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Computers and Chemical Engineering 60 (2014) 1– 16

Contents lists available at ScienceDirect

Computers and Chemical Engineering

jo u r n al homep age: www.elsev ier .com/ locate /compchemeng

FD–DEM modeling of gas–solid flow and catalytic MTO reactionn a fluidized bed reactor

a-Qing Zhuanga, Xiao-Min Chena, Zheng-Hong Luob,∗, Jie Xiaoc

Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, PR ChinaDepartment of Chemical Engineering, School of Chemistry and Chemical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR ChinaCollege of Chemistry, Chemical Engineering and Materials Science, Soochow University, 215123, PR China

r t i c l e i n f o

rticle history:eceived 15 February 2013eceived in revised form 12 August 2013ccepted 14 August 2013vailable online 29 August 2013

eywords:luidizationranulationultiphase reactorsathematical modeling

a b s t r a c t

The methanol-to-olefins (MTO) process is currently being implemented successfully in fluidized bedreactors (FBRs) in China. Characterizing the gas–solid flow is crucial in operating MTO FBRs effectively. Inthis work, a combined discrete element method (DEM) and computational fluid dynamics (CFD) model isdeveloped to describe the gas–solid flow behavior in an MTO FBR. In this model, the particles are modeledusing DEM, and the gas is modeled using Navier–Stokes equations. The combined model incorporatesthe lumped kinetics in the gas phase to achieve the MTO process. Moreover, the combined model cancharacterize the heat transfer between particles as well as that between the gas and the particles. Thedistinct advantage of the combined model is that real-time particle activity can be calculated by trackingthe motion history of the catalyst particle with respect to heat transfer. The simulation results effectivelycapture the major features of the MTO process in FBR. Moreover, the simulation results are in good agree-

EMTO process

ment with the classical calculation and experimental data. The particle motion pattern and distributionsof a number of key flow-field parameters in the reactor are analyzed based on the validated model. Theeffects of operating conditions on FBR performance are also investigated. The simulation results showthat the particle motion exhibits a typical annulus–core structure, which promotes excellent transferefficiency. The results also demonstrated that the feed temperature, inlet gas velocity, and feed ratio ofwater to methanol significantly affect reaction efficiency.

. Introduction

A computational fluid dynamics (CFD) model was recentlyroposed to describe the gas–solid flow in fixed-bed methanol-to-lefins (MTO) reactors (Zhuang, Gao, Zhu, & Luo, 2012). Interestingow behavior, such as coke deposition, as well as componentnd temperature distributions was observed in fixed-bed reactors.he coke deposition and the component distributions were alsoimulated in a fixed-bed reactor as a function of feed tempera-ure, composition, and space velocity (Zhuang et al., 2012). Theaboratory-scale reactor filled with catalyst particles was assumedo be a continuous porous medium. Given that the continuous Eule-ian scheme is incapable of characterizing discrete solid particlesWu, Cheng, Ding, & Jin, 2010a), some types of important solidow behavior, such as particle motion pattern, temperature, and

elocity, were not studied. Consequently, several important floweatures in reactors, particularly in fluidized bed reactors (FBRs),uch as excellent solid mixing, as well as heat and mass transfer

∗ Corresponding author. Tel.: +86 21 54745602; fax: +86 21 54745602.E-mail address: luozh@sjtu.edu.cn (Z.-H. Luo).

098-1354/$ – see front matter © 2013 Elsevier Ltd. All rights reserved.ttp://dx.doi.org/10.1016/j.compchemeng.2013.08.007

© 2013 Elsevier Ltd. All rights reserved.

properties, were not analyzed (Zhu, Zhou, Yang, & Yu, 2008). Mean-while, considering that the MTO reaction is highly exothermic, FBRis a more appropriate reactor for the MTO process compared with afixed-bed reactor because of the excellent heat transfer capabilityof FBRs (Levenspiel, 2002). The FBR-based MTO process is currentlybeing industrialized in China (Xing, Yue, Zhu, Lin, & Li, 2010; Zhuet al., 2010). To the best of our knowledge, the application of CFD tothe MTO process in FBRs has not been reported because of the com-plexity of particle motion in FBRs. Particle motion, particularly itspattern, is reported crucial for CFD modeling (Chu, Wang, Xu, Chen,& Yu, 2011; Chu & Yu, 2008; Wu, Cheng, et al. 2010; Wu, Yan, Jin, &Cheng, 2010b; Zhao, Ding, Wu, & Cheng, 2010a; Zhao, Cheng, Wu,Ding, & Jin, 2010b). Thus, the effect of particle motion pattern onthe flow-field parameters of the reactor requires further investiga-tion to achieve the proper scaling up and design of reactors (Deen,Annaland, van der Hoef, & Kuipers, 2007; van der Hoef, Annaland,Deen, & Kuipers, 2008; Zhu et al., 2008). Understanding FBRs in theMTO process requires a fundamental knowledge of the gas–solid

flow behavior while considering the motion of discrete particles inthe gas phase.

CFD approaches that can simulate gas–solid flow in FBRs aregenerally classified into two categories: Eulerian–Lagrangian and

2 Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16

Notation

Cj,r molar concentration of species j in reaction r,kmol/m3

Cp heat capacity at constant pressure, J/kmol KCp,c heat capacity of molten salt, kJ/(kmol K)Cp,g heat capacity of gas, kJ/(kmol K)Cp,p heat capacity of particles, kJ/(kmol K)CDS standard drag coefficientCAMF feed rate of methanol, gMeOH/gCatdp particle diameter, mDi,m diffusion coefficient for species i in gas mixture,

m3/sE activation energy, kJ/kmolfs static friction coefficient�F interaction term between gas and particles, N/m3

�FD,i drag force from gas to ith particle, N�Fn,ij/�Ft,ij normal (tangential) contact force between the ith

and jth particles, N�g gravitational acceleration, m/s2

hgs solid-to-gas convective heat transfer coefficient,W/(m2 K)

hi species enthalpy of formation, kJ/kmolHf,298 enthalpy at 298 K, kJ/kmolHc contact conductance, W/K�Hj heat of reaction j, J/kgI inertia of moment, kg m2

kc molten salt thermal conductivity, W/(m K)keff effective thermal conductivity of the medium,

W/(m K)kf fluid phase thermal conductivity, W/(m K)km mixture thermal conductivity, W/(m K)ks/kg solid (gas) thermal conductivity, W/(m K)kn/kt normal (tangential) spring constant, N/mki reaction rate constantKc initial rate constant for coke formationkf,r forward rate constant for reaction rKfc total heat transfer coefficient, W/(m2 K)mi mass of the ith catalyst particle, kgMi molecular weight, kg/molMm molecular weight of gas mixture, kg/kmolMw,i molecular weight of species i, kg/kmol�nij normal unit vector between two contacted particlesNu Nusselt number in the tubeNuD Nusselt number outside the tubep pressure, kPaPr Prandtl numberq heat flux, W/m2

Qgs,i heat transferred from gas to ith particle, WQi,k heat transferred from kth particle to ith particle, WQsg heat source per unit volume in gas phase, W/m3

R universal gas constant, kJ/kmol KS mean strain rate, 1/sSct turbulent Schmidt number, dimensionlessSi mass source of species j, kg/m3 srp particle radius, mRep Reynolds numberRi reaction rate, kg/(m3 s)R̂i,r arrhenius molar rate of creation of species i in reac-

tion r, kmol/(m3 s)t time, s

T temperature, KTg gas mixture temperature, KTp,i temperature of ith particle, K�Tij torque due to tangential contact force, N m�ug gas velocity, m/s�up,i ith particle velocity, m/s�Vn,ij/ �Vt,ij normal (tangential) relative particle velocity

between particle i and j, m/sVcell volume of computational cell, m3

vT transpose of velocity vector, m/sWHSV weight hourly space velocity, gMeOH/gCat hXA methanol mole fraction on a water-free basisXi outlet mole fraction of component iXw mole fraction of water in the feedYi mass fraction of species i˛f fluid side convective heat transfer coefficient at wall,

W/(m2 K)˛c salt bath side convective heat transfer coefficient at

wall, W/(m2 K) ̌ inter-phase momentum transfer coefficient,

kg/(m3 s)�ın/�ıt normal (tangential) displacement vector, mε turbulent kinetic energy dissipation, m2/s3

�g viscosity of gas phase, Pa s�c viscosity of molten salt, Pa s�t turbulent viscosity, Pa s�̃ turbulent kinematic viscosity, m2/s�

′i,r

stoichiometric coefficient for reactant i in the rthreaction

�′′i,r

stoichiometric coefficient for product i in the rthreaction

�n/�t damping coefficient, N s/m�

′j,r

rate exponent for reactant species j in the rth reac-tion

�′′j,r

rate exponent for product species j in the rth reac-tion

�b bulk density of bed, kg/m3

�g density of gas mixture, kg/m3

�s density of solid, kg/m3

�c density of molten salt, kg/m3

� thermal conductivity of steel, W/(m K)¯̄� shear stress of gas phase, Pa medium porosityϕi deactivation rate constant

tos time on stream, s�tij tangential unit vector between two contacted par-

ticles

ϕc carbon deposition rate constant

Eulerian–Eulerian methods (Ranade, 2000; Lim, Zhang, & Wang,2006; Utikar & Ranade, 2007; Vaishali, Roy, & Mills, 2008). Conti-nuity and momentum equations are used in the Eulerian–Eulerianmethod, because this method considers the full interpenetrationof continual subjects, suggesting that this method requires lessnumerical effort compared with the Eulerian–Lagrangian method,in which the motion of particles is calculated individually (Zhang,Lim, & Wang, 2007; Mahecha-Botero, Grace, Elnashaie, & Lim,2006, 2009; Yan, Luo, Lu, & Chen, 2012). Given the high compu-tational cost required to calculate the motion for a large numberof particles, the application of Eulerian–Lagrangian method isrestricted to low particle density. Most of the models proposed

in the literature to describe gas–solid flows were based on theEulerian–Eulerian method (Chen, Luo, Yan, Lu, & Ng, 2011; Gao,Chang, Lu, & Xu, 2008; Gao et al., 2009; Mahecha-Botero, Grace,Elnashaie, & Lim, 2006; Shi, Luo, & Guo, 2010). Although capable of

nd Ch

pfimatL2atatptwha22OZu2itwpTtao(1omsetaiutsndi(maLtcwtecetibmC

MCMB

Y.-Q. Zhuang et al. / Computers a

roviding quantitative agreement with the limited experimentalndings, these CFD models cannot physically describe the particleotion in the solid phase. Thus, the gas–particle, particle–particle,

nd particle–reactor wall interactions must be fully considered athe micro-scale to describe particle motion effectively (Xu, Ge, &i, 2007; Zhou, Pinson, Zou, & Yu, 2011; Zhu, Zhou, Yang, & Yu,007; Zhu et al., 2008). The Eulerian–Lagrangian method is prefer-ble for this endeavor because in this method, the particles areracked individually by solving Newtonian equations of the motion,nd the gas phase is treated as a continuum that is also coupled tohe motion of particles through an interphase interaction term. Thearticle motion in FBRs has recently received considerable atten-ion. Several models based on the Eulerian–Lagrangian method,hich were pioneered by Tsuji, Kawaguchi, and Tanaka (1993),ave been proposed to describe the gas–solid flows in FBRs. Inddition, numerous groups (including Cheng’s group (Xu et al.,007; Wu, Cheng, 2010; Wu, Yan, et al. 2010b; Zhao, Ding, et al.,010; Zhao, Cheng, et al., 2010b), Li’s group (Ouyang & Li, 1999a,uyang & Li, 1999b), Yu’s group (Feng, Xu, Zhang, Yu, & Zulli, 2004;hang, Chu, Wei, & Yu, 2008)) have also made significant contrib-tions (please refer to the reviews by Yu’s group (Zhu et al., 2007,008)). For instance, Zhang et al. (2008) used CFD and DEM to

nvestigate the particle clustering behavior in a riser/downer reac-or. Results showed that the existence of particle clusters, whichere unique to the solid flow behavior in such reactor, can beredicted by the first-principles approach. Tsuji, Yabumoto, andanaka (2008) used CFD–DEM coupling simulation to investigatehe flow structures induced by bubbles formed in 3D shallow rect-ngular gas-fluidized beds. A numerical code was parallelized, andver 4.5 million particles were tracked by 16 CPUs. Zhao et al.2010a) simulated the gas–solid flows in a 2D downer (height:0 m; width: 0.10 m) using CFD–DEM method, in which the motionf the particles was modeled using DEM, and the gas flow wasodeled using by Navier–Stokes equations. The simulation results

howed a rich variety of flow structures in the downer under differ-nt operating conditions. Geng and Che (2011) proposed a transienthree-phase numerical model for simulating multiphase flow, heatnd mass transfer and combustion in a bubbling fluidized bed ofnert sand. The gas phase was treated as a continuum and solvedsing CFD approach, whereas the solid particles were treated aswo discrete phases with different reactivity characteristics andolved using extended DEM based on individual particle scale. Aew char combustion sub-model with inhibitory effects was alsoeveloped to describe the combustion behavior of char particles

n FBRs. Karimi, Mansourpour, Mostoufi, and Sotudeh-Gharebagh2011) simulated a gas-phase polyethylene reactor using CFD–DEM

ethod. A comprehensive kinetic mechanism was used to evalu-te the reaction rate of ethylene and 1-butene copolymerization.i and Guenther (2012) applied an open-source MFIX-DEM codeo simulate the effect of gas volume change resulting from chemi-al reactions on the flow hydrodynamics in bubbling FBRs. In theirork, 2D simulations of ozone decomposition and the reverse reac-

ion were conducted for systems with different particles. Previousfforts prove that CFD–DEM method can be used to describe parti-le motion and to capture particle activity. Although pressure dropvolution, particle mixing, gas and particle velocity vectors, andemperature with respect to fluidization time were characterizedn previous studies by employing CFD–DEM method, the bubbleehavior in FBRs was not revealed. To date, no attempt has beenade to study the gas–solid flow in FBRs for the MTO process using

FD–DEM method.Reports on the MTO process are largely available (Aguayo,

ier, Gayubo, Gamero, & Bilbao, 2010; Alwahabi & Froment, 2004;hen, Rebo, Gronvold, Moljord, & Holmen, 2000; Chen, Gronvold,oljord, & Holmen, 2007; Gayubo, Benito, Aguayo, Castilla, &

ilbao, 1996; Gayubo, Aguayo, del Campo, Tarrio, & Bilbao, 2000;

emical Engineering 60 (2014) 1– 16 3

Lwahabi & Forment, 2004; Park & Froment, 2001a, Park & Froment,2001b). However, these reports focused on the catalyst and thekinetics in the MTO process. For instance, Schoenfelder, Hinderer,Werther, and Keil (1995) developed a lumped kinetic model whichwas then incorporated into a reactor model of circulating flu-idized bed (CFB) for the MTO process. Soundararajan, Dalai, andBerruti (2001) also simulated the MTO process in a CFB reactor.In the simulation, the kinetic model with SAPO-34 as catalystwas combined with a core-annulus type hydrodynamic model.Fatourehchi, Sohrabi, Royaee, and Mirarefin (2011) investigatedthe MTO reaction in a differential fixed-bed reactor using acidicSAPO-34 molecular-sieve as catalyst. In addition, a mechanism forthis process based on Langmuir–Hinshelwood formulation was alsoproposed, and the kinetic parameters were evaluated as functionsof temperature. Mier, Gayubo, Aguayo, Olazar, and Bilbao (2011)studied the joint transformation of methanol and n-butane fed intoa fixed-bed reactor on an HZSM-5 zeolite catalyst. In their work, theproposed kinetic scheme of lumps integrated the reaction steps cor-responding to the individual reactions (cracking of n-butane andMTO process at high temperature) and considered the synergiesbetween the steps of both reactions. These reactors consist of bothCFB and fixed-bed reactors. However, no reports were found on thesolid-solid flow in the MTO FBRs based on the CFD–DEM method.Nevertheless, related studies can still provide some insight into thiswork.

In this study, a combined CFD–DEM model, which incorporatesthe heat transfer between the particles and between the gas andthe particles, as well the lumped kinetics in the gas phase for theMTO process, is applied to study the flow behavior in an MTO FBR.The distinctive advantage of the proposed model is that the real-time particle activity can be calculated by tracking the history of theparticle motion with respect to heat transfer. This presumed advan-tage is validated by classical calculation and experimental data. Thecombined model is also used to identify the gas–solid flow field,particularly the particle flow structure and the MTO reaction effi-ciency in MTO FBR. Simulations are then performed to understandthe effects of the operating conditions on MTO FBR performance.

2. Mathematical model and numerical simulations

Under the Eulerian-Lagrangian scheme, the governing equa-tions of the gas–solid flows include the Navier–Stokes equationsfor gas flow and the DEM for particle motion, thereby comprisingthe CFD–DEM model. Given the wide applications of this approachin multiphase flow, the CFD–DEM model is well documented in theliterature (Hoomans, Kuipers, Briels, & van Swaaij, 1996; Xu & Yu,1997; Ouyang and Li, 1999a,b; Zhou et al., 2011). For brevity, only anumber of core governing equations, such as the equations for gas-phase flow, particle motion, and the interaction between gas andparticles, are discussed and listed in Table 1 For example, the gasphase is modeled by the conservation equations of mass, momen-tum, energy, species, and the turbulence model (i.e., Realizable k − εturbulent model (Shih, Liou, Shabbir, Yang, & Zhu, 1995)); the par-ticle movement is described by the translational and rotationalmotions of a particle at any time, which follows the Newton’s lawsof motion. The equation shown in Table 1 on particle movement ispresented as follows

mid�up,i

dt= �FD,i + mi �g +

ni∑j=1

(�Fn,ij + �Ft,ij) (1)

In practice, the instantaneous particle velocity is calculatedusing Eq. (1), which is determined by the drag force (�FD,i), thegravity (mi �g), and the contact force (�Fn,ij, �Ft,ij). In addition, thegravity and the drag force act on the mass center of the ith particle,

4 Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16

Table 1Main governing equations of the DEM–CFD model.

Governing equations for gas phase flowGas phase continuity equation: ∂

∂t(�g ) + ∇ · (�g �ug ) = 0

Gas phase momentum equation: ∂∂t

(�g �ug ) + ∇ · (�g �ug �ug ) = −∇p − ⇀ F + ∇ · (�g ) + �g �gGas phase equation of state: p = �gRTg/Mm

Gas phase energy equation: ∂∂t

(�gCp,gT) + ∇ · (�gCp,g �ugT) = ∇ · (kg∇T) + Qsg

Species conservation equation: ∂∂t

(�gYi) + ∇ · (�g �ugYi) = −∇ · (�Ji) + Ri, i ∈ [1, Nr ], where, �Ji = −(

�gDi,m + �tSct

)∇Yi

Mass rate of reaction: Ri = Mw,i

Nr∑r=1

⎡⎢⎣(

�′′i,r − �′

i,r

)⎛⎜⎝kf,r

Nr∏j=1

[Cj,r

](�′+�′′

j,r

j,r)

⎞⎟⎠

⎤⎥⎦

Governing equations for particle motion

mid�up,i

dt= �FD,i + mi �g +

ni∑j=1

(�Fn,ij + �Ft,ij) and Ii d �widt

=ni∑

j=1

�Tij where, �Fn,ij = −kn�ın − �n

�Vn,ij , �Ft,ij ={

−kt�ıt − �t

�Vt,ij

∣∣�Ft,ij

∣∣ ≤ fs∣∣�Ft,ij

∣∣−fs

∣∣�Ft,ij

∣∣ �tij

∣∣�Ft,ij

∣∣ > fs∣∣�Ft,ij

∣∣ �Tij = rp �nij × �Ft,ij

Interaction between gas and particle, �F

�F =−∑n

i=1�FD,i

Vcelland �FD,i = �FD0,i−(ˇ+1), FD0 = 1

2 �f CDS d2

p4 2

∣∣�ug − �up,i

∣∣ (�ug − �up,i), ̌ = 3.7 − 0.65exp[− (1.5 − lgRe)2/2], CDS ={

24/Re Re ≤ 1

(0.63 + 4.8Re−1/2)2

Re > 1, where,

wit

ofe

I

wotdf

ic

2

nittflwgptWf

a

Q

w&

e

�g 1.72 × 10

Therefore, the convective heat transfer coefficient can beexpressed as follows:

Nu = 0.03Re1.3p = 0.51, (10)

Re =�f dp

∣∣�ug −�up,i

∣∣�g

hereas the contact force acts at the contact point between theth and jth particles, thereby generating a torque (�Tij) and causinghe ith particle to rotate. For a spherical particle with the radius

f rp, �Tij is given by �Tij = rp �nij × �Ft,ij , where→nij is a vector running

rom the mass center of the particle to the contact point. Thus, thequation governing the rotational motion of the ith particle is

id �wi

dt=

ni∑j=1

�Tij, (2)

here→wi is the angular velocity, and Ii is the moment of inertia

f the ith particle that can be obtained using Ii = (2/3)mir2p . Thus,

he magnitude and the vector of the velocity of the ith particle areetermined by Eqs. (1) and (2). The equations for calculating theseorces are also listed in Table 1 (Di Felice, 1994).

For the gas–solid MTO reacting flow, the hydrodynamic modelncorporates the sub-models describing the heat transfer and thehemical reactions, which are presented in the following sections.

.1. Heat transfer sub-model

Borkink and Westerterp (1992) proposed a seven-step mecha-ism to describe intraparticle heat transfer. Considering the physics

n a fluid catalytic cracking (FCC) process, Wu et al. (2010a) usedwo of the seven mechanisms (i.e., the thermal conduction throughhe contact area between two particles and the heat transfer by theuid convection) to construct the heat transfer sub-model, whichas then incorporated into the CFD–DEM model to simulate the

as–solid reacting flows in the FCC processes. Given that the intra-article heat transfer characteristic of the MTO process is similar tohat of the FCC process, the heat transfer sub-model suggested by

u et al. (2010a) is also adopted in this work. The main equationsor the heat transfer sub-model are listed as follows

The heat flow between the ith and kth particles can be calculateds follows (Vargas & McCarthy, 2001):

ik = HC (Tk − Ti), (3)

here the contact conductance can be expressed as follows (Vargas McCarthy, 2001):

HCks

= 2[

3Fn·r∗4E∗

]1/3 = 2˛. (4)

For the particle–gas convective heat transfer, the followingquations are used to calculate the convective heat transfer from

the gas phase to the ith particle (Ranz, 1952; Kaneko, Shiojima, &Horio, 1999):

Qgs,i = d2phgs(Tk − Ts,i), (5)

where hgs is the heat transfer coefficient than can be obtainedusing Eq. (6):

Nu = hgs · dp

kg=

{0.03Re1.3

p Rep ≤ 100

2.0 + 0.6Re1/2p Pr1/3 Rep > 100

, (6)

where Rep = �gdp

∣∣�ug − �up,i

∣∣/�g , and Pr = Cp,g�g/kg.In addition, the volumetric heat source in a computational cell

of the gas phase can be expressed as follows:

Qsg = −∑n

i=1Qgs,i

Vcell. (7)

Meanwhile, the particle–particle and particle–gas heat trans-fers determine the temperature of each particle. The temperatureof each particle is also determined by the heat released from thereaction because the particles are used as catalysts.

miCp,pdTp,i

dt=

∑k

Qik + Qgs,i. (8)

The temperature within each particle is assumed to be uniform.This assumption is valid based on the Biot number (i.e., Bi), whichrepresents the ratio of the intraparticle heat transfer resistanceto the external heat transfer resistance of the particles (Deliang,Watson, & McCarthy, 2008). The rate of convective heat transferat the inlet conditions was estimated as follows: First, Rep wasobtained using Eq. (9):

Rep = �gdpuinlet = 0.54 × 1.0 × 10−3 × 2.8−4

= 8.79 < 100, (9)

hgs = Nu · kg

dp= 0.51 × 0.0254

1 × 10−3= 12.95 W/(m2 K), (11)

Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16 5

(a) det

B

d

B

dtet

rha

2

Rram3lCfpnas

w

TT

Fig. 1. Lumped-species reaction scheme: (

Therefore,

i = hgs · dp

ks= 12.95 × 1 × 10−3

0.156= 8.3 × 10−2 << 1, (12)

In addition, the value of Bi based on the solid conduction can beetermined using the following equation:

i = HC

ksA/r= HC

ks r= 2

˛

r<< 1. (13)

Accordingly, the sum of Bi that incorporates convective and con-uctive heat transfers is significantly lower than 1, suggesting thathe intraparticle heat transfer resistance is much smaller than thexternal heat transfer resistance of the particles. This finding proveshat the temperature within one particle is uniform.

According to the above equations, the heat released from theeaction causes the higher temperature of the particles, which theneat up the surrounding gases. Thus, the temperature of the gasesnd the particles is increased by the reaction.

.2. MTO reactions sub-model

Chen, Gronvold, Moljord, Fuglerud, and Holmen (1999), Chen,ebo, Moljord, and Holmen (1999), Chen et al. (2000, 2007)eported an elaborate coking rate equation, which showed goodgreement with the actual data. Therefore, Chen et al.’s kineticodel is applied in this work. Similar to Chen et al.’s work, SAPO-

4 is used as the MTO reaction catalyst in this study. The adoptedumped-reaction scheme for the MTO process is shown in Fig. 1a.5 is assumed to represent C5 and C6 together because of the lowraction of both C5 and C6 as macromolecular compound and by-roduct in the lumped-species scheme. In addition, methane iseglected because of its low concentration. Ethane and propanere selected to represent paraffin. Therefore, the reaction networkhown in Fig. 1a can be simplified as Fig. 1b (Zhuang et al., 2012).

The reaction model is given by

→

dXi

d(W/FM0)= Ri. (14)

Moreover, Chen et al.’s kinetic equations for the reaction net-ork, which are presented in Fig. 1b, are also adopted in this study

able 2he kinetic equations and their parameters (Chen, Gronvold, Moljord, Fuglerud, & Holme

Kinetic expression (ri) Reaction rate constant (ki/(mol g−1 kP

r1 = k1(1 − ϕ1C)pA k1 = 209 · exp(− 38, 400/RT)

r2 = k2(1 − ϕ2C)pA k2 = 40 · exp(− 27, 000/RT)

r3 = k3(1 − ϕ3C)pA k3 = 15 · exp(− 26, 900/RT)

r4 = k4(1 − ϕ4C)pA k4 = 17 · exp(− 49, 800/RT)

r5 = k5(1 − ϕ5C)pA k5 = 181 · exp(− 59, 600/RT)

ailed scheme and (b) simplified scheme)).

and presented in Table 2, where the subscripts 1 to 5 representethene, propene, butene, C5, and (ethane + propane), respectively.The coke formation equation is listed as follows:

C = 1ϕc

[1 − exp(−ϕckcCAMF(1 − XA))], (15)

Kc = 1.27 exp( −6707

8.314T

), (16)

ϕc = 1.07T2 − 0.00181T + 0.7954, (17)

CAMF = WHSV × tos. (18)

2.3. Numerical simulation

The CFD–DEM coupled model was successfully solved using thecommercial CFD code FLUENT 6.3.26 (Ansys Inc., US). The equationsof gas flow were solved using the SIMPLER algorithm and the DEMmodel was solved using the finite difference algorithm. In addition,the DEM model and the other sub-models were coded with the C++language as their user defined functions (UDFs), and the UDFs wereimplemented in FLUENT.

Meanwhile, the velocity of the particle was computed by theDEM model, and the gas velocity at the position of the correspond-ing particle was computed by the FLUENT solver. The velocities ofparticle and gas were compared. If the velocity of the gas blownfrom the bottom of the reactor was greater than that of the par-ticle, then the particle moved toward the top of the reactor, andvice versa. Then, the positions, the velocities and the other datarelated to the particles were expressed using the Tecplot software.Thus, not only the particles trajectories, but also the temperatureand the components of the gas surrounding the particles, could beinvestigated using the CFD–DEM coupled model.

All simulations were performed in 2D domains for a laboratoryscale FBR (width: 0.16 m; height: 0.8 m). The computational condi-

tions and the additional parameters are given in Table 3. In addition,model parameters related to the gas and catalyst properties arelisted in Tables 4 and 5 (Reid, Prausnitz, & Poling, 1987; Shackelford,Alexande, & Pork, 2002). These parameters, expect otherwise noted,

n, 1999; Chen, Rebo, Moljord, & Holmen, 1999; Chen et al., 2000, 2007).

a−1 s−1)) Deactivation rate constant (ϕi)

ϕ1 = −3 × 10−7 · T2 + 0.0006 · T − 0.2365ϕ2 = −6 × 10−7 · T2 + 0.0011 · T − 0.4143ϕ3 = −9 × 10−7 · T2 + 0.0014 · T − 0.5148ϕ4 = −8 × 10−7 · T2 + 0.0013 · T − 0.44532

ϕ5 = 2 × 10−6 · T2 − 0.0032 · T + 1.247

6 Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16

Table 3Computation conditions and additional parameters.

Parameters Value

ParticlesShape SphereDiameter (m) 1.0 × 10−3

Density (kg/m3) 640Initial temperature of particle (K) 300Number of particles 8000 ∼ 40,000DEM–CFD model parametersParticle normal stiffness coefficient (N/m) 20,000Particle tangential stiffness coefficient (N/m) 10,000Particle normal damping coefficient 0.5Particle tangential damping coefficient 0.3Time step for particle phase (s) 5.0 × 10−7

Time step for gas phase (s) 2.5 × 10−6

w(ntawMcb

3

idtisr

3

mty1ctv1ua

Table 5Model parameters (Shackelford et al., 2002; Zhuang et al., 2012).

Descriptions Value

Thermodynamic and physical parametersGas mixtureCp,g (kJ/(kmol K)) “Mixing law”�g (kg/m3) “Idea gas”�g (Pa s) 1.72 × 10−4

kg (W/(m K)) 0.0254Di,m (m2/s) 2.393 × 10−5

Solid phaseCP,s (kJ/(kmol K)) 774ks (W/(m K)) 0.156

The total pressure drop of FBR (i.e., the pressure drop from the

TT

Computation mesh for gas phase (m × m) 0.004 × 0.004

ere used in the following simulations. Three boundary conditions:1) the uniform mass flow inlet, (2) the pressure outlet, and (3) theon-slip and zero heat flux for the wall, were applied in the simula-ions. The under-relaxation factors are set to 0.9 for the equations ofll species to achieve better convergence. A two-stage calculationas implemented. First, the flow field was simulated without theTO reaction until a fully fluidized flow field was obtained under a

old-flow condition. Thereafter, the reaction process was triggeredy incorporating the DEM part and other sub-models.

. Results and discussion

In this section, the grid sensitivity study for the gas phase models first investigated. The coupled model is then verified using theata calculated from the classical methods (see Eqs. (14)–(16)) andhe experimental data. A number of basic particle flow character-stics are predicted using the coupled model without the reactionub-models (i.e., under cold-flow conditions). In addition, the maineacting flow behavior is also obtained using the complete model.

.1. Grid sensitivity study

Simple grid sensitivity was conducted to determine the mini-um number of cells for the gas phase to reach the convergence of

he model. Five cases were designed for the grid sensitivity anal-sis. The simulation domain for the FBR was divided into 12,800,9,200, 25,600, 32,000 and 38400 cells, respectively. The effect ofell number on the radial velocity of the gas at a height of 0.1 m wasested in the simulation. As shown in Fig. 2, the radial velocity con-erged when the number of cells exceeded 12,800. Accordingly,9200 cells were selected for the gas phase in the following sim-

lations. The instantaneous radial gas velocity data were plottedgainst the width, as shown in Fig. 2, and the data show asymmetry.

able 4he thermodynamic data of the components in the reaction system (Reid et al., 1987).

Components �Hf,298 × 10−5 (J mol−1) �Gf,298 × 10−5 (J mol−

CH3OH (g) −2.013 −1.618

C2H4(g) 0.523 0.682

C3H6 (g) 0.204 0.628

C4H8 (g) 0.00126 0.716

H2O (g) −2.420 −2.286

C2H6 (g) + C3H8 (g) −0.847 −0.328

C5(g) −1.262 −0.17

Fig. 2. Radial velocity distribution using different grids.

3.2. Particle flow characteristics

3.2.1. Pressure drop and model verification under cold-flowconditions

Pressure drop, which can reflect particle flow behavior, is oneof the most important parameters to achieve proper scaling up andreactor design. The pressure drop in a fluidized bed can always bedescribed by the buoyant weight of the suspension, which can beexpressed as follows (Chai & Zhang, 2004; Lettieri, Felice, Pacciani,& Owoyemi, 2006; Shi et al., 2010):

�Ps = (�s − �g)(1 − )gL. (19)

In this work, the gas phase density is 1.4 kg/m3. The effect of gasphase weight on the pressure drop is described by

�Pg = �ggL. (20)

FBR inlet to its outlet) can be calculated using Eq. (20).

�Pt = �Ps + �Pg. (21)

1) Cp = A + B · T + C · T2 + D · T3 (j mol−1 K−1)

A B × 102 C × 105 D × 108

21.150 7.092 2.587 −2.8523.806 15.660 −8.348 1.7553.710 23.450 −11.600 2.205

−2.994 35.320 −19.900 4.46332.240 0.192 1.055 −0.36019.250 5.409 17.800 −6.93890.487 33.13 −11.08 −0.282

Y.-Q. Zhuang et al. / Computers and Ch

F

tavcttptittflifipctpta

adiflats

be fluidized, that is, the bed is at the fluidization vanishing state. Thecomparisons are only qualitative, because the present simulationswere not conducted under the same conditions as in the theory (Jinet al., 2001).

ig. 3. The bed pressure drop as fluidization proceeds (space velocity = 2.8 m/s).

The corresponding pressure drop data calculated by these equa-ions are shown in Fig. 3, which shows the bed pressure drop profiles a function of flow time in FBR. As shown in Fig. 3, the calculatedalues of the bed pressure drop are slightly higher than the data cal-ulated from classical equations. This discrepancy may be caused byhe disregard given to the pressure drop resulting from friction andhe particle collision in the classical calculation. Nevertheless, Fig. 3roves that the simulated pressure drop data are in agreement withhe classical data. Moreover, as shown Fig. 3, three typical regionsn the MTO FBR at cold-flow conditions can be identified beforehe formation of a stable fluidization state; these regions consist ofhe bed expansion and slug formation stage (t ≤ 0.2 s), the gas–soliduidization establishment stage (0.2 s < t < 0.5 s), and the stable flu-

dization stage (t ≥ 0.5 s). The maximum bed pressure drop in therst stage is higher than those in the other stages because the inter-article locking is overcome. Evident bed expansion and sluggingan be observed at this stage. After the bed expansion and slugging,he interparticle locking is broken. Hence, the fluctuation of the bedressure drop shifts from an irregular to a regular pattern (Fig. 3). Athe third stage (t ≥ 0.5 s), the bed pressure drop fluctuates regularlynd the stable gas–solid fluidization state is then established.

The gas–solid fluidization in FBRs is known to be significantlyffected by the inlet gas velocity, which causes the existence ofifferent pressure drop profiles. According to a well-known flu-

dization theory (Jin, Zhu, Wang, & Yu, 2001), there exist four typical

uidization states that correspond to different gas velocities in

typical FBR. The effect and the four states can be captured byhe current numerical model. As shown in Fig. 4, the four typicaltates in FBR can be identified as follows: fixed-bed state (from A

Fig. 4. The effect of the space velocity on the bed pressure drop.

emical Engineering 60 (2014) 1– 16 7

to B, A → B), complete fluidization state (from C to D, C → D), initialfluidization state (from C to E, C → E), and fluidization vanishingstate (from E to F, E → F). At the fixed-bed state, the pressure dropincreases with the increase in inlet gas velocity. In practice, par-ticle interactions result in a particle bridge and particle scarfing.Accordingly, a greater driving force is needed to loosen the bed,that is, to form a high bed pressure drop. At the maximum pres-sure drop (i.e., position B in Fig. 4), the bed begins to loosen andits voidage starts to increase. At the complete fluidization state(C → D), continuous bubbles come into being, and the bed pres-sure drop is kept unchanged. With the decrease in the inlet gasvelocity (C → E), the fluidization degree in FBR and the pressuredrop decrease, and the gas velocity reaches the minimum/initialfluidization velocity, which is approximately 1.8 m/s. When the gasvelocity is lower than 1.8 m/s (E → F), the particles in the bed cannot

Fig. 5. Particle configurations at different fluidization time positions (space veloc-ity = 2.8 m/s).

8 Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16

e velo

dcstfl

3

ptems

Fig. 6. Velocity vector profiles at t = 0.312 s ((a) particle-phas

The information shown in Figs. 3 and 4 suggest that theeveloped CFD–DEM model can capture the major particle flowharacteristics in an MTO FBR at cold-flow conditions. The pres-ure drop analysis, together with detailed information provided inhe following sections, can result in a better understanding of theow structure and the mechanisms in MTO FBR.

.2.2. Gas–solid flow patternAs previously described, the gas–solid flow pattern in the gas

hase, particularly the solid flow pattern, cannot be obtained using

he Eulerian–Eulerian method (Mahecha-Botero et al., 2009; Yant al., 2012; Zhang et al., 2007). However, the current CFD–DEModel can successfully capture the gas–solid flow pattern, as

hown in Fig. 5. The different particles are labeled using different

Fig. 7. Velocity vector profiles at t = 0.52 s ((a) particle-phase veloc

city vector profile and (b) gas-phase velocity vector profile).

colors at 0 s to distinguish these particles and to investigate theirmixing (Fig. 5). During the bed-expansion and slug-formation stage(t ≤ 0.2 s, see Fig. 5), these particles move upward, and the spoutedjet zone forms near the FBR inlet because of the drag acting onthese particles at the bottom of FBR. Meanwhile, a number of topparticles in FBR move downward to the bottom to fill the voidsin FBR (Fig. 5a–c). In addition, at this stage, the bubbles come intobeing and develop over time. Accordingly, the bed expands andits height increases over time. After the first stage, the processproceeds to the second stage (i.e., the gas–solid fluidization estab-

lishment stage, 0.2 s < t < 0.5 s, Fig. 3), these bubbles aggregate toform two big bubbles, which move toward the two walls of the FBR(Fig. 5d). These particles near the bottom of FBR are blown upwardand a convex forms with respect to time (Fig. 5d–f). At the stable

ity vector profile and (b) gas-phase velocity vector profile)).

Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16 9

veloc

flbgp(u

mwpstc

3

ip

aFooaagfpputfapbbcbc

Fig. 8. Velocity vector profiles at t = 1.04 s ((a) particle-phase

uidization stage (t ≥ 0.5 s, Fig. 3), the films between two bubblesecome thinner over time (Fig. 5g–i) and ultimately rupture. Theseases in the bubble move circularly from left to right, causing thearticles adjacent to the bubble to move. Furthermore, at t = 1.3 sFig. 5m–r), the particles in FBR move circularly around the bubblender the influence of the inlet gas.

In summary, Fig. 5 proves that the particles in the middle of FBRove upward, and the particles near the two walls move down-ard, generating a typical annulus-core structure in FBR. Strongarticle back mixing and internal circulation exist for this flowtructure in FBR. This type of particle flow pattern promotes thehorough mixing of particles, resulting in high heat transfer effi-iency.

.2.3. Gas–solid velocity vectorThe gas and the solid phase velocity profiles at three typical time

nstants are obtained using the proposed model to verify the flowattern further (Figs. 6–8).

Fig. 6 shows that the particles in the middle of FBR move up, and convex forms because of the blowing up of the inlet gas along theBR axis at 0.312 s (Fig. 6a). This phenomenon is identical to thatbserved in Fig. 5e. Meanwhile, the gas velocity in the axial middlef FBR decreases with the increase in the bed height (Fig. 6b). Inddition, the particles at the top of FBR are initially thrown upwardnd subsequently fall down toward the two walls. Given that theas velocity near the two walls is lower than that in the middle, theallen particles along the two walls must move down to the densehase zone of particles. These fallen particles, as well as the otherarticles in the dense phase zone, then move slowly downwardntil these particles are rolled into the spouted jet zone and even-ually sprayed out again. Therefore, a typical annulus-core structureor the solid particles in FBR as described in Section 3.2.2 is formed,s shown in Fig. 6a. Fig. 6b describes the velocity vector of the gashase in FBR at 0.312 s. As shown in Fig. 6b, some gases near theottom of the FBR diffuse toward the two walls and form two small

ubbles, with the gas flowing into FBR (Fig. 5e). This phenomenonan be clearly observed on the magnified images. As shown in theottom-right image in Fig. 6b, one portion of the gases move cir-ularly around the bubble, resulting in the circular movement of

ity vector profile and (b) gas-phase velocity vector profile).

some particles in the FBR surrounding the bubbles. Meanwhile,another portion of the gases, along with the entering particles,move upward from the gap between the two bubbles, as illustratedin the local magnified image in Fig. 6b.

Fig. 7 describes the gas and solid velocity vector profiles at0.52 s. The annulus-core structure for the solid particles in FBR canstill be observed. However, the right bubble becomes larger andwould ultimately break (Figs. 5g and 7b), suggesting that the par-ticle movement is primarily determined by the entrainment of thegas. The gas and solid velocity vector profiles at 2.6 s are listed inFig. 8, which corresponds to the gas–solid flow pattern shown inFig. 5r. As shown in Fig. 8a, a large bubble can be formed, and theparticles move circularly around the bubble. The same result is alsoobtained from the gas velocity vector profile, as shown in Fig. 8b.

In summary, the information shown in Figs. 6–8 is consistentwith that presented in Fig. 5, further proving that a typical annulus-core structure in the MTO FBR can be formed.

3.2.4. Particle trajectoryCompared with the Eulerian method, DEM can track the history

of the particle motion in real time. In this study, the particle tra-jectory in the fluidization process is simulated using the coupledmodel, as shown in Fig. 9. The selected particle is one of the par-ticles entering FBR at 0 s. The particle temperature is described inFig. 9, because the heat transfer sub-model is incorporated into thecoupled model. In addition, the particle temperature profile withrespect to time is shown in Fig. 10.

As shown in Fig. 9, the particle is first blown up by the inlet gas.The particle then moves circularly from left to right in FBR as thefluidization proceeds. Meanwhile, the particle is heated up con-tinuously, resulting in the increase in particle temperature overtime. However, based on the local magnified image on the rightside of Fig. 9, the particle temperature is always low when the par-ticle moves across the right bottom of FBR because of the low gastemperature at this position. Fig. 10 shows that the particle temper-

ature increases quickly and reaches a plateau value, which is the gastemperature. In practice, the fluctuation of particle temperature isdue to the circular movement of the particle, as shown in Fig. 9. Insummary, the information shown in Figs. 9 and 10 suggest that the

10 Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16

dttsF

3

3

vfltdattI0c

Fig. 11. Main reaction parameter distribution profiles in the MTO FBR at t = 0.052 s((a) gas-phase temperature, (b) particle temperature, (c) coke content, (d) ethene

Fig. 9. Single-particle trajectory profile (space velocity = 2.8 m/s).

eveloped CFD–DEM can also capture the particle trajectory whenhe heat transfers between the particles and between the gas andhe particles are considered. Furthermore, Figs. 9 and 10 demon-trate that excellent heat transfer efficiency can be achieved in theBR.

.3. Reacting flow behavior

.3.1. Reacting flow field distribution and model verificationDuring the preliminary work (Zhuang, 2012b), methanol con-

ersion was found to reach approximately 100% during the initialuidization stage (the simulated profiles are not listed because ofhe limitation in space). Given that the SAPO-34 catalyst is easilyeactivated, the gas and particle temperatures, the coke content,nd the product concentrations in the reactor would change ashe reaction and the fluidization proceed. Therefore, the distribu-ions of these parameters in the reactor should be investigated.

n this study, four typical time instants during the process (0.052,.312, 0.520, and 2.600 s) are selected as representatives, whichorrespond to the simulations mentioned in Sections 3.2.1.

Fig. 10. Single-particle temperature profile (space velocity = 2.8 m/s).

mole concentration, (e) propene mole concentration, and (f) butene mole concen-tration; space velocity = 2.8 m/s, inlet feed temperature = 723 K, feed ratio of waterto methanol = 0).

Fig. 11 describes these parameter distributions in FBR at 0.052 s.Meanwhile, according to Fig. 3, the reacting flow is in the bed expan-sion and the slug formation stage (t ≤ 0.2 s). Given that the inlet rawgases have the highest concentration, when the raw gases comein contact with the particles, the particles are heated up by theexothermic heat released from the reaction. The gases surround-ing the particles are then heated up by the heat transfer from theparticles. Therefore, the temperature of the gases and the parti-cles are highest at the inlet. The gas with the highest temperaturediffuses upward to both sides, as shown in Fig. 11a. Accordingly, asshown in Fig. 11b and c, both the particle temperature and the cokecontent profiles exhibit a distribution similar to that of the gas tem-perature in FBR because of the close positive relations among thethree parameters, as shown in Fig. 11b and c. Meanwhile, productconcentrations (Fig. 11d–f).exhibit distributions similar to those oftemperature profiles, thus proving that the change in gas/particle

temperature is determined by the exothermic heat of the MTOreaction.

The parameter distributions at 0.208 s described in Fig. 12suggest that the reacting flow is in the gas–solid fluidization

Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16 11

Fig. 12. Main reaction parameter distribution profiles in the MTO FBR at t = 0.208 s((a) gas-phase temperature, (b) particle temperature, (c) coke content, (d) ethenemole concentration, (e) propene mole concentration, and (f) butene mole concentra-tt

ettit(bFguebibbcttl

Fig. 13. Main reaction parameter distribution profiles in the MTO FBR at t = 0.52 s((a) gas-phase temperature, (b) particle temperature, (c) coke content, (d) ethenemole concentration, (e) propene mole concentration, and (f) butene mole concen-

ion; the space velocity = 2.8 m/s, inlet feed temperature = 723 K, feed ratio of water

o methanol = 0).

stablishment stage (0.2 s < t < 0.5 s, Fig. 3). As shown in Fig. 12a,he gas with the highest temperature continuously diffuses towardhe outlet of FBR. Given that the total temperature in FBR is primar-ly controlled by the reaction heat, the zone with the highest gasemperature should be the place stacked with the catalyst particlesFig. 5d). Meanwhile, the gas temperature in the zone with the bub-les (i.e., the “bubble” zone) is lower, as shown in Figs. 5d and 12a.or the particle temperature, the highest temperature is still at theas inlet of the bed, as shown in Fig. 12b. However, a relativelyniform temperature distribution exists in the other zones in FBRxcept in the “bubble” zones. Meanwhile, the coke content distri-ution is similar to the particle temperature distribution described

n Fig. 12c, that is, the coke contents in the “bubble” zones of theed are low. However, the total coke content increases over timeased on comparison between Figs. 11c and 12c. The products alsoontinuously diffuse along the axial outlet direction in the bed as

he fluidization and the reaction proceed (Figs. 12d–f). Meanwhile,he product concentrations in the “bubble” zones of the bed remainow.

tration; space velocity = 2.8 m/s, inlet feed temperature = 723 K, feed ratio of waterto methanol = 0).

At the stable fluidization stage (t ≥ 0.5 s), the bubbles in FBRundergo breakage and aggregation to form a big bubble. In addition,the particles are at the entire fluidization state (Fig. 3). In this study,two series of parameter distribution profiles at two time instants(0.52 s and 2.6 s) during this period are presented in Figs. 13 and 14.

At 0.52 s, the left bubble breaks, and the fluidization in the bed isjust at the entire fluidization state. The highest gas temperature inthe “bubble” zone is approximately 750 K, which is lower than thatat 0.208 s (Fig. 12) because of the increase in coke content during thereaction and the fluidization. The products diffuse into the entireFBR, and all their concentrations are uniform because of the entirefluidization. During the fluidization at 2.6 s, both the gas and solidtemperatures in the bed are lower than those at 0.52 s because ofdue to the increase in coke concentration.

When the fluidization reaches a stable state, the MTO reactions

are at the steady state. In this case, the product concentrationsin the outlet of FBR can be used to verify the coupled modelof the reacting flow. In addition, the selectivity of ethylene and

12 Y.-Q. Zhuang et al. / Computers and Ch

Fig. 14. Main reaction parameter distribution profiles in the MTO FBR at t = 2.6 s((a) gas-phase temperature, (b) particle temperature, (c) coke content, (d) ethenemole concentration, (e) propene mole concentration, and (f) butene mole concen-tt

pirbtc2crevd

to propene and an increase in coke content (Fig. 15c and d).

TC(

ration; space velocity = 2.8 m/s, inlet feed temperature = 723 K, feed ratio of watero methanol = 0).

ropylene, as well as the methanol conversion, is almost identicaln any type of reactor (including microbalance reactor, fixed-bedeactor, and FBR) during the MTO process, suggesting that theulk kinetic behavior in a microbalance reactor is almost identicalo that in an FBR under the reaction conditions of high methanoloncentrations (Hu, Cao, Ying, Sun, & Fang, 2010; Zhuang et al.,012). Although deduced at the laboratory scale, the kinetic modelan be applied for the macro-reactor because the influence ofeactor type on the bulk reaction mechanisms is negligible. The

xperimental data collected from a practical FBR can be used toalidate the simulated data. Table 6 shows that the simulationata are in good agreement with the experimental data (Qi et al.,

able 6omparison between the practical data and the simulation data (the space velocity = 2.8 mQi et al., 2010).

Methanol conversion (%) Ethene (%)

Practical data 99.13 42.58

Simulation data 100 40.2

emical Engineering 60 (2014) 1– 16

2010), indicating that the coupled model of the reacting flow iscapable of simulating the MTO process in FBR.

3.3.2. Effects of key operation parametersThe SAPO-34 catalyst becomes deactivated because of coke for-

mation. The coke covers the active sites of the catalyst, therebyreducing the free space in the cavities of the catalyst and ultimatelyinfluencing the MTO reaction. The catalyst was completely deacti-vated when the MTO reaction proceeds to 3600 s. Simulating thecomplete MTO reaction is time consuming. However, the catalystwas found to be deactivated rapidly at the beginning of the reaction,and the change in reaction parameters is evident at 26 s. Therefore,investigating the effects of the operating conditions on the MTOreaction from the beginning up to ∼26 s is sufficient.

The coupled model can be used to evaluate the effects of feedtemperature, ratio of water to methanol in the feed, and feed veloc-ity on the reactor performance. The results are shown in Figs. 15–17.

Fig. 15a and b display the predicted average bed and particletemperature profiles at different feed temperatures, respectively.Both the average bed and particle temperatures initially increaseand then decrease at certain feed temperatures. Moreover, bothparameters increase with the increase in feed temperature, becausethe MTO process is highly exothermic, that is, the exothermicheat increases when methanol is totally converted and decreasesbecause of the deactivation of catalysts. The increase in feed tem-perature also results in the increase in bed temperature. In practice,the bed temperature can be reflected by the particle temperature.The average outlet mole ratio of ethane to propene and the cokecontent profiles at different feed temperatures are presented inFig. 15c and d, respectively. As shown in Fig. 15c, the average ratioof ethane to propene increases with the increase in feed tempera-ture. This finding is consistent with that reported by Wu, Michael,and Rayford (2004). In addition, the average outlet mole ratio ofethane to propene decreases with catalyst deactivation at certainfeed temperatures. These results can be explained using the MTOreaction sub-model. When the catalyst is deactivated, the exother-mic heat decreases, and then the bed temperature decreases aswell, resulting in the decrease in ratio, as shown in Fig. 15c. All ofthese findings indicate that the MTO reaction rate indirectly affectsall of these changes, which are related to catalyst deactivation, asshown in Fig. 15d. Moreover, the catalyst decays faster at highertemperatures, suggesting that a higher feed temperature results ina higher coke content.

Fig. 16 shows the simulated effect of the feed ratio of water tomethanol on the average bed parameters, which are in contrast tothose described in Fig. 15. With the increase in feed ratio of water tomethanol, the simulated average bed and particle temperatures, aswell as the average outlet mole ratio of ethane to propene, decrease,whereas, coke content increases. For the bed and particle temper-atures, the addition of water initially slows down the average bedtemperature and then reduces the partial pressure of methanol andthe heat released from the reaction. Therefore, the lower bed andparticle temperatures resulting from the increase in the feed ratioof water to methanol must result in a decrease in the ratio of ethane

Fig. 17 shows the simulated effect of space velocity on theaverage bed parameters, and the obtained results are similarto those described in Fig. 16. Fig. 17a to c prove that all of the

/s, the inlet feed temperature = 723 K and the feed ration of water to methanol = 0.)

Propene (%) Butene (%) C5 (%)

38.63 10.96 3.4738.3 13.2 2.15

Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16 13

Fig. 15. Effects of feed temperature on the reacting flow field parameters ((a) the average bed temperature, (b) the average particle temperature, (c) the ratio of ethene topropene, and (d) the coke content; space velocity = 2.8 m/s, feed ratio of water to methanol = 0).

Fig. 16. Effects of the feed ratio of water to methanol on the reacting flow field parameters ((a) the average bed temperature, (b) the average particle temperature, (c) theratio of ethene to propene, and (d) the coke content; inlet feed temperature = 673 K, space velocity = 2.8 m/s).

14 Y.-Q. Zhuang et al. / Computers and Chemical Engineering 60 (2014) 1– 16

F ge bec

srvsrhra

4

tbggcitadoa

(

ig. 17. Effects of the space velocity on the reacting flow field parameters ((a) averaoke content; inlet feed temperature = 673 K, feed ratio of water to methanol = 0).

imulated average bed and particle temperatures, as well as theatio of ethane to propene, decrease with the increase in spaceelocity. By contrast, coke content increases with the increase inpace velocity, as described in Fig. 17d. These changes are alsoelated to the reaction rate, that is, a lower space velocity (or aigher conversion with longer contact time) results in a fastereaction rate and the release of more heat, resulting in higher bednd particle temperatures.

. Conclusions

A coupled CFD–DEM model, which integrates the sub-modelshat describe the heat transfer behavior between particles and thatetween gas and particles as well as the lumped kinetics in theas phase for the MTO process, was developed to characterize theas–solid flow behavior in an MTO FBR. This model successfullyaptured the important flow features in an MTO FBR; such featuresnclude the bed pressure drop profiles at cold-flow conditions andhe outlet product concentrations at reacting-flow conditions. Inddition, the particle motion pattern and key flow-field parameteristributions in the reactor were analyzed. The effects of the keyperation parameters on the reacting flow field were also analyzed,nd the findings are summarized as follows

1) The evolution of three typical regions in the FBR and four typicalfluidization states with different gas velocities was investigatedusing CFD–DEM model. In addition, the gas–solid flow pattern,particularly the solid flow pattern, which cannot be obtainedusing the Eulerian–Eulerian method, was also successfully cap-tured by the CFD–DEM model. A typical annulus-core structurefor particle motions was observed in the simulation results

under cold-flow conditions. This type of particle flow patternpromotes excellent particle mixing and heat transfer efficiency,which is essential to the MTO reactor because the MTO processis exothermic.

d temperature, (b) average particle temperature, (c) ratio of ethene to propene, (d)

(2) The simulation by the CFD–DEM model under reaction-flowconditions were conducted, and the distributions of tempera-ture, coke content and product mass fractions in FBR at differentregions were obtained. The results showed that for the MTOprocess, the parameter distributions at different regions havesignificant differences. The temperature distribution in FBR isdetermined by the exothermic heat of the MTO reaction, andthe product fraction distributions in FBR are uniform becauseof the excellent mass transfer capability of FBR.

(3) The feed temperature, the feed ratio of water to methanol,and the space velocity have significant effects on the reactorparameter distributions. All of the average bed and particletemperatures, as well as the average ratio of ethane to propene,increase with the increase in feed temperature. However, ahigher feed temperature results in higher coke content. More-over, the feed ratio of water to methanol and the space velocityhave opposing effects on the reactor performance.

Acknowledgments

The authors thank the National Natural Science Foundationof China (No. 201076171), the National Ministry of Science andTechnology of China (No. 2012CB21500402) and the State-KeyLaboratory of Chemical Engineering of Tsinghua University (No.SKL-ChE-13A05) for supporting this work.

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