CFD Simulation of fluid catalytic cracking in downer reactors

CHINA PARTICUOLOGY Vol 4 Nos 3-4 160-166 2006

CFD SIMULATION OF FLUID CATALYTIC CRACKING IN DOWNER REACTORS

Fei Liu Fei Wei Yu Zheng and Yong Jin Beijing Key Laboratory of Green Chemical Reaction Engineering and Technology Department of Chemical Engineering

Tsinghua University Beijing 100084 PR China Author to whom correspondence should be addressed Fax 0086-10-62772051 E-mail weifeiflotuorg

Abstract A mathematical model has been developed for the simulation of gas-particle flow and fluid catalytic cracking in downer reactors The model takes into account both cracking reaction and flow behavior through a four-lump reaction kinetics coupled with two-phase turbulent flow The prediction results show that the relatively large change of gas velocity affects directly the axial distribution of solids velocity and void fraction which significantly interact with the chemical reaction Furthermore model simulations are carried out to determine the effects of such parameters on prod-uct yields as bed diameter reaction temperature and the ratio of catalyst to oil which are helpful for optimizing the yields of desired products The model equations are coded and solved on CFX44 Keywords downer fluid catalytic cracking (FCC) lumping kinetic model computational fluid dynamics (CFD)

1 Introduction In the past twenty years a new type of gas-solids reactor

the co-current down-flow circulating fluidized bed (downer) has gained considerable attention (Gross 1983 Gartside amp Ellis 1983) Many studies on downer reactor structure hydrodynamics transport phenomena and industrial ap-plications have revealed many advantages including much more uniform gas-solids flow shorter residence time and much less gas-solids back-mixing (Zhu et al 1995 Jin et al 2002) With the development of high-activity and high-selectivity catalysts a downer reactor promises im-provement to the current fluid catalytic cracking process

In recent years among large amount of research in-creasing attention has been paid to method using im-proved computer ability to develop mathematical models to study the multiphase reaction and transport in downer reactors Theologos and Markatos (1993) constructed a three-dimensional model of the two-phase flow heat transfer and reaction in a riser reactor Although it ignored the turbulence of gas and solids and used a simple 3-lump kinetic model the model predicted the flow field heat dis-tribution and concentrations of all species throughout the reactor which testified the importance of such a method Gao et al (1999) developed a three-dimensional flow- reaction model which combines two-phase turbulent flow with 13-lump reaction kinetics for predicting the perform-ance of FCC riser reactors Soundararajan et al (2001) simulated the methanol-to-olefins (MTO) process in a cir-culating fluidized bed reactor using a model combining a kinetic model using SAPO-34 as the catalyst and the core-annulus type hydrodynamic model Through this semi-empirical model abundant predictions about the behavior of the MTO process were obtained Deng et al (2002) developed a two-dimensional two-phase diffusion model for circulating fluidized bed downer reactors by combining hydrodynamics FCC kinetics and gas-solids mixing in downers to study an industrial-scale reactor

However an empirical formula was adopted to predict the hydrodynamics which decreased the accuracy and usage of the diffusion model under different conditions

For catalytic cracking due to the two-phase flow in the direction of gravity the downer demonstrates improved flow dynamics calling for a unique reactor model of its own Cheng et al (2000) combined the particle kinetic theory with the gas-solids turbulence k-ε-kp model (Zhou 1993) to build a k-ε-kp-Θ two-fluid model to successfully simulate the main flow and inlet flow of a downer (Cheng et al 2000 Zheng et al 2002)

This work proposes an integrated downer reactive flow model as shown in Fig 1 by coupling the k-ε-kp-Θ two-fluid model with a FCC lumped kinetics model which is coded and solved on the CFX44 package

Fig 1 Schematic of the downer reactor model based on CFD

2 Mathematical Model The proposed mathematic model is based on physics to

satisfy the following assumptions (1) both gas and solids are considered continuous phases

described by the k-ε-kp-Θ two-fluid model (2) the reaction process is described by a lumped kinetics

model (3) the feed oil rapidly vaporizes as it enters the reactor

and the carbon lump is considered as gas (4) the gas phase (hydrocarbon) is considered as an ideal

gas

Liu Wei Zheng amp Jin CFD Simulation of Fluid Catalytic Cracking in Downer Reactors

161

21 Governing equations The general form of the governing equations for steady

flow in two-dimensional cylindrical coordinate is the fol-lowing

( ) ( ) i iji ii i

u r v r S Sx r r x x r r rϕ ϕ ϕ ϕ

ϕ ϕαρ ϕ αρ ϕ αΓ αΓpart part part part part part⎛ ⎞ ⎛ ⎞+ = + + +⎜ ⎟ ⎜ ⎟part part part part part part⎝ ⎠ ⎝ ⎠

where ϕ denotes general variables ϕΓ is a diffusion

coefficient iSϕ is the source term ijSϕ is the source

term due to the interaction between the two phases i and j denote the gas and solids phases respectively as shown in detail in Tables 1 and 2 (Cheng et al 2000)

Table 1 Governing equations of the gas phase (hydrocarbon)

Equations gϕ gϕΓ gSϕ gpSϕ

Continuity equation 1 0 0 0

Momentum equation in x-direction

u eμ g e e g g xp u vr gx x x r r x

α μ μ α ρpart part part part part⎛ ⎞ ⎛ ⎞minus + + +⎜ ⎟ ⎜ ⎟part part part part part⎝ ⎠ ⎝ ⎠ ( )pu uβminus minus

Momentum equation in r-direction v eμ

2g g e

g e e g g r2wp u v vr g

r x r r r r r r rα ρ μα μ μ α ρpart part part part part⎛ ⎞ ⎛ ⎞ ⎛ ⎞minus + + + minus +⎜ ⎟ ⎜ ⎟ ⎜ ⎟part part part part part⎝ ⎠ ⎝ ⎠ ⎝ ⎠

( )pv vβminus minus

Turbulent kinetic en-ergy equation k e

k

μσ

k g gG α ρ εminus pG

Dissipation rate equa-tion of turbulent energy

ε e

ε

μσ

( )1 k 2 g gC G Ckε α ρ εminus ( )1 pC G

kε

Species equation iY e

Y

μσ

iW 0

Enthalpy equation gh e

h

μσ

0 s g sQ W Qminus

g gi

idYWdt

ρ ε= gpMRT

ρ = 1

( )i

i

MYM

=

sum g iW W= sum 2 2 2 2

k e [2(( ) ( ) ( ) ) ( ) ]u v v u vGx r r r x

μ part part part part= + + + +

part part part part p

p p p2 ( ( ) )G C k k kβ Θ= + minus

Table 2 Governing equations of the particle phase (FCC catalyst)

Equations pϕ pϕΓ pSϕ gpSϕ

Continuity equation pρ p

p

μσ

0 0


pu pμ p p sp p p p p p p x

p p pp p p p p s

2 23 3

u v pp r gx x x r r x x

u v vk

x x r r

α α μ α μ α ρ

ρ α α μ ζ

part part⎛ ⎞ ⎛ ⎞ partpart part partminus + + + minus⎜ ⎟ ⎜ ⎟part part part part part part⎝ ⎠ ⎝ ⎠

⎛ ⎞part part⎛ ⎞part ⎛ ⎞minus + minus + +⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟part part part⎝ ⎠⎝ ⎠⎝ ⎠

( )pu uβ minus

Momentum equation in r-direction

pv pμ p p p p p sp p p p p p p r2

p p pp p p p p s

2

2 23 3

u v v pp r gr x r r r r r r

u v vk

r x r r

α μα α μ α μ α ρ

ρ α α μ ζ

part part⎛ ⎞ ⎛ ⎞ partpart part partminus + + minus + minus⎜ ⎟ ⎜ ⎟part part part part part part⎝ ⎠ ⎝ ⎠


( )pv vβ minus

Turbulent energy of particle equation pk st

p

μσ

p pst stkp p p

p pxG k rk

x r r rρ ρν ν

σ σ⎛ ⎞ ⎛ ⎞part partpart part

+ +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟part part part part⎝ ⎠ ⎝ ⎠ gpG

Temperature of parti-cle equation

Θ st

p

23 Θ

μΓ

σ+ p p p p p p 2s

kp s s sst

2 2 2 2 2( ) ( )( )3 3 3 3 3

u v v u v vG p

x r r x r rμ ξ μ γμ

part part part partminus + + + minus + + minus

part part part part 0

Enthalpy equation ph e

p

μσ

0 s-Q

p p p p p2 2 2 2kp st [2(( ) ( ) ( ) ) ( ) ]

u v v u vG

x r r r xμ

part part part part= + + + +


gp p p p2 ( )G C kk kβ= minus

(1)

CHINA PARTICUOLOGY Vol 4 Nos 3-4 2006

162

22 Lumped kinetics model Since the 1960s lumping techniques have been used to

develop kinetic models for catalytic cracking (Weekman 1968 Wei amp Kuo 1969) which involves large number of individual species present in the gas oil feedstock with boiling points ranging between 220deg and 530degC The large number of chemical species are grouped into smaller groups of pseudo-species in order to obtain a tractable number of kinetic equations Species can be lumped only if the dynamic behavior of the resulting pseudo-species is independent of the species composition (Coxson amp Bisch-off 1987) In this work a typical four-lump kinetic model (Gianetto et al 1994) is adopted and combined with the hydrodynamics as shown in Fig 2 for the following four lumps unconverted gas oil gasoline light gases and coke This model also accounts for catalyst deactivation as a function of coke on catalyst Despite its simplicity it can predict the yield distribution of the main products in the whole reactor and is sufficient for studying the interaction between hydrodynamics and chemical reaction Detailed reaction rate equations and kinetic constants are given in Tables 3 and 4 (Gianetto et al 1994)

k1=individual kinetic constant for gas oil cracking to gasoline m6sdotkmol-1middotkgcat

-1middots-1 k21=individual kinetic constant for gasoline cracking to light gases m3sdot kgcat

-1middots-1 k22=individual kinetic constant for gas oil cracking to coke m6sdotkmol-1middotkgcat

-1middots-1 k31=individual kinetic constant for gas oil cracking to light gases m6sdotkmol-1middotkgcat

-1middots-1 k32=individual kinetic constant for gas oil cracking to coke m3sdot kgcat

-1middots-1 Fig 2 Schematic of the 4-lump model

Table 3 Reaction rate equations of the four-lump kinetic model

2 211 3 1 c A T( ) ( )total

dY k k Y W m M Vdt

φminus = + sdot sdot sdot

22A T 1 1 2 2 c T[ ( ) ] total

dY W M V k Y k Y m Vdt

φ= sdot sdot minus sdot

23A T 31 1 21 2 c T[ ( ) ] total


φ= sdot sdot + sdot

24A T 32 1 22 2 c T[ ( ) ] total



0 1 3k k k= + 3 31 32k k k= + 2 21 22k k k= +

4 cexp[ ]totalY W mφ α= minus sdot sdot

Table 4 Kinetic constants of the four-lump kinetic model

Constant m6sdotkmol-1middotkgcat-1middots-1 Activation energy calmiddotg-1middotmol-1

k10 04272times1013 E1 210099 k310 01012times1014 E31 233379 k320 3252times1011 E32 20934 k20 01337times106 E2 174614 α 391

23 Numerical methods The flow and reaction model equations are coupled and

coded according to the finite-volume solver CFX44 The SIMPLEC iterative algorithm is used to relate the velocity the Inter-Phase Slip Algorithm (IPSA) that uses the Partial Elimination Algorithm (PEA) developed by Spalding (1977) and used by the CFX44 solver

According to the nearly axi-symmetrical hydrodynamics in the downer the computational space is two-dimensioned with a 300times30 (x-r) grid Detailed hydrodynamic boundary conditions are provided by Zheng et al (2002) The simu-lation conditions are given in Table 5

Table 5 Physical properties and operating conditions

H m D m ρp kgsdotm-3 dp μm μg Pasdots 45 014 0418 10 1545 54 185times10-5

Gas oil 340 Gasoline 110 Light gases 26 Molecular weight kgsdotkmol-1

Coke 12 Y1=10 Y2=Y3=Y4=00 Ug=50 msdots-1 Gs=200-300 kgsdotm-2s-1 CO=9-18

Inlet conditions

Tin=500-700degC

3 Results and Discussion For simplification the simulations are carried out without

considering reaction heat and heat transfer in the reactor that is enthalpy balance is neglected and temperature inside the reactor is assumed constant and equal to that of the gas phase at the inlet This simplification does not represent limitations on the modeling procedure for the aim of this work is mainly to illustrate the feasibility and capability of the new approach to predict the hydrodynam-ics and chemical reaction in downer reactors using the coupled model and to show the interaction between flow behavior and chemical reaction

Figure 3 shows the axial profiles of the species concen-trations in a downer with a diameter of 0418 m With the conversion of feed gas oil to lower molecular weight prod-ucts the yields of gasoline light gases and coke increase rapidly and 80 of the reaction is completed in a region of 0-10 m after the inlet There are large concentration gra-dients of all species along both the axial and the radial directions which requires quick and uniform mixing of the feed oil and the catalyst in the inlet region in order to de-crease negative effect on reaction yield and selectivity The predictions also demonstrate the important effects of the inlet structure on downer applications Fig 4 shows the overall distribution of all species under the same condition As can be seen the inlet structure and the initial inlet gas phase velocity affect the distribution significantly The dis-tribution has a tangent due to the parabolic initial velocity distribution and the flow field distribution


163

0 10 20 30 4000

02

04

06

08

10 Gasoil Gasoline Gas Coke

D=0418 m H=45 mUg=50 msdots-1 Gs=3000 kgsdotm-2s-1

Tin=8232 K CO=13

Yiel

d w

twt

Axial location m Fig 3 Yields profiles along axial location for the downer reactor

Fig 4 Concentration distribution (wtwt) of species in the downer

reactor (T=8232 K H=45 m D=0418 m Ug=5 msdots-1 Gs=300 kgsdotm-2sdots-1 x-coordinate radial distance of downer m y-coordinate downer height m)

Figure 5 illustrates the prediction of the hydrodynamic field distribution in the downer Typical solids ring can be seen near rR=09-095 The solids axial velocity is high in the central region and gradually decreases along the radial direction to the wall Reaction does not appear to have significant effect on solids fraction distribution though the overall numerical value is lower than for flow without reac-tion Fig 6(a) compares the averaged axial distributions of flow field with or without reaction Fig 6(b) shows the detail for the first four meters from the inlet The cross-sectional averaged solids volume fraction and axial velocity of gas and solids phases can be calculated according to Eqs 2 and 3 respectively

Fig 5 Distributions of flow field in the downer reactor (T=8232 K

H=45 m D=0418 m Ug=5 msdots-1 Gs=300 kgsdotm-2sdots-1 x-coordinate radial distance of downer m y-coordinate downer height m)

s s2 0

1 2 dR

r rR

α π απ

= int (2)

s p s p0 0p 2

ss0

2 ( )d ( )d2

2 d

R R

R

r u r r ru r ru

Rr r

π α α

απ α= =int int

int (3)

When cracking takes place the axial solids velocity in-creases rapidly reaching some five to six times the inlet velocity as heavy hydrocarbons are converted to light hydrocarbons causing changes in hydrocarbon densities Fig 6 reveals that with reaction the cross-sectional aver-aged solids axial velocity is always smaller than that of the gas there being a large inter-phase slip velocity This is quite different from the hydrodynamics without reaction for which Up could even exceed Ug Both cold-model meas-urements (Wang et al 1997) and simulation showed three accelerating regions in which axial solids velocity can ex-ceed gas velocity The solids velocity can exceed the gas velocity after acceleration over a distance of two to three meters from the inlet Beyond the acceleration zone for approximately five or more meters a steady solids velocity is reached and a relatively small inter-phase slip velocity is maintained Kwauk (1963 amp 1964) explained such changes in detail

Figure 6 also shows that momentum transfer between the gas and solids phase and the expansion of the gas velocity with reaction leads to an increase of the solids velocity and also causes the solids volume fraction to

0 10 20 30 400

5

10

15

20

25

30D=0418 m H=45 m Tin=8232 K

Ug=50 msdots-1 Gs=3000 kgsdotm-2sdots-1

u p amp u

g m

sdots-1

Axial location m

ug up

Without Reaction With Reaction

(a)

000

002

004

006

008

010

αs

α s

0 1 2 3 40

5

10

15

20

25

30

u p amp u

g m

sdots-1

Axial location m

ug up


(b)

000

002

004

006

008

010 αs

α s

Fig 6 Averaged axial distributions of flow field


164

decrease In fact in the cold model of the downer reactor the three acceleration regions of the solids phase is a dy-namic equilibrium process due to the relative change of the gravity and its effect on the solids phase and the interac-tion between the gas and solids phases With the inclusion of FCC chemical reactions the transformation of the hy-drocarbon species concentrations in the gas phase causes the averaged density of the gas to change and leads to a substantial change in the gas phase velocity which corre-spondingly influences the velocity and mass distribution of the solids phase through the drag force interaction be-tween the two phases At the same time gravity effects on the solids phase become relatively weak

It should be mentioned that due to the simplicity of the present four-lump kinetic model there are likely differences between model predictions and real reactive flow On the other hand comparison between cold flow and reactive flow has to consider the effects of chemical reaction on hydrodynamic and transport behaviors Deviations are likely to arise when empirical equations deduced from cold-model experimental data are used to predict hydro-dynamics under reaction conditions

Figure 7 shows the effects of reactor diameter on pre-dicted outlet yield distribution Prediction indicates that with the increase of bed diameter from 014 m to 10 m the outlet percent conversion of gasoil falls by about 5 and the yield of products shows also a decreasing tendency Figs 8 and 9 show the effect of reactor diameter on the

02 04 06 08 1000

01

02

03

04

05


T=8232 K CO=13 H=45

Yiel

d w

twt

Bed diameter m

Gasoil Gasoline Gas Coke

Fig 7 Effects of reactor diameter on yield

00 02 04 06 08 10000

001

002

003

004Ug=50 msdots-1 Gs=3000 kgsdotm-2sdots-1 T=8232 K H=45 m CO=13

D=014 m D=0418 m D=10 m

α s

rR Fig 8 Radial distribution of solids fraction

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1 Gs=3000 kgsdotm-2sdots-1 T=8232 K H=45 m CO=13

D=10 m D=0418 m D=014 m

Us

msdots

-1

rR Fig 9 Radial distribution of solids velocity

radial distribution at the reactor outlet of respectively sol-ids fractions and solids velocity increase of bed diameter leads to uneven radial solids distribution exhibiting a flat core region and a dense ring near the wall and moving the solids concentration peak toward the wall This conforms to the cold-model study of Zhang et al (2003) As can be seen in Fig 9 increasing bed diameter lowers the solids velocity at the center of the downer thus decreasing gas-solids interaction and therefore gasoline yield and the gasoil conversion Such scale-up effect on the downer re-actor should be studied in detail in the future and considered in industrial design

4 8 12 16 2000

01

02

03

04

05

Yie

ld

wtw

t

CatGasoil wtwt


D=0418 m T=8232 KH=45 m U g=50 m sdots-1

Fig 10 Effects of catalyst-to-gasoil (wtwt) ratio on yields

00 02 04 06 08 10000

001

002

003

004

005

α s

rR

Ug=50 msdots-1 T=8232 K H=45 m D=0418 m

GS=120 kgsdotm-2sdots-1





Fig 11 Radial distribution of solids fraction


165

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1

T=8232 KH=45 mD=0418 m






US

msdots

-1


Figure 10 illustrates the effects of the catalyst-to-gas oil ratio (wtwt) on yield distribution the higher this ratio the higher the conversion of gas oil to products much in agreement with the experiments in the literature (Talman amp Reh 2001) Figs 11 and 12 show both higher solids frac-tion and higher solids velocity with increase of solids cir-culation rate Gs

Figure 13 illustrates that both conversion of gas oil and the yield of products increase with increasing reaction temperature Figs 14 and 15 show respectively that higher temperature leads to higher solids velocity but lower solids fraction Although lowered solids fraction lowers both conversion and the yield of products it is rather insignifi-cant as compared to the enhancement of reaction Differ-ent species respond differently to these parameter varia-tions Under the condition used in this work the coke lump compared with other lumps is less sensitive to the three parameters while the gasoline and light gases lumps are influenced greatly by changes in operating conditions As the reaction temperature rises the conversion from gas oil to light gases increases rapidly while the yield of gasoline reacts relatively slowly

Since the emphasis of this work is to explore the cou-pling of hydrodynamics with reaction kinetics to simulate the reactive flow in a downer the proposed model is rela-tively simple Still more detailed work is as follows

500 550 600 650 70000

01

02

03

04

05

DownerD=0418 m H=45 mUg=50 msdots-1 Gs=3000 kgsdotm-2sdots-1

Yie

ld

wtw

t

Temperature oC


Fig 13 Effects of the reaction temperature on yields

00 02 04 06 08 10000

001

002

003Ug=50 msdots-1 GS=300 kgsdotm-2s-1 H=45 m D=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

α s


00 02 04 06 08 100

8

16

24

32

40

48

56

64 Ug=50 msdots-1


H=45 mD=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

US

msdots

-1


(1) Inlet structure The feed-injection area where pre-heated liquid feed oil is injected into the reactor and comes into contact with hot regenerated catalyst is a three-phase contact zone accompanied by rapid flow mixing heat transfer and reaction which calls for mathematical modeling as well as appropriate indus-trial design

(2) Heat and mass transfer The simple model based on the coupling of hydrodynamics and the reaction kinetics on the assumption of isotropic space needs upgrading to conform to the real process of two-phase dynamics and axial diffusion in the downer

4 Conclusions In this work a reactor model coupled with the k-ε-kp-Θ

two-fluid model and the FCC lumped kinetic model is de-veloped to simulate a downer reactor based on the CFX44 software Compared to non-reactive flow the molar gas phase flow changes as reaction proceeds leading to ob-vious changes in gas velocity thus affecting directly the axial distribution of solids velocity and void fraction The simulation also shows that with increasing bed diameter conversion and the yield of products decrease while the radial concentration gradients of all lumps increase Oper-ating conditions such as reaction temperature and cata-lyst-to-oil ratio can affect both conversion and yield distri-bution as well The influence of reaction greatly affects the hydrodynamics in the reactor Future work will consider the


166

calculation of the vaporization of gas oil at the entrance of the reactor and effects of the feed injector geometry on this model

Acknowledgment We are grateful to the financial assistance from the Natural

Science Foundation of China under contract number 20176024

Nomenclature A interphase area m2sdotm-3 CO catalyst-to-oil ratio wtwt

ppC model constant 085

dp particle diameter m D downer diameter m E activation energy calsdotg-1sdotmol-1 GS solids circulation rate kgsdotm-2sdots-1 h heat transfer coefficientWsdotm-2sdotK-1 H downer height m k kinetic constants m6sdotkmol-1sdotkgcat

-1sdots-1 mc mass of catalyst kg MA molecular weight of gas oil kgsdotkmol-1

u v x r direction velocity msdots-1 p pressure Pa Qr reaction heat Jsdotmol-3 Qs interphase heat transfer Jsdotm-3 r radial position m R gas constant Jsdotmol-1sdotK-1 R radius m S source t time s T temperature K Ug superficial gas velocity msdots-1 VT internal volume of the reactor m3 W chemical reaction rate kgsdotm-3sdots-1 Yi component mass fraction wtwt Greek letters α volume fraction β interphase mass transfer coefficient kgsdotm-3sdots-1 γ dissipation rate of particle temperature kgsdotm-1sdots-3 k turbulent energy m2sdots-2 ε dissipation rate of turbulent kinetic energy m2sdots-3 ρ density kgsdotm-3 σk model constant for the k equation 10 σε model constant for the ε equation 13 σY model constant for the species equation 10 σh model constant for the enthalpy equation 10 σp model constant for particle phase 07 μ viscosity Pamiddots Θ particle temperature m2sdots-2 Γ diffusivity kgsdotm-1sdots-1 φ general variable

Subscripts and superscripts ￣ average magnitude e effective i j gas and solids phase respectively g gas phase p s solids phase t T turbulence in inlet

References Cheng Y Wei F Zheng Y Jin Y Guo Y C amp Lin W Y

(2000) Computational fluid dynamic modeling of hydrody-nam-ics in downer reactors J Chem Ind Eng 51(3) 344-352 (in Chinese)

Coxson P G amp Bischoff K B (1987) Lumping strategy 1 In-troductory techniques and applications of cluster analysis Ind Eng Chem Res 26(6) 1239-1248

Deng R S Wei F Liu T F amp Jin Y (2002) Radial behavior in riser and downer during FCC process Chem Eng Proc 41(3) 259-266

Gao J S Xu C M Lin S X Yang G H amp Guo Y C (1999) Advanced model for turbulent gas-solid flow and reaction in FCC riser reactors AIChE J 45(5) 1095-1113

Gartside R J amp Ellis A F (1983) Thermal regenerative cracker A development update Chem Eng Prog 79(3) 82-85

Gianetto A Farag H I Blasetti A P amp de Lasa H I (1994) Fluid catalytic cracking catalyst for reformulated gasolines ki-netic modeling Ind Eng Chem Res 33(12) 3053-3062

Gross B (1983) Fluid catalytic cracking using downflow riser ⎯ With heat transfer from riser to regenerator US Pat 4411773 Mobil Oil Co

Jin Y Zheng Y amp Wei F (2002) State of the art review of downer reactors In J R Grace J X Zhu amp H I de Lasa (Eds) Proc 7th International Conference on Circulating Fluidized Beds (CFB7) (pp 40-60) Niagara Falls Ontario Canada

Kwauk M (1963) Generalized fluidization I steady state motion Scientia Sinica 12(4) 587-612

Kwauk M (1964) Generalized fluidization II accelerative motion with steady profiles Scientia Sinica 13(9) 1477-1492

Soundararajan S Dalai A K amp Berruti F (2001) Modeling of methanol to olefins (MTO) process in a circulating fluidized bed reactor Fuel 80(8) 1187-1197

Spalding D B (1977) The calculation of free-convection phe-nomena in gas-liquid mixtures In N Afgan amp D B Spalding (Eds) Turbulent buoyant convection Washington DC Hemi-sphere

Talman J A amp Reh L (2001) An experimental study of fluid catalytic cracking in a downer reactor Chem Eng J 84(3) 517-523

Theologos K N amp Markatos N C (1993) Advanced modeling of fluid catalytic cracking riser-type reactors AIChE J 39(6) 1007-1017

Wang Z W Wei F Jin Y amp Yu Z Q (1997) Fundamental studies on the hydrodynamics and mixing of gas and solid in a downer reactor Chin J Chem Eng 5(3) 236-245

Weekman V W (1968) Model of catalytic cracking conversion in fixed moving and fluid-bed reactors Ind Eng Chem Process Des 7(1) 90-95

Wei J amp Kuo J C W (1969) Lumping analysis in monomo-lecular reaction systems Analysis of the exactly lumpable sys-tem Ind Eng Chem Fundam 8(1) 114-123

Zhang M H Qian Z Yu H amp Wei F (2003) The near wall dense ring in a large-scale down-flow circulating fluidized bed Chem Eng J 92(1-3) 161-167

Zheng Y Cheng Y Wei F amp Jin Y (2002) CFD simulation of hydrodynamics in downer reactors Chem Eng Commun 189(12) 1598-1610

Zhou L X (1993) Theory and numerical modeling of turbulent gas-particle flows and combustion Beijing Science Press and CRC Press Inc

Zhu J X Yu Z Q Jin Y Grace J R amp Issangya A (1995) Cocurrent downflow circulating fluidized bed (downer) reactors ⎯ A state of the art review Can J Chem Eng 73(5) 662-677

Manuscript received January 4 2006 and accepted April 12 2006


161

21 Governing equations The general form of the governing equations for steady

flow in two-dimensional cylindrical coordinate is the fol-lowing

( ) ( ) i iji ii i

u r v r S Sx r r x x r r rϕ ϕ ϕ ϕ

ϕ ϕαρ ϕ αρ ϕ αΓ αΓpart part part part part part⎛ ⎞ ⎛ ⎞+ = + + +⎜ ⎟ ⎜ ⎟part part part part part part⎝ ⎠ ⎝ ⎠

where ϕ denotes general variables ϕΓ is a diffusion

coefficient iSϕ is the source term ijSϕ is the source

term due to the interaction between the two phases i and j denote the gas and solids phases respectively as shown in detail in Tables 1 and 2 (Cheng et al 2000)

Table 1 Governing equations of the gas phase (hydrocarbon)

Equations gϕ gϕΓ gSϕ gpSϕ

Continuity equation 1 0 0 0


u eμ g e e g g xp u vr gx x x r r x

α μ μ α ρpart part part part part⎛ ⎞ ⎛ ⎞minus + + +⎜ ⎟ ⎜ ⎟part part part part part⎝ ⎠ ⎝ ⎠ ( )pu uβminus minus

Momentum equation in r-direction v eμ

2g g e

g e e g g r2wp u v vr g

r x r r r r r r rα ρ μα μ μ α ρpart part part part part⎛ ⎞ ⎛ ⎞ ⎛ ⎞minus + + + minus +⎜ ⎟ ⎜ ⎟ ⎜ ⎟part part part part part⎝ ⎠ ⎝ ⎠ ⎝ ⎠

( )pv vβminus minus

Turbulent kinetic en-ergy equation k e

k

μσ

k g gG α ρ εminus pG

Dissipation rate equa-tion of turbulent energy

ε e

ε

μσ

( )1 k 2 g gC G Ckε α ρ εminus ( )1 pC G

kε

Species equation iY e

Y

μσ

iW 0

Enthalpy equation gh e

h

μσ

0 s g sQ W Qminus

g gi

idYWdt

ρ ε= gpMRT

ρ = 1

( )i

i

MYM

=

sum g iW W= sum 2 2 2 2

k e [2(( ) ( ) ( ) ) ( ) ]u v v u vGx r r r x

μ part part part part= + + + +


p p p2 ( ( ) )G C k k kβ Θ= + minus

Table 2 Governing equations of the particle phase (FCC catalyst)

Equations pϕ pϕΓ pSϕ gpSϕ

Continuity equation pρ p

p

μσ

0 0


pu pμ p p sp p p p p p p x

p p pp p p p p s

2 23 3

u v pp r gx x x r r x x

u v vk

x x r r

α α μ α μ α ρ

ρ α α μ ζ

part part⎛ ⎞ ⎛ ⎞ partpart part partminus + + + minus⎜ ⎟ ⎜ ⎟part part part part part part⎝ ⎠ ⎝ ⎠


( )pu uβ minus

Momentum equation in r-direction

pv pμ p p p p p sp p p p p p p r2

p p pp p p p p s

2

2 23 3

u v v pp r gr x r r r r r r

u v vk

r x r r

α μα α μ α μ α ρ

ρ α α μ ζ

part part⎛ ⎞ ⎛ ⎞ partpart part partminus + + minus + minus⎜ ⎟ ⎜ ⎟part part part part part part⎝ ⎠ ⎝ ⎠


( )pv vβ minus

Turbulent energy of particle equation pk st

p

μσ

p pst stkp p p

p pxG k rk

x r r rρ ρν ν

σ σ⎛ ⎞ ⎛ ⎞part partpart part

+ +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟part part part part⎝ ⎠ ⎝ ⎠ gpG

Temperature of parti-cle equation

Θ st

p

23 Θ

μΓ

σ+ p p p p p p 2s

kp s s sst

2 2 2 2 2( ) ( )( )3 3 3 3 3

u v v u v vG p

x r r x r rμ ξ μ γμ

part part part partminus + + + minus + + minus

part part part part 0

Enthalpy equation ph e

p

μσ

0 s-Q

p p p p p2 2 2 2kp st [2(( ) ( ) ( ) ) ( ) ]

u v v u vG

x r r r xμ

part part part part= + + + +


gp p p p2 ( )G C kk kβ= minus

(1)


162










2 211 3 1 c A T( ) ( )total

dY k k Y W m M Vdt


22A T 1 1 2 2 c T[ ( ) ] total



23A T 31 1 21 2 c T[ ( ) ] total



24A T 32 1 22 2 c T[ ( ) ] total



0 1 3k k k= + 3 31 32k k k= + 2 21 22k k k= +












Inlet conditions

Tin=500-700degC





163

0 10 20 30 4000

02

04

06

08



Tin=8232 K CO=13

Yiel

d w

twt







s s2 0

1 2 dR

r rR

α π απ

= int (2)

s p s p0 0p 2

ss0

2 ( )d ( )d2

2 d

R R

R

r u r r ru r ru

Rr r

π α α

απ α= =int int

int (3)



0 10 20 30 400

5

10

15

20

25

30D=0418 m H=45 m Tin=8232 K


u p amp u

g m

sdots-1

Axial location m

ug up


(a)

000

002

004

006

008

010

αs

α s

0 1 2 3 40

5

10

15

20

25

30

u p amp u

g m

sdots-1

Axial location m

ug up


(b)

000

002

004

006

008

010 αs

α s



164




02 04 06 08 1000

01

02

03

04

05


T=8232 K CO=13 H=45

Yiel

d w

twt

Bed diameter m



00 02 04 06 08 10000

001

002

003


D=014 m D=0418 m D=10 m

α s


00 02 04 06 08 100

8

16

24

32

40


D=10 m D=0418 m D=014 m

Us

msdots

-1



4 8 12 16 2000

01

02

03

04

05

Yie

ld

wtw

t

CatGasoil wtwt


D=0418 m T=8232 KH=45 m U g=50 m sdots-1


00 02 04 06 08 10000

001

002

003

004

005

α s

rR

Ug=50 msdots-1 T=8232 K H=45 m D=0418 m








165

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1

T=8232 KH=45 mD=0418 m






US

msdots

-1





500 550 600 650 70000

01

02

03

04

05


Yie

ld

wtw

t

Temperature oC



00 02 04 06 08 10000

001

002


T=7732 K T=8232 K T=8732 K T=9732 K

α s


00 02 04 06 08 100

8

16

24

32

40

48

56

64 Ug=50 msdots-1


H=45 mD=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

US

msdots

-1







166


































162










2 211 3 1 c A T( ) ( )total

dY k k Y W m M Vdt


22A T 1 1 2 2 c T[ ( ) ] total



23A T 31 1 21 2 c T[ ( ) ] total



24A T 32 1 22 2 c T[ ( ) ] total



0 1 3k k k= + 3 31 32k k k= + 2 21 22k k k= +












Inlet conditions

Tin=500-700degC





163

0 10 20 30 4000

02

04

06

08



Tin=8232 K CO=13

Yiel

d w

twt







s s2 0

1 2 dR

r rR

α π απ

= int (2)

s p s p0 0p 2

ss0

2 ( )d ( )d2

2 d

R R

R

r u r r ru r ru

Rr r

π α α

απ α= =int int

int (3)



0 10 20 30 400

5

10

15

20

25

30D=0418 m H=45 m Tin=8232 K


u p amp u

g m

sdots-1

Axial location m

ug up


(a)

000

002

004

006

008

010

αs

α s

0 1 2 3 40

5

10

15

20

25

30

u p amp u

g m

sdots-1

Axial location m

ug up


(b)

000

002

004

006

008

010 αs

α s



164




02 04 06 08 1000

01

02

03

04

05


T=8232 K CO=13 H=45

Yiel

d w

twt

Bed diameter m



00 02 04 06 08 10000

001

002

003


D=014 m D=0418 m D=10 m

α s


00 02 04 06 08 100

8

16

24

32

40


D=10 m D=0418 m D=014 m

Us

msdots

-1



4 8 12 16 2000

01

02

03

04

05

Yie

ld

wtw

t

CatGasoil wtwt


D=0418 m T=8232 KH=45 m U g=50 m sdots-1


00 02 04 06 08 10000

001

002

003

004

005

α s

rR

Ug=50 msdots-1 T=8232 K H=45 m D=0418 m








165

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1

T=8232 KH=45 mD=0418 m






US

msdots

-1





500 550 600 650 70000

01

02

03

04

05


Yie

ld

wtw

t

Temperature oC



00 02 04 06 08 10000

001

002


T=7732 K T=8232 K T=8732 K T=9732 K

α s


00 02 04 06 08 100

8

16

24

32

40

48

56

64 Ug=50 msdots-1


H=45 mD=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

US

msdots

-1







166


































163

0 10 20 30 4000

02

04

06

08



Tin=8232 K CO=13

Yiel

d w

twt







s s2 0

1 2 dR

r rR

α π απ

= int (2)

s p s p0 0p 2

ss0

2 ( )d ( )d2

2 d

R R

R

r u r r ru r ru

Rr r

π α α

απ α= =int int

int (3)



0 10 20 30 400

5

10

15

20

25

30D=0418 m H=45 m Tin=8232 K


u p amp u

g m

sdots-1

Axial location m

ug up


(a)

000

002

004

006

008

010

αs

α s

0 1 2 3 40

5

10

15

20

25

30

u p amp u

g m

sdots-1

Axial location m

ug up


(b)

000

002

004

006

008

010 αs

α s



164




02 04 06 08 1000

01

02

03

04

05


T=8232 K CO=13 H=45

Yiel

d w

twt

Bed diameter m



00 02 04 06 08 10000

001

002

003


D=014 m D=0418 m D=10 m

α s


00 02 04 06 08 100

8

16

24

32

40


D=10 m D=0418 m D=014 m

Us

msdots

-1



4 8 12 16 2000

01

02

03

04

05

Yie

ld

wtw

t

CatGasoil wtwt


D=0418 m T=8232 KH=45 m U g=50 m sdots-1


00 02 04 06 08 10000

001

002

003

004

005

α s

rR

Ug=50 msdots-1 T=8232 K H=45 m D=0418 m








165

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1

T=8232 KH=45 mD=0418 m






US

msdots

-1





500 550 600 650 70000

01

02

03

04

05


Yie

ld

wtw

t

Temperature oC



00 02 04 06 08 10000

001

002


T=7732 K T=8232 K T=8732 K T=9732 K

α s


00 02 04 06 08 100

8

16

24

32

40

48

56

64 Ug=50 msdots-1


H=45 mD=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

US

msdots

-1







166


































164




02 04 06 08 1000

01

02

03

04

05


T=8232 K CO=13 H=45

Yiel

d w

twt

Bed diameter m



00 02 04 06 08 10000

001

002

003


D=014 m D=0418 m D=10 m

α s


00 02 04 06 08 100

8

16

24

32

40


D=10 m D=0418 m D=014 m

Us

msdots

-1



4 8 12 16 2000

01

02

03

04

05

Yie

ld

wtw

t

CatGasoil wtwt


D=0418 m T=8232 KH=45 m U g=50 m sdots-1


00 02 04 06 08 10000

001

002

003

004

005

α s

rR

Ug=50 msdots-1 T=8232 K H=45 m D=0418 m








165

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1

T=8232 KH=45 mD=0418 m






US

msdots

-1





500 550 600 650 70000

01

02

03

04

05


Yie

ld

wtw

t

Temperature oC



00 02 04 06 08 10000

001

002


T=7732 K T=8232 K T=8732 K T=9732 K

α s


00 02 04 06 08 100

8

16

24

32

40

48

56

64 Ug=50 msdots-1


H=45 mD=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

US

msdots

-1







166


































165

00 02 04 06 08 100

8

16

24

32

40

Ug=50 msdots-1

T=8232 KH=45 mD=0418 m






US

msdots

-1





500 550 600 650 70000

01

02

03

04

05


Yie

ld

wtw

t

Temperature oC



00 02 04 06 08 10000

001

002


T=7732 K T=8232 K T=8732 K T=9732 K

α s


00 02 04 06 08 100

8

16

24

32

40

48

56

64 Ug=50 msdots-1


H=45 mD=0418 m

T=7732 K T=8232 K T=8732 K T=9732 K

US

msdots

-1







166


































166

































Documents

CFD Simulation of fluid catalytic cracking in downer reactors