

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Therefore, the resolution with medium grids is fine enough to achieve reasonable grid-independent results and such a resolution is used in the following CFD simulations.

3.2. Flow field distributions. 3.2.1. Distributions of hydrodynamics. Figure 5 plots the instantaneous solid concentration pattern over the bed and the transient radial solid concentration profiles at a gas inlet velocity 0.087m/s. Figure 5 shows that the secondary phase volume fraction is basically denser in the annular areas than that in the core regions and is larger at the lower part of the bed than that at the higher part of the bed. A relatively realistic bed expansion height, about 1.3 times the initial bed height, is qualitatively acceptable, plotted in Figure 5. It’s also shown that there exist heterogeneous structures such as bubbles and streamers in the bed. Such simulation results further demonstrate the capability of the reactor model utilized in this work to capture the macroscopic gas-solid behavior. In addition, it’s noted that there is no unexpected phenomena such as slugging, choking and channeling behavior in the simulated contours in this work. According to an empirical correlation for calculating the minimum slugging velocity proposed by Baeyens and Geldart69 and an empirical inequality for judging the minimum slugging bed height reported by Yagi and Muchi70: U ms = U mf + 0.16(1.34 D 0.175 − H mf ) 2 + 0.07( gD ) 0.5

(19)

H mf / D > 1.9 / ( ρ s d p )0.3

(20)

The U ms is about 0.1087m/s calculated from eq 19, larger than the gas inlet

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velocity (0.087m/s) in this work; and the flowing parameters used in this work does not satisfy the inequality in eq 20. In other words, the bed in this work would not be operated in slugging fluidization according to the above two empirical equations. Thus, the calculated results qualitatively specify the validity of the coupled model.

3.2.2. Distributions of components. Figure 6 describes transient mass fraction contours of different components with flow time elapsing. It is observed in Figure 6 that, at the first stage (before 4000s) of the reaction, the ethylene concentration on a water present basis basically increases, whereas the propylene content exhibits an opposite trend with the rapid coke deposition proceeding, implying that a certain degree of coke deposition would be beneficial for the improvement of the ethylene selectivity in the reactor. This phenomenon can be attributed to the coke formation inside the MTO catalyst pores, thereby resulting in a certain degree of these small pores blockage. Correspondingly, smaller molecules such as alkenes are generated inside the catalyst pores more easily. With the reaction in progress, the coke deposition gradually spreads from gas inlet to pressure outlet in the bed. It seems that the coke deposits more severely in the vicinity of the gas inlet, thereby leading to incomplete reaction of the methanol in this zone. At the second stage (after 4000s), the mass fraction of all lumps decreases sharply. That is, “a transition point”, can be observed in Figure 7. In order to avoid a significant decrease of the methanol conversion, an optimum residence time (about 65-67 min) and an average coke content (about 6.77%~7.00%) for MTO catalysts are suggested. It is also helpful to guide the scaling-up of MTO reactors in the future work.

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3.3. Comparison of predicted results between CFD and REA. A lack of fundamental comprehension of hydrodynamics in multiphase chemical reactors usually leads to uncertainty in designing reactors.71 In this section, the reactor behavior obtained from CFD and REA was compared. The establishment of the REA in this work is by means of a continuous stirred tank reactor (CSTR) approach, and the corresponding gaseous mass conversion equations of species are given as follows:

dX i = (mcat Ri + Qm,in X i ,in − Qm,out X i ,out ) / m dt

(21)

Where Q (kg/s) represents the gaseous mass flow rate, m (kg) is the sum of the gaseous mass and mcat (kg) the mass of catalyst in the reactor, respectively.

m=

PVMwmix RT

(22)

Where V (m3) is the total reaction volume and the pressure and reaction temperature are assumed to be constant (1 atm; 723K) in this CSTR modeling. The average molecule weight for all gas mixture is calculated as follows: Mwmix = 1/ ∑ ( X i / Mwi )

(23)

The coke formation relation is as follows:

dCc = 100Mwcoke k7θ wϕ7 CMeOH dt

(24)

Figure 8 displays the comparison of the predicted results between CFD and REA along with the reaction time. Qualitatively, a similar trend of the predicted curves is shown in Figure 8. Around the reaction time of 4000s, the inflection point predicted by both CFD approach, whereas that point for REA occurs a few minutes earlier, as plotted in Figure 8a. Before the transition point the methanol conversion predicted 14


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through the CFD simulation is higher than that by the REA. In particular, in the later reaction stage (about 4000~4500s) a steeper decline of the methanol conversion predicted with the CFD method is displayed. In Figure 8b, before the transition point, the ethylene selectivity predicted through CFD code is basically higher than that through REA, whereas an opposite trend for the propylene selectivity is plotted. Around the transition point, the ethylene selectivity predicted by means of REA seems to gradually increase and is eventually higher than that through the CFD method.

Figure 8b shows that the gradient of the growth or decrease gradually changes after the rapid variation of the selectivity at the early period, when the computation is implemented based on of REA. This is consistent with the trend of the coke content, as plotted in Figure 8a, resulting from the selectivity of light olefin rapidly responding to the coke deposition as mentioned earlier. Definitely, the increasing gradient of the coke content computed based on REA also shows a smooth trend and is higher than that simulated through the CFD method at the early stage. Consequently, this phenomenon leads to the evident differences on the selectivity of the light olefins, as shown in Figure 8b. The sum of the selectivity to ethylene and propylene for REA is ~75% and that for CFD is ~79.5%. Empirically, the sum of the selectivity to ethylene and propylene is ~80%. The difference would be because REA used in this study is a CSTR model, with the assumption that the temperature and pressure fields are both homogeneous; and thus the influence of the flow structures on the MTO reaction rate is neglected. These flow structures include two parts: macro-structures and heterogeneous sub-grid structures such as bubbles, clusters and streamers, which

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in fact are in the state of persistent mutual evolution. Therefore, qualitative similarities and quantitative differences can be expected. In summary, predictions through CFD approach match the experimental data well, whereas seriously under predicted olefins selectivity to ethylene by REA in the present contribution is unacceptable in comparison with the experimental data. In addition, Figure 8a shows that the average coke content predicted by the CFD method grows from ~7.0% to 7.9% in the last 1000 s, which indicates that there is only about a 0.0009% increase of the average coke content per 1.0-second reaction time. Specifically, the growth of the average coke content seems to be negligible during a relatively short reaction time and hence this leads to a relatively stable selectivity of the gaseous products when studying the effect of the solid catalyst polydispersity on reactor performance in the following section.

3.4. Effect of solid particle ploydispersity. In this part, the polydisperse components of solid particles with continuous PSD involve three different initial Sauter mean diameters (d32). Both aggregation and breakage dynamic evolution characteristics were considered in this section. Furthermore, the hydrodynamic characteristics of polydisperse catalyst particles were also explored numerically on the basis of CFD-PBM coupled method. The experimental data72 for gaseous product selectivity and methanol conversion are shown in Table 4 to validate the CFD-PBM coupled method. It can be found that the predicted main olefin product selectivity (C2~C4 lumps) and methanol conversion match the experimental data well although there are quantitative differences for C1 and C3 paraffin lumps.

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Figure 9 displays initial PSDs of the solid catalyst particles with three different Sauter mean diameters (d32). As illustrated in Figure 10, for three different initial PSDs, the peak value of the number density distribution in each case increases significantly and the profile curves become narrower with the flow time proceeding. As shown in Figure 11, it can be found the volume-average solid particle diameter becomes smaller as the flow time proceeds and this decreasing trend becomes gentler as the flow time proceeds. Actually, this behavior can be due to the dynamic evolution between the aggregation and breakage process, in which the breakage process seems to be stronger. Therefore, the investigation shows that the breakage of solid particles, attributed to the abrasion and break-up with the collision and friction from particle-particle and particle-wall, is very significant in the present MTO reaction system.

Figure 12 shows the particle component concentration distributions varies at different flow time. As discussed in Figures 10 and 11, compared with the single particle component system, the polydisperse systems in this work consider both the dynamic breakage and aggravation processes and the breakage seems to be strongly dominant, causing the particle size decreases. Especially, for the system with 82.3µm particles, the expansion bed height in the polydisperse systems evidently exceeds that in the monodiperse system (Figure 5). Therefore, the evolution of the PSD has a significant effect on the fluidization. Furthermore, for the polydisperse systems with three different initial PSDs, the bed expansion height decreases significantly with the particle sizes enlarging, shown in Figure 12. This would be because the drag force

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exerted on the solid particle becomes weaker with the particle diameter increasing. In such a case, bubbles generation suffers from the larger particle diameters, resulting in the difficulty of larger particles flowing upward. Thus, lower expansion height for the bed with larger particles could be expected. As delineated in Figure 13, for the polydisperse systems with the same initial volume-average particle diameter, the contours show that the methanol mass fraction at the bottom of the bed becomes larger and ethylene and propylene component mass fraction decreases with the fluidization in progress. This may be because that the bed expansion height gets higher with the fluidization proceeding and then the solids catalyst concentration becomes lower in the bed. As a result, the reaction rate decreases and hence a lower methanol conversion near the gas inlet could be found. For the polydisperse systems with three different initial volume-average particle diameters, remarkable differences for gaseous species near the gas inlet are seen for all these three different polydisperse systems, mainly resulting from the different solids concentrations in the bed (in Figure 12). Figure 12 plots that the gradient of the particle holdup grows greatly with the increase of the particle diameters. Actually, solid catalyst particle concentration performs a key function in the methanol reaction rate as discussed above. Therefore, a higher catalyst concentration leads to a higher methanol conversion.

4. CONCLUSIONS In this contribution, a reactor model is first developed to comprehend the influence of the solid phase polydispersity on MTO reactor performance. As a consequence of the

18


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above simulated results, several conclusions can be drawn as follows: (1) The optimum average coke content along the bed, about 6.77%~7.00%, was firstly obtained on the basis of a filtered CFD model in a monodisperse reactor system. There exists a transition point for the methanol conversion at about 65-67 min reaction time. Moreover, simulation results basically show an acceptable match with the experimental data. (2) Comparison of predicated results through a CFD method and classic reaction engineering approach (REA) was explored. It is observed that qualitatively similar predictions through these two methods are obtained, whereas quantitative differences can also be found, due to neglecting the effect of flow structures when using REA. (3) For three cases with different initial PSDs, as flow time proceeds, the peak value of the number density distribution in each case increases and the profile curves become narrower. The volume-average mean particle size evidently decreasing indicates that the effect of particles breakage is stronger than particles aggregation. (4) For the polydisperse systems with the same initial volume-average particle diameter, the methanol mass fraction at the bottom of the bed becomes larger and ethylene and propylene component mass fraction decreases as the fluidization proceeds. For three different polydisperse systems, the Sauter average particle diameter performs a significant function on the hydrodynamic features and reaction behavior in the bed. The current work is a first necessary step to assess the capability of the coupled method to simulate breakage and aggregation progress that all particles in the same

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PSD only move with the same velocity acceptable in a MTO polydisperse reaction system. The second step is to simulate a more realistic 3-D study that all the solid particles move with particle-size-dependent velocities73 in a MTO fluidized bed.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI…. Identification of the used model, study of different time steps and the thermodynamic data of the species and the kinetic parameters are provided as Supporting

Information. AUTHOR INFORMATION Corresponding Author Professor Z. H. Luo; E-mail: [email protected]; Tel.: +86-21-54745602; Fax: +86-21-54745602

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS The authors thank the National Natural Science Foundation of China (Nos. U1462101 and 21625603), the National Ministry of Science and Technology of China (No. 2012CB21500402) and the Center for High Performance Computing, Shanghai Jiao Tong University for supporting this work.

NOMENCLATURE 20


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−1 Bag ,kk = birth rate of catalyst because of aggregation, s −1

Bbr ,kk = birth rate of catalyst because of breakage, s Cc = coke content over the catalyst, g coke / 100 g cat

Ci = mole concentration, mol / L d s = solid catalyst diameter, m

d32 = the Sauter average particle diameter, m Dag , kk

= death rate of catalyst particles because of aggregation, s−1 −1

Dbr , kk = death rate of catalyst particles because of breakage, s

Ei = the activation energy divided by the ideal gas constant

Eai = the activation energy f ext , finf = the extrapolation to infinite resolution −1

G ( L ) = particle growth rate, m · s

H , h = the correction factor for the drag coefficient

L, Li , L j = solid catalyst diameter, m L32 = Sauter average particle diameter, m

mkk = the kkth moment of number density function M wi = molecular weight, g / mol

n = the ratios of filter length to grid length v = velocity, m·s

-1

vslip = dimensionless slip velocity, m·s-1 Vcell = grid cell volume, m3 X w = water content in the feed

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Greek letters

α = volume fraction

ρ = density, kg·m-3 ∆p = bed pressure drop, pa ∆f = dimensionless filter length ∆f fil = filter length ∆g = grid size

θ w = water function ϕi = catalyst deactivation function for specie i Subscripts env = envelope

g = gas phase

s = solid phases fil = filtered

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Tables Table 1．．Governing relations and closures. Continuity equation (i=g, s) → ∂ (α i ρ i ) + ∇ ⋅ (α i ρi vi ) = 0 ∂t

(1)

Momentum balance equations ur ∂ r r r r r (α g ρ g vg ) + ∇ ⋅ (α g ρ g vg ⋅ vg ) = −α g ∇p + ∇ ⋅ (τ g + τ gRe ) + K gs (vs − vg ) + α g ρ g g ∂t → ∂ r r r r r (α s ρs vs ) + ∇⋅ (α s ρs vs ⋅ vs ) = −αs∇p − ∇ps + ∇⋅ (τ s + τ sRe ) + Ksg (vg − vs ) + α s ρs g ∂t Gas and solid phases stress tensors r r 2 r τ g = α g µ g (∇ ⋅ v g + ∇ ⋅ v g T ) + α g ( λ g − µ g ) ∇ ⋅ v g ⋅ I 3 r rT 2 r τ s = α s µ s (∇ ⋅ vs + ∇ ⋅ vs ) + α s (λs − µ s )∇ ⋅ vs ⋅ I 3 Gas and solid phases Reynolds stress tensors 2 r r r τ gRe = − (α g ρ g k g + µ g ,t ∇ ⋅ vg ) I + µ g ,t (∇vg + ∇vg T ) 3 2 r r r τ sRe = − (α s ρ s k s + µ s ,t ∇ ⋅ vs ) I + µ s ,t (∇vs + ∇vsT ) 3 Filtered drag correlation r r K sg , fil = K sg (1 − H ) = 0.75C Dα sα g ρ g vs − vg / d pα g −2.65 (1 − H ) CD = 24[1 + (0.15α g Re s )0.687 ] / α g Re s

(2) (3)

(4) (5)

(6) (7)

(8) (9)

r r Re s = ρ g d p vs − vg / µ g

(10)

Species transport equations r ∂ (α g ρ g X i ) / ∂t + ∇ ⋅ (α g ρ g vg X i ) = −∇ ⋅ (α g J g ,i )] + α g M i ∑ Ri

Energy conservation equations r ∂ (α g ρ g hg ) + ∇ ⋅ (α g ρ g vg hg ) = α g ∇ ( keff , g ∇Tg ) + H sg (Ts − Tg ) + α g ∑ Ri ⋅ ∆H i ∂t ∂ r (α s ρ s hs ) + ∇ ⋅ (α s ρ s vs hs ) = α s ∇ ( keff , s ∇Ts ) + H gs (Tg − Ts ) ∂t Solid phase pressure and bulk viscosity ps = α s ρ s Θ s [1 + 2 g 0α s (1 + es )]

(11)

(12) (13)

(14)

Θ s 1/ 2 4 ) 3 π Radial distribution function

λs = α s ρ s d p g 0 (1 + es )(

(15)

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g 0 = 1 / [1 − (α s − α s ,max )1/3 ]

(16)

Granular temperature

Θ s = vs' vs' / 3

(17)

Granular temperature equation 3 ∂ r r [ (α s ρ s Θ s ) + ∇ ⋅ (α s ρ s vs Θ s )] = ∇ ⋅ ( kΘ s ∇Θ s ) + ( − ps I + τ s ) : ∇vs − γ Θ s + φgs 2 ∂t Collisional energy dissipation

(18)

0.5 γ Θ = 12(1 − es2 ) g 0 ρ sα s2 Θ1.5 ) s / ( d sπ

(19)

s

The diffusion coefficient

kΘ s =

150ρ s d s πΘ s 6 Θs [1 + α s g 0 (1 + e)]2 + 2 ρ sα s2 (1 + e) g 0 π 384(1 + e) g 0 5

(20)

Solid phase shear viscosity

µ s = µ s ,col + µ s , kin + µ s , fr

(21)

µs ,col = 0.8α s ρ s d p g 0 (1 + es )(Θ s / π )0.5

(22)

µs ,kin = 10d p ρ s πΘ s / (96α s (1 + es ) g0 )[1 + 0.8(1 + es )α s g0 ]2

(23)

µs , fr = 0.5 ps sin θ / I 2 D

(24)

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Table 2．．Filtered drag model. Filtered interphase momentum exchange coefficient

K sg , fil = K sg (1 − H )

(1)

The correction factor

H = Min(henv ,1 or henv ,2 , hlin )

(2)

 0.5643(1 + α )α 0.15 s s  0.3 0.5766 + 0.1997 α  s  0.8428 + 0.6393α − 0.6743α 2  s s henv ,1 =  0.25  0.4099(0.65 − α s )  α −0.25 − 0.9281 s   0

(α s ≤ 0.10) (0.10 < α s ≤ 0.54)

(3)

(0.54 < α s ≤ 0.65) (α s > 0.65)

henv ,2 = 0.8428 + 0.6393α s − 0.6743α s2 (0 ≤ α s ≤ 0.65)

(4)

hlin = h1 ( h 1 > 0) or 0 ( h1 < 0)

(5)

h1 = (1.076 + 0.12vslip − 0.02 / (vslip + 0.01))α s + + (0.084 + 0.09vslip − 0.01 / (0.1vslip + 0.01)) ( ∆f ≤ 1.028)

h1 = (1.268 − 0.2vslip − 0.14 / (vslip + 0.01))α s + + (0.385 + 0.09vslip − 0.05 / (0.2vslip + 0.01)) (1.028 < ∆f ≤ 2.056) h1 = α s (0.018vslip + 0.1) / (0.14vslip + 0.01) + + (0.9454 − 0.09 / (0.2vslip + 0.01)) (2.056 < ∆f ≤ 4.112)

h1 = α s (0.05vslip + 0.3) / (0.4vslip + 0.06) + + (0.9466 − 0.05 / (0.11vslip + 0.01)) (4.112 < ∆f ≤ 8.224) h1 = α s (1.3vslip + 2.2) / (5.2vslip + 0.07) + + (0.9363 − 0.11/ 0.3vslip + 0.01) (8.224 < ∆f ≤ 12.336) h1 = α s (2.6vslip + 4) / (10vslip + 0.08) + + (0.926 − 0.17 / (0.5vslip + 0.01)) (12.336 < ∆f ≤ 16.448)

h1 = α s (2.5vslip + 4) / (10vslip + 0.08) + + (0.9261 − 0.017 / (0.5vslip + 0.01)) (16.448 < ∆f ≤ 20.560) h1 = α s (1.6vslip + 4) / (7.9vslip + 0.08) + + (0.9394 − 0.22 / (0.6vslip + 0.01)) (∆f > 20.560)

34


(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

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The dimensionless filter size 1/3 ∆f = g ∆f fil / vt2 ; ∆f fil = n ⋅ Vcell

(14)

For large filter sizes

hlin = f ext ⋅ h1 (h 1 > 0) or 0 (h1 < 0)

(15)

f ext = ( 3.494 / (1 + 8(∆f )0.4 ) + 0.882 ) finf

(16)

f inf = 0.882 ( 2.145 − 7.8(vslip )1.8 / (7.746(vslip )1.8 + 0.5586) )

(17)

For very small filter sizes

H = 0; K sg , fil = K sg

(18)

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Table 3. Model parameters Description

Value

Catalyst density

1220 kg ⋅ m−3

Sauter Mean Particle Diameter

82.3 µ m

Velocity inlet boundary condition

0.087 m ⋅ s −1

weight hour space velocity

−1 −1 2.1 g MeOH gcat h

Catalyst heat capacity

800 J ⋅ kg −1 ⋅ m −3

Catalyst thermal conductivity

0.192 W ⋅ m−1 ⋅ K −1

Gas thermal conductivity

0.0242 W ⋅ m−1 ⋅ K −1

Diffusion coefficient

2.88×10-5 m2 ⋅ s −1

Gas viscosity

2.4×10-5 Pa ⋅ s

Outlet boundary condition

Pressure outlet

Wall thermal conditions

723 K

Gravitational acceleration

9.81 m ⋅ s −2

Operating pressure

101.325 kPa

Inlet temperature

723K

Mass Ratio of water to methanol

1:4

Packing limit

0.63

Initial bed height

0.09m

Initial solid concentration

0.5

Convergence criteria

10−3

Time step size

10−3 s

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Table 4. Comparing results through CFD-PBM coupled method and experimental data.

Ych4

Prediction/% 1.88

EXP./% 1.12

Error/% 40.43

Yc2h4

42.73

42.58

0.35

Yc3h6

38.12

38.63

-1.34

Yc3h8

2.93

3.25

-10.92

Yc4

10.83

10.96

-1.20

Yc5

3.51

3.47

1.12

Conversion

99.07

99.13

0.06

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Figure captions Figure 1 The kinetic network. Figure 2 Geometrical features of the MTO fluidized bed reactor employed in this work.

Figure 3 (a) Average solid concentration field contour, (b) The product concentration without a water present basis and (c) inlet coke content predicted with different grid resolutions.

Figure 4 Comparing the predicted component mass fraction based on medium grids −1 −1 with the measured experimental data (1 atm; 723K; 2.1 g MeOH g cat h ; X w0 = 0.2 ,

on a water free basis).

Figure 5 The average solid concentration field contour over the bed and the average radial solid concentration profiles at a bed height of Y=0.04m, 0.08m, 0.12m, respectively.

Figure 6 (a) The transient mass fraction contours of the methanol and ethylene components with flow time advancing. (b) The transient mass fraction contours of the propylene and coke components (on a water present basis).

Figure 7 Methanol conversion and MTO inlet coke content vs. flow time. Figure 8 The comparison of the predicted (a) methanol conversion and average coke content and (b) gaseous specie concentration without a water present basis between CFD and REA along with reaction time.

Figure 9 Initial PSDs of the solid catalyst particles with three different Sauter mean diameters (d32).

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Figure 10 PSDs in the bed at different flow time: (a) d p0 =82.3µ m ; (b) d p0 =110 µ m ; (c) d p0 =150 µ m ( N = 3 ).

Figure 11 Evolution of Sauter mean solid particle diameter with flow time ( N = 3 ). Figure 12 Transient solid volume fraction profiles at the gas inlet velocity 0.087m/s with the polydisperse solid particle components across the flow time (0~15s: without coupling aggregation and breakage kernels; 15~175s: with coupling aggregation and breakage kernels).

Figure 13 Transient gaseous species distributions at the gas inlet velocity 0.087m/s with the polydisperse solid particle components across the flow time (0~15s: without coupling aggregation and breakage kernels; 15~175s: with coupling aggregation and breakage kernels).

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For Table of Contents Only

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Figure 1 17x21mm (600 x 600 DPI)



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Figure 3 101x84mm (300 x 300 DPI)



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Figure 6a 54x39mm (300 x 300 DPI)


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Figure 6b 54x39mm (300 x 300 DPI)



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Figure 10 114x88mm (300 x 300 DPI)



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Figure 11 29x20mm (600 x 600 DPI)


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Figure 12 65x56mm (300 x 300 DPI)



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Figure 13 93x104mm (300 x 300 DPI)


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Effect of Particle Polydispersity on Flow and Reaction Behaviors of

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