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INTERNATIONAL JOURNAL OF CHEMICAL

REACTORENGINEERING

Volume8 2010 ReviewR6

Modeling of Fluid Catalytic Cracking Riser

Reactor: A Review

Raj Kumar Gupta Vineet Kumar

V.K. Srivastava

Thapar University, [email protected] Institute of Technology Roorkee, [email protected] Institute of Technology, [email protected]

ISSN 1542-6580

Copyright c2010 The Berkeley Electronic Press. All rights reserved.

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Modeling of Fluid Catalytic Cracking Riser Reactor:

A Review

Raj Kumar Gupta, Vineet Kumar, and V.K. Srivastava

Abstract

This work aims at compiling the important works on the modeling of a fluid

catalytic cracking (FCC) riser reactor. The modeling of a riser reactor is very

complex due to complex hydrodynamics and unknown multiple reactions, coupledwith mass transfer resistance, heat transfer resistance and deactivation kinetics.

A complete model of the riser reactor should include all the important physical

phenomena and detailed reaction kinetics. As the computational fluid dynamics

(CFD) is emerging as a powerful tool for modeling the FCC riser, various works

on riser modeling using CFD are also included in the paper.

KEYWORDS: fluid catalytic cracking, riser modeling, riser kinetics, riser hydro-

dynamics, CFD modeling

Please send correspondence to Raj Kumar Gupta, phone: +91-175-2393442; email:

[email protected].

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1.

Introduction

Fluid catalytic cracking unit (FCCU) converts heavy hydrocarbon petroleum

fractions into more usable products such as gasoline, middle distillates, and light

olefins. This unit mainly consists of a riser reactor, a catalyst stripper, and a

regenerator. Fluid Catalytic cracking (FCC) is the most important and profitableprocess in petroleum refining industry (Marcilly, 2003).

Riser reactor is the most important part of this unit as the cracking

reactions take place in the riser. Modern FCC units have short diameter risers(0.8-1.2 m) with lengths varying from (30-40 m). In the riser reactor, the contact

time between the gas oil and the catalyst is very short (less than 5 seconds). At the

bottom of the riser, the gas oil feed comes in contact with the hot regeneratedcatalyst coming from the regenerator and consequently vaporizes. As a result, the

cracking reactions start and the density of the oil decreases causing an increase in

the velocity of the vapor/gas phase. The increasing gas phase velocity accelerates

the velocity of the catalyst and the riser behaves as a transport bed reactor. Thecracking reactions by product (coke) gets deposited on the catalyst surface and

decreases its activity as the catalyst moves toward the exit of the riser. At the riser

exit, the deactivated (spent) catalyst is separated from the hydrocarbon productsvapor through specially designed riser termination device and sent to the

regenerator for burning off the coke from its surface. The product vapors are sent

to the main fractionator for recovery.Many researchers have worked on the various aspects of riser modeling.

Corella and Frances (1991a) reviewed the works related to FCC riser modeling

and listed some of the assumptions made by the early workers. Biswas and

Maxwell (1990) discussed the process and catalyst related developments in fluidcatalytic cracking process. Otterstedt et al. (1986) reviewed the problems

associated with fluid catalytic cracking of heavy oil fractions. This work aims at

compiling the work done by various researchers for modeling the different aspectsof fluid catalytic cracking riser reactor.

2.

Riser Modeling

Modeling of riser reactor is very complex due to complex hydrodynamics,

unknown multiple reactions coupled with mass transfer and heat transferresistances. Also, the conditions keep changing all along the riser height due to

cracking which causes molar expansion in the gas phase and influences the axial

and radial catalyst density in the riser. In the literature, numerous models of FCCriser are available with varying degrees of simplifications and assumptions. A

complete physical model of the FCC riser reactor should include all the

phenomena shown in Figure 1.

Gupta et al.: Modeling of Fluid Catalytic Cracking Riser Reactor: A Review

Published by The Berkeley Electronic Press, 2

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Figure 1. Physical model of gas-liquid-solid flow and reaction in FCC riser

reactor (Source: Gao et al., 2001)

In the present work, various aspects of riser modeling are organized into:feed atomization and vaporization, hydrodynamics, cracking kinetics, interphase

heat transfer and mass transfer, and catalyst deactivation.

2.1. Feed atomization and vaporization

Vaporization of liquid feed is a key step in the FCC reaction process. In an FCC

riser reactor, liquid feed is sprayed into a flow of hot, fluidized catalyst. Feedmolecules are cracked only after they are transported in the vapor phase to an

active site in the solid catalyst. The gas oil is fed into the riser through feed

Characteristics of gas

phase flow and reaction

Gas

phase

Momentum

transfer

Heat

transfer

Mass

Transfer

Turbulent

energy transfer

Turbulent flow characteristics of

catalyst particle phase

Solid

phase

Spray

phase

Flow and vaporization

characteristics of feed spray phase

2 International Journal of Chemical Reactor Engineering Vol. 8 [2010], Review

http://www.bepress.com/ijcre/vol8/R6

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nozzles. The size of feed droplet affects the vaporization rate and hence the

performance of the riser.

Atomization of feed into fine drops facilitates high rates of heat transfer

between catalyst and feed and thus fast vaporization of the feed drops. Whereas,large feed drops vaporize slowly leading to low gas velocities in the riser entry

zone thus lowering the drag force exerted on the catalyst. Slow vaporization offeed also leads to very high catalyst to vaporized feed ratio coupled with high

catalytic activity and higher temperature in the riser entry zone. These factors can

lead to undesirable secondary cracking reactions. Dean et al. (1982) showed that

the heat-transfer-rate between feed droplets and catalyst particles variesexponentially with droplet size. The smaller droplet diameter leads to faster

evaporation rates, better mixing with the catalyst, and uniform cooling of the

catalyst.Faster vaporization rates can be realized by effective feed atomization into

fine drops (Mauleon and Courelle, 1985; Avidan et al., 1990). Most of the newdevelopments related to feed injection systems therefore have their primaryobjective as the atomization of feed into very minute drops (Johnson et al., 1994).

Mauleon and Courcelle (1985) obtained the experimental data, for various initial

droplet sizes, for feed atomization nozzles (Table 1) for a nozzle exit velocity of

50 m/s.

Table 1. Experimental data for feedstock atomization (Source: Mauleon and

Courcelle, 1985)

Droplet size (m) 500 100 30

Relative no. of droplets 1 125 4630Droplets per catalyst particle 0.001 0.11 4

Vaporization time (ms) for 50% vaporizationfor 90% vaporization

220 11 4

400 20 8

Johnson et al. (1994) showed that proper nozzle design could improve the

gas oil conversion by 1.4 wt% and gasoline yield by 5 wt%. Goelzer (1986) andBienstock et al. (1991) have reported the improvement in conversions and yield

patterns due to the replacement of feed injection system of older designs by newer

ones. Buchanan (1994) did extensive work on the heat-transfer coefficients ofgas/solids and liquid/gas/solids systems. He considered two different schemes for

the direct contact between droplets and catalyst particles: the first schemeassumes that infinitely fast heat transfer occurs as soon as a droplet contacts aparticle; the second scheme assumes that true direct contact between a droplet and

a hot particle is prevented by the Leidenfrost effect, that is, the vapors evolving

from the droplet surface push back the particle, and heat transfer occurs through a



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thin gas film. For typical FCC conditions, he found that the time required for

complete vaporization of a 100 m droplet ranges from 0.3 to 30 ms depending

on the model selection. He further showed that the time required to vaporize a

droplet was directly related to its size and concluded that the vaporization timeswere proportional to the 1.1 to 1.5 power of initial droplet diameter.

Mirgain et al. (2000) modeled the homogeneous vaporization (in gasphase) and heterogeneous vaporization (on collision with catalyst particles) of the

feed drops. Authors attempted to understand the physical phenomena affecting oil

vaporization by considering a conceptual mixing chamber and made the following

conclusions for FCC risers and downers: homogenous vaporization cannotvaporize feedstock droplets of the same size as used in current FCC feedstock

sprays, and mixing of the feedstock droplets into a vigorously agitated suspension

of hot catalyst particles is needed for complete, fast vaporization; the Leidenfrosteffect does not occur, and direct contact between droplets and particles is

unavoidable; the best results for heterogeneous vaporization are obtained with acatalyst jet of intermediate porosity (70-95%).

Nayak et al. (2005) proposed a phenomenological model to predict the

heat transfer coefficient of droplet vaporization in gassolid flow. The model

relates the evaporation rate of droplet with rate of collisions of solid particles,

specific heat capacities of solid and liquid, latent heat of vaporization, relativevelocity of gas and liquid and temperatures of three phases. With the help of one

adjustable parameter, the model captures the key features of heat transfer between

liquid drop and gassolid mixture. The model also accommodated the presence ofmultiple volatile components in feed oil and boiling of oil over a range of

temperatures instead of a specific boiling point. Authors used this approach to

simulate evaporation of liquid drops injected in FCC risers.

2.2. Hydrodynamics

After complete vaporization of feed, only solid phase (catalyst & coke) and vapor

phase (steam, hydrocarbon feed and product vapor) are left. The vapor phase

expands due to cracking and accelerates the solid phase. Both vapor and solidsmove upwards, and velocities of both phases keep on increasing along the riser

height. The simplest hydrodynamic models assume plug flow for both the phases.

However, there is considerable back mixing in the solid phase because of slipbetween the solid and vapor phase which makes the prediction of solid velocity

profile difficult. The gas-solid suspension density within the riser is greatlyinfluenced by both gas superficial velocity and solids mass flux, and therefore,

these operating parameters directly affect heat transfer, mass transfer, andchemical reaction rates (Berruti et al., 1995).



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Risers exhibit an axial solids holdup distribution showing densification at

the entry point of solids. The holdup decreases along the riser height as the solids

are accelerated by the gas (acceleration zone) and eventually the fully developed

flow condition is reached where the solids holdup is invariant with the riser height(fully developed flow region). At the outlet of the FCC riser, the riser termination

device enhances local back-mixing that results in an increase in the suspensiondensity. Some of the early studies provided some experimental evidence that the

riser flow structure consists of two characteristic regions: a dilute gas-solid

suspension travelling upwards in the center (core) and a dense phase of particle

clusters, or strands, moving downward along the wall (annulus). Such core-annulus structure is usually assumed for modeling the riser reactor.

In order to examine the gas-solid flow patterns, a CFB riser can generally

be divided into two distinct regions (Weinstein et al., 1984; Matsen, 1988). In thelower part of the CFB riser there is a dense region that is considered to be a

turbulent or bubbling fluidized region. In the upper part of CFB riser there is adilute region that is considered as a transport region. A third region ofdensification may be present depending on the exit geometry. Bai et al. (1992)

and Xu (1996) have considered five sections in CFB risers: acceleration,

developed bottom-dense, transition, top-dilute, and exit. An inflection point,Zinf,

was defined by Li and Kwauk (1980) and Li et al. (1981) to demarcate the lowerdense section and top-dilute section. Sabbaghan et al. (2004) considered lower

dense region, located right above the distributor, and the upper region. They

further divided the upper region into three zones: acceleration, fully developed,and deceleration or exit. In contrast to the upper dilute zone of the riser, where

several studies on local flow structure have been conducted, there exist only few

studies concerning the flow structure in the acceleration zone of a riser.Several modeling efforts, of CFB risers, employing different mathematical

formulations are reported in literature to predict the relationship between solidconcentration, operating conditions, and riser geometry. Harris and Davidson

(1994) proposed three broad categories of these models: (i) the models that

predict the axial variation of the solid suspension density, but not the radialvariation; (ii) the models that predict the radial variation and the high average slip

velocities by assuming two or more regions, such as core-annulus or clustering

annulus flow models; and (iii) the models which are based on the numerical

modeling of the conservation equations for mass, momentum, and energy for gasand solid phases. The type (i) models are mathematically straightforward and

compares well with the experimental data. However, the highly empirical natureof these models makes them unsuitable for design and scale-up purposes.Experimental evidence suggests that the core-annulus formulation of type (ii)

models better approximates the time-averaged radial flow structure in CFB risers

than the clustering annular models, especially in fast fluidization regime. Their



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main drawback is the requirement of experimental data. The type (iii) models are

the most rigorous, but the required simplifying assumptions limit their usefulness

for design purposes.

The selection of a particular type of model depends on its intendedapplication. Models of type (i) and type (ii) are best suited to investigate the effect

of operating conditions and riser dimensions on the riser flow structure. Thesemodels can be easily coupled with the reaction kinetic models to simulate the

performance of CFB risers (Pugsley et al., 1992; Bolkan-Kenny et al., 1994).

Type (iii) models are suitable to investigate the local flow structure and the

impact of geometry in CFB risers. Type (i) models account for increased solidsholdup higher than predicted by using single particle settling velocities.

Yerushalmi et al. (1976) experimentally studied the axial solids distribution in

CFB risers. They observed that the increased solids holdup causes the clusteringof particles. The clustering is responsible for large slip velocities measured

experimentally, because of the high settling velocity of the cluster as compared tothe single particle settling velocity.

For fully developed region in the industrial-scale FCC risers, Matsen

(1976) reported that the slip factor (), defined as the ratio of interstitial gas

velocity to average solids velocity, is approximately 2. For FCC powders van

Swaaij et al. (1970) reported slip factors in the range 1.6 2.2. Patience et al.(1992) developed an empirical correlation for calculating the slip factor,

considering the effect of particle characteristics, riser diameter, and gas velocity

on the slip factor:

41.00

47.0

6.5

1 tp FrFrV

U

(1)

The drag force is exerted on the particles by the carrier gas. This force

controls the slip velocity between the two-phases, and the acceleration of the

particulate phase. The drag coefficient, CD, can be estimated by standard drag

curve. Littman et al. (1993) showed that the drag curve may severely overestimatethe value of CD. Pugsley and Berruti (1996) modified the equation for standard

drag coefficient for use in their work.

Type (ii) models characterize the radial solids distribution and explain thereason for the higher solids holdups. At the riser wall, the velocity of the solid and

vapor stream is nearly zero and the effect of back mixing is also prominent. The

velocity is maximum at the center of the riser and minimum near the wall. Sincethe flow in the riser is turbulent, the wall effect is confined to a small portion of

the riser cross section. In the rest of the cross section the velocity is almost same.

Hence the flow can be divided into two regions; one is a turbulent core region inthe centre and an annulus region near the wall. Also, the radial measurements of



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particle velocity and solids flux are approximately parabolic, often with negative

velocities along the riser wall. Grace et al (1990) experimentally measured the

downward particle velocity at the riser wall ranging from 0.5 to 1.5 m/s.

A core-annulus type of flow pattern in CFBs has been shown to exist inseveral studies (Capes and Nakamura, 1973; Hartge et al., 1988; Bader et al.,

1988; Berruti and Kalogerakis, 1989; Tsou and Gidaspow, 1990; Rhodes, 1990;Samuelsberg and Hjertager, 1996; Sun and Gidaspow, 1999; Huilin and

Gidaspow, 2003). Brereton and Stromberg (1986), Jin et al. (1998), and

Schnitzlein and Weinstein (1988) showed in their works that the Geometry of the

CFB riser considerably influences its hydrodynamics. Zhou et al. (1994, 1995)measured the particle concentrations in the risers of square cross section and

predicted a core-annulus flow structure. Author predicted that the exit effects are

more significant in a square riser than in a riser of circular cross-section. van derMeer et al. (1999) studied the dimensionless groups for hydrodynamic scaling of

a CFB. Authors demonstrated that at least five dimensionless groups are requiredfor full hydrodynamic scaling of a CFB. Viitanen (1993) conducted tracer studieson the industrial scale riser reactor to obtain axial and radial dispersion

coefficients which are useful for modeling purposes.

Internal recirculation of solids in CFB risers occurs due to interchange of

solids between heterogeneous flow structures. In a FCC riser reactor, internalcirculation of deactivating catalyst particles affects the reactor performance. Wirth

(1991) developed a model for the momentum transfer arising from collisions

between discrete particles and clusters dispersed throughout the riser cross-section. Pugsley and Berruti (1995) modified the model of Wirth (1991) by

considering the solids flow in core and annulus regions and calculated the core-to-

annulus solids interchange coefficient. Senior and Brereton (1992) showed that avalue of 0.2 m/s for core-to-annulus solid interchange coefficient gave the best fit

of their experimental data of axial suspension density profile. Pugsley and Berruti(1996) presented a type (ii) predictive model based on fundamental principles and

empirical relations. Godfroy et al. (1999) described a simple two-dimensional

hydrodynamic model for CFB riser in fully developed region. The modelpredicted solid holdup, radial void fraction, and the radial profiles of axial gas and

solid velocity and mass flux. Density is calculated using a correlation based on

slip factor, and the radial voidage profile is calculated solely on the basis of cross-

sectional average void fraction.Horio et al. (1988) and Horio and Tekei (1991) proposed core-annulus

clustering flow structures in their models. Bhusarapu et al. (2006) in theirexperimental studies predicted the clustering phenomena throughout the risercross-section (more likely near the wall) along with the particle exchange between

core and annulus. The clusters play a major role in axial dispersion of particle and

gas, radial distribution of particles, chemical reaction, and heat transfer at the



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wall, and thus affect the overall performance of a CFB (Huilin et al., 2005).

Sabbaghan et al. (2004) in their hydrodynamic model of the acceleration zone

considered that all solids moved as clusters in the riser (cluster based approach) as

rigid spheres. In this approach, the solid phase experiences higher drag force thanthe single particle based approach. Authors used the correlations proposed by Xu

and Kato (1999) for the cluster size. The effective drag coefficient for clusters canbe obtained by using the correlations proposed by Mostoufi and Chaouki (1999)

and Turton and Levenspiel (1986). The formulas used by the authors for the

estimation of cluster size and effective drag coefficient are listed in Table 2.

Subbarao (2010) proposed a model for the cluster size estimation. The modelpredicted the cluster size as a function of fluid and particle properties, and riser

diameter.

Table 2. Correlations for cluster size and effective drag coefficient

Correlations for cluster size:

cl

p

p

cl Ad

d

p

gpmfd

MQ

MgUA

)2(

))(1)(3333(

21

2

gUU

UM mfsmf

mfs

mf

)1(2

Correlations for effective drag coefficient:

09.1

657.0

0,Re163001(

413.0Re173.01

Re

24

p

p

p

DC

0,DD fCC mf

p

clt

d

dArm 33.0.22.0 Re02.3

Most hydrodynamic models of type (i) and type (ii) attempt to predict gas-

solid flow in risers using correlations mostly based on experimental data

generated for cold-flow conditions. In cold-flow studies, the solids are accelerated

4)1(

)( 7.4

01

mft

mf

mfs

p

gp UUU

gQ



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by the incoming gas and as a result, the gas velocity along the riser decreases as it

loses momentum in accelerating the solids. Arastoopour and Gidaspow (1979)

and Theologos and Markatos (1993) predicted, for vertical pneumatic conveying,

that the gas velocity decreases as the solid particles accelerate; the solid volumefraction therefore decreases due to increase in solid velocity at a constant solid

mass flux. However, in a FCC riser reactor the gas phase expands due to cracking,resulting in the gas velocity increase along the riser height.

Gupta et al. (2007) predicted the phase velocities and increase in molar

flux of gas all along the riser height (Figure 2). Malay et al. (1999) and Han and

Chung (2001b), in their FCC riser simulations, have also predicted similar phasevelocity profiles. Also, density, viscosity, and void fraction change due to

modifications in the operating conditions (temperature and pressure) and because

of mole generation (Leon-Becerril et al. 2004). Correlations proposed in type (i)and type (ii) lumped hydrodynamic models ignore these variations. Sundaresan

(2000) have also concluded that the main challenge in modeling the performanceof multiphase flow reactors is to integrate detailed chemistry and transportmodels.

Riser height (m)0 5 10 15 20 25 30 35

Velocity(m/s)

0

2

4

6

8

10

12

14

GasPhasemolarflux

(kmol/m

2.s

)

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Gas Phase velocity

Solid phase velocity

Gas phase molar flux

Figure 2. Axial phase velocity and gas phase molar flux profiles in FCC riser

(Source: Gupta et al., 2007)



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In the last two decades, many researchers have shown great potential for

employing CFD for the simulation of type (iii) models. Two different classes of

CFD models can be made: Eulerian-Eulerian models and Eulerian-Lagrangian

models. Eulerian-Eulerian models consider both gas and solid phases ascontinuous and fully interpenetrating. The equations employed are a

generalization of the NavierStokes equations for interacting continua. Owing tothe Eulerian representation of the particle phases, Eulerian-Eulerian models

require additional closure laws to describe the rheology of particles. In most

recent continuum models constitutive equations according to the kinetic theory of

granular flow are incorporated. Eulerian-Lagrangian models solve the Newtonianequations of motion for each individual particle, taking into account the effects of

particle collisions and forces acting on the particle by the gas. In the Eulerian

approach, an arbitrary control volume in a stationary reference frame is used toderive the basic governing equations. In Lagrangian approach, equations are

derived by considering a control volume (material volume) such that the velocityof the control volume surface always equals the local fluid velocity.

Two types of type (iii) models are used for the particulate phase

turbulence: the concentration-dependent solid viscosity model and the kinetic

theory of granular flow model with and without gas turbulence. The solids

viscosity is needed to account for the energy dissipation between solid particles.The model with solids viscosity as an input was first proposed by Tsuo and

Gidaspow (1990). Authors used the solid viscosity reported by Gidaspow et al.

(1989) in their model. The computation of viscosity by the method of Gidaspowet al. (1989) becomes highly inaccurate when there is strong down-flow of solids.

Miller and Gidaspow (1992) determined the solid viscosity for FCC particles

from a mixture momentum balance, neglecting transient effects and assuming thatthe gas and solid velocity gradient are of same order. The authors proposed a

linear correlation between solid viscosity and solid concentration. Sun andGidaspow (1999) used the viscosity data predicted by Miller and Gidaspow

(1992) in their model. The authors predicted core-aanular flow in the riser and a

unique phenomena: an off-center maximum flux. Gidaspow et al. (1996) proposeda better correlation for solid viscosity, partially based on the kinetic theory of

granular flow:

0

3/1165.0 gss (2)

The radial distribution function, g0, used in the above equation accountsfor the probability of particle collisions. The value ofg0is near 1.0 when the flow

is dilute and becomes infinity when the flow is so dense that motion of particles is

impossible. The equations for radial distribution function are given by Carnahan

and Starling (1969) and by Bagnold (1954). Gidaspow and Huilin (1998) found



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the experimental data to lie between these theoretical expressions. Huilin and

Gidaspow (2003) used equation (2) in their model. Authors predicted two types of

core-annulus flow regimes at high solids flux: a regime with a parabolic flux and

downflow at the wall and a regime with a low flux at the pipe center and amaximum near the wall with no downflow. Gidaspow and Huilin (1998) proposed

an equation of state for determining solids pressure, incorporating the effect ofcohesive pressures as a function of volume fraction of particles. Authors

concluded that the derivative of the solids pressure with respect to volume

fraction can be used in the hydrodynamic models for predicting the particle and

velocity distribution profiles inside the CFBs.The pioneering work of Lun et al. (1984) applied the kinetic theory of

gases to granular flow. The kinetic theory approach uses a one equation model to

determine the turbulent kinetic energy (granular temperature) of the particles. Thegranular temperature is defined as the sum of the squares of random particle

oscillations in three directions. The kinetic theory approach for granular flowallows the determination of the viscosity of the solids in place of empiricalrelations. Using this theory the viscosity of particles can be computed from

granular temperature measurements (Gidaspow and Huilin, 1996) or from

granular pressure measurements (Chen et al. 1994). Sinclair and Jackson (1989)

applied the granular flow model to a fully developed flow in a pipe. Ding andGidaspow (1990) derived the expressions for solids viscosity and pressure of a

dense gas-solid flow. Mathesian et al., (2000), Neri and Gidaspow (2000), Van

Wachem et al. (2001) used the kinetic theory of the granular flow to simulate gassolid flow in risers. Das et al. (2004) in their model, based on the kinetic theory of

granular flow, incorporated an extra transport equation correlating the gas phase

and solid phase fluctuating motion. The authors proposed a solution algorithmthat allows simultaneous integration of all the model equations in contrast to the

sequential multi-loop algorithms commonly used in riser simulations. Huilin et al.(2005) used a cluster based approach and predicted the hydrodynamics of cluster

flow in circulating fluidized beds. Authors showed a considerable improvement in

the model predictions using cluster based approach as compared to the modelbased on original kinetic theory of granular flow. Lu et al. (2008) presented a gas-

solid multi-fluid model with two granular temperatures of the dispersed particles

and the clusters in risers, to predict the hydrodynamics of dispersed particles and

clusters flow in CFBs.In addition to the basic governing equations developed from the universal

laws, it is necessary to develop relevant constitutive equations and equations ofstate for the fluids under consideration to close the system of equations. Severalclosure models have been proposed to define the appropriate constitutive

equations for binary or multi-phase flows based on the kinetic theory of granular

flow. The constitutive equations are needed to close the solid phase momentum



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conservation equation for phase stress tensor, solid pressure, and momentum

exchange between the solid and gas phases.

The gas solid momentum exchange coefficient is assumed to only include

the drag contribution. Several drag models exist for the gas-solid interphaseexchange coefficient. Almuttahar and Taghipour (2008) in their CFD model

compared the performance of different drag models. Authors concluded that theGidaspow et al. (1992), Arastoopour et al. (1990), and Syamlal and OBrien

(1987) drag models predicted similar profiles for the solid volume fraction and

axial particle velocity; however, the Syamlal OBrien drag model, based on

minimum fluidization velocity of the particle, showed a better solid volumefraction prediction at the core area. Heynderickx et al. (2004) studied the effect of

particle clustering on the interphase momentum-transfer coefficient by

introducing the concept of effective drag. Authors concluded that for solidsfractions greater than 1%, clustering phenomena become increasingly important,

resulting in an appreciable decrease of the interphase momentum-transfercoefficient.

According to the turbulent flow behavior of FCC particles and void

fraction profile observed in experiments, four zones (dense phase, subdense

phase, subdilute phase, and dilute phase zone) can be identified in a turbulent

fluidized bed (Gao et al., 2009). Authors have summarized the various dragmodels applicable in these zones. Jiradilok et al. (2006) used the standard kinetic

theory based model with the modified drag (corrected for clusters) suggested by

Yang (2004), and simulated the turbulent fluidization of FCC particles in a riser.In addition to the drag force model, the flow behavior may be influenced

by inelastic interparticle collisions resulting in kinetic energy dissipation. The

restitution coefficient, e, represents the elasticity of particle collisions and rangesfrom fully inelastic (e= 0) to fully elastic (e= 1). Goldschmidt et al. (2001) and

Therdthianwong et al. (2003)reported that in the kinetic theory model there is adegree of sensitivity to the coefficient of restitution.

The simulations performed by Jiradilok et al. (2006) with the coefficient

of restitution of 0.99 did not give a good resolution for the bubble formation in thebottom part of turbulent fluidized bed. Therefore, the coefficient of restitution

was reduced to get reasonable results for the turbulent regime due to the increased

effect of particleparticle collisions in the dense phase. Authors used a value of

0.9 for their model simulation.Gao et al. (2009) reported that increasing the valueof restitution coefficient from 0.9 to 0.95, the coexisting dilute and dense phase in

the turbulent fluidized bed could be correctly predicted.The boundary conditions for the particulate turbulent energy (granular

temperature) and axial velocity are complex; a particle colliding with the wall

may slide or bounce back tangentially depending on the value of the angle of

collision, as described by Jenkins (1992). In two-fluid model, the collisional angle



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is not accounted for explicitly by the boundary conditions. There are two limits in

collisional exchange of momentum and kinetic energy between particles and wall:

a small-friction/all-sliding limit and a large-friction/no-sliding limit. Jenkins and

Louge (1997) have suggested that the appropriate boundary conditions could befound by interpolating between these two limits. Another type of boundary

condition commonly used in fluidization was derived by Johnson and Jackson(1987). This boundary condition uses a specularity coefficient, which may depend

on the flow conditions, to characterize the extent of sliding and bouncing back.

The use of specularity coefficient allows more flexibility in adjusting this

parameter to fit a certain flow behavior (Benyahia et al., 2005).For FCC riser modeling, most works used EulerianEulerian approach

where the dispersed solid particles are treated as interpenetrating continuum

(Theologos and Markatos, 1993; Benyahia et al., 2003; Zimmermann andTaghipour, 2005; Lan et al. 2009). Few works have used EulerianLagrangian

approach (Nayak et al. 2005; Wu et al., 2010). In this approach, the motion ofsolid catalyst particles is modeled in the Lagrangian framework and the motion ofcontinuous phase is modeled in the Eulerian framework. This approach offers a

more natural way to simulate complex particle level processes like cracking

reactions. Also, heat and mass transfer and chemical reactions occurring at the

individual particle scale can be conveniently accounted using this approach. Theapproach however requires significantly more computational resources and

therefore rarely used for dense gassolid risers.

Theologos and Markatos (1993) proposed a three dimensionalmathematical model considering two phase flow, heat transfer, and three lump

reaction scheme in the riser reactor. The authors developed the full set of partial

differential equations that describes the conservation of mass, momentum, energyand chemical species for both phases, coupled with empirical correlations

concerning interphase friction, interphase heat transfer, and fluid to wall frictionalforces. The model can predict pressure drop, catalyst holdup, interphase slip

velocity, temperature distribution in both phases, and yield distribution all over

the riser. Theologos et al. (1997) coupled the model of Theologos and Markatos(1993) with a ten lump reaction scheme to predict the yield pattern of the FCC

riser reactor. Theologos et al. (1999) accounted for feed atomization effect on

riser performance in their CFD model. Gao et al. (1999) developed a model

that predicted three-dimensional, two-phase flow inside the riser-type reactor. Theauthors used a thirteen lump kinetic scheme and demonstrated that excessive

cracking occurred beyond the 10 m riser height, and resulted in the increase of by-products yield at the expense of desirable products. Authors further extended thismodel to three-phase flow model (Gao et al., 2001) by incorporating the effect of

feed vaporization.



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Benyahia et al. (2003) presented a two phase 2-D flow model using

transient Eulerian approach with a simple three lumps kinetic scheme.

Zimmermann and Taghipour (2005) simulated the hydrodynamics and reaction

kinetics of gas-solid fluidized beds containing fluid catalytic cracking (FCC)particles. The authors included the kinetic term in an additional transport equation

for modeling the reaction kinetics. Novia et al. (2007) developed a model tosimulate the 3-D hydrodynamics and reaction kinetics (3-lump) in FCC riser

reactor. Baurdez et al. (2010) proposed a method for steady-state/transient, two-

phase gassolid simulation of a FCC riser reactor. Authors used a simple four

lump kinetic model to demonstrate the feasibility of the method.Nayak et al. (2005) used the EulerianLagrangian approach to simulate

simultaneous evaporation and cracking reactions occurring in FCC riser reactors.

Wu et al. (2010) used EulerianLagrangian approach for the simulation of gas-solid flow in FCC process. Authors concluded that by using this approach the

catalyst activity can be calculated in time by tracking the history of particlemovement undergoing the heat transfer and chemical reactions. Therefore, theeffect of the residence time distributions of catalyst particles on the reactor

performance is well revealed by considering the instantaneous catalyst

deactivation.

2.3 Cracking kinetics

Describing the kinetic mechanism for the cracking of petroleum fractions is

difficult because of the presence of thousands of unknown components in a

petroleum fraction. However, the important chemical reactions occurring during

catalytic cracking are given by Gates et al. (1979).For modeling of cracking kinetics, Weekman and Nace (1970) divided the

FCC feed stock and products into three components (lumps): the original

feedstock, the gasoline (boiling range C5 4100F), and the remaining C4s (dry

gas and coke); and developed a predictive kinetic model for the FCC riser. The

kinetic parameters of the model were evaluated using the experimental data. This

model was capable of predicting gasoline yield. However, it did not predict thecoke yield separately.

Prediction of coke is important as the coke supplies the heat required for

endothermic cracking reactions in the reactor. Lee et al. (1989) proposed a fourlump kinetic model by separating the coke from the three lump model of

Weekman and Nace (1970). The rate constants and activation energies for thereaction scheme were obtained by regression using the experimental data of Wang

(1974). This four lump kinetic scheme was used by several investigators (Farag etal., 1993; Zheng, 1994; Gianetto et al., 1994; Ali and Rohani, 1997; Blasetti et al.,

1997; Gupta and Subba Rao, 2001; Han and Chung, 2001a; Abul-Hamayel et al.,



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2002; Gupta and Subba Rao, 2003; Jia et al., 2003; Nayak et al., 2005;

Hernandez-Barajas et al., 2009) for the analysis of many other aspects of FCC

modeling. The model is still popular because of its simplicity, and ease of

formulation and solution of kinetic, material and energy equations.This simple lumping approach for kinetic modeling was further extended

by various researchers by increasing the number of lumps in their models. Effortsmade in this direction are: five lump models proposed by Larocca et al. (1990)

and Ancheyta-Juarez et al. (1999), six lump model by Coxson and Bischoff

(1987) and Takatsuka et al. (1987), ten lump model by Jacob et al. (1976), eleven

lump model by Mao et al. (1985), Sa et al. (1985) and Zhu et al. (1985), twelvelump model by Oliveira (1987), thirteen lump model by Sa et al. (1995), and

nineteen lump model by Pitault et al. (1994).

Jacob et al. (1976) included the chemical composition of the feed in their tenlump kinetic model by considering the paraffins, naphthenes, aromatic rings and

aromatic substituent groups in light and heavy fuel oil fractions. Their model alsoaccounted for the nitrogen poisoning, aromatic adsorption and time dependentcatalyst decay. Rate constants of the model were determined using the

experimental data obtained in a fluidized dense bed with a commercial FCC

catalyst. This model is used by Arbel et al. (1995), Ellis et al. (1998), and Nayak

et al. (2005) for their FCC modeling studies. This idea was further extended byOliveira (1987), Coxson and Bischoff (1987), and Theologos et al. (1997) for the

kinetics studies of FCC riser reactor. Ten lump scheme for catalytic cracking of

gas oil is shown in Figure 3.Oliveira (1987) proposed a twelve lump scheme in which the coke lump of

ten lump scheme of Jacob et al. (1976) is divided into two gas lumps (gas 1 and

gas 2) and a coke lump. Sa et al. (1995) proposed a thirteen lump kinetic modelconsidering coke and cracking gas as two separate lumps and dividing the

aromatic part of the vacuum residue into two parts, (in resin and asphaltenefraction & in saturate and aromatic fraction). Pitault et al. (1994) developed a

nineteen lump kinetic model comprising twenty five chemical reactions, this

kinetic scheme was used by Derouin et al. (1997) in their hydrodynamic modelfor the prediction of FCC products yields for an industrial FCC unit.



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PH = wt% paraffinic molecules, 6500F+

NH = wt% naphthenic molecules, 6500F+

SH = wt% aromatic side chains, 6500F+

AH = wt% carbon atoms among aromatic rings, 6500F+

PL = wt% paraffinic molecules, 4300-650

0F

NL = wt% naphthenic molecules, 4300-650

0F

SL = wt% aromatic side chains, 4300-650

0F

AL = wt% carbon atoms among aromatic rings, 4300-650

0F

G = gasoline lump (C5- 4300F)

C = C-lump (C1to C4+coke)

Figure 3. Ten lump scheme for catalytic cracking (Source: Coxson and

Bischoff, 1987)

Another method called structure-oriented lumping (SOL) was developed

by Quann and Jaffe (1992) for describing the composition, reactions andproperties of complex hydrocarbon mixtures. This lumping technique represents

individual hydrocarbon molecules as a vector of incremental structural features

thus a mixture of hydrocarbons can be represented as a set of these vectors, eachwith an associated weight percent. This type of representation of molecules

provides a convenient framework for constructing reaction networks of arbitrarysize and complexity, for developing molecular-based property correlations, and

for incorporating existing group contribution methods for the estimation ofmolecular thermodynamic properties. Christensen et al. (1999) used the SOL for

specifying the reaction chemistry of FCC feedstocks using over 3000 molecular

Gasoline

PL NL SL AL

PH NH SH AH

C-Lump



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species with over 60 reaction rules and generated a network of 30,000 elementary

chemical reactions. They included the monomolecular reactions (cracking,

isomerization, and cyclyzation), bimolecular reactions (hydrogen transfer, coking,

and disproportionation), and the effects of thermal cracking and metal-catalyzeddehydrogenation for the reaction network generation. The kinetic parameters for

the model were regressed using a wide range of FCC process conditions, feedcompositions, and catalyst formulations. The integrated FCC process model

developed by the authors using this kinetic model is claimed to be capable of

predicting the complex non-linear phenomena of FCC units.

Feng et al. (1993) proposed single-events method for the FCC kineticmodeling. This method permits a mechanistic description of catalytic cracking

based on the detailed knowledge of the mechanism of various reactions involving

the carbenium ions. Determination of the kinetic constants for these single eventsrequires some key reactions of pure hydrocarbons.

Based on the single-events method, Dewachtere et al. (1999) developeda kinetic model for catalytic cracking of VGO in terms of elementary steps ofchemistry. For the reaction network generation, all likely chemical species are

considered and accounted for in each lump. Fifty single event rate parameters

were determined from an extensive experimental program on catalytic cracking of

key components with relevant structures. Landeghem et al. (1996) proposed anew kinetic model based on the molecular description of cracking and hydrogen

transfer reactions. This scheme is an intermediate approach between simple

lumping of cuts and single events method. The authors determined the kineticconstants of the model using a microactivity test reactor.

The concept of continuous description of catalytic cracking of petroleum

fractions incorporating kinetics and other physical rate steps using advancedcomputational techniques is proposed by Peixoto and de Medeiros (2001). They

characterized the petroleum fractions using multi indexed concentrationdistribution function (CDF) developed by Aris (1989). Authors used the twelve

lump scheme, instantaneous adsorption hypothesis of Cerqueira (1996) and

deactivation hypothesis of Oliveira (1987) in their work.Recently, Gupta et al. (2007) proposed a new kinetic scheme based on

pseudocomponents cracking and developed a semi-empirical model for the

estimation of the rate constants of the resulting reaction network. Fifty

pseudocomponents (lumps) are considered in this scheme resulting in more than10,000 reaction possibilities. The model can be easily used to incorporate other

aspects of the riser modeling. This kinetic model is used by Gupta and Kumar(2008) in a three phase FCC riser model and by Ruqiang et al. (2008) for theproduction planning optimization of FCC.

Various other works on kinetic modeling include: a study (Fisher, 1990)

on the effect of feedstock variations on the catalytic cracking yields; a study



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(Farag et al., 1993) on the effects of metal traps in a FCC catalyst contaminated

with high levels of nickel and vanadium using pulse reaction technique for testing

of FCC catalysts in a down-flow micro activity reactor at different carrier gas

flows and at different temperatures; a strategy proposed by Ancheyta-Juarez et al.(1997) to estimate kinetic constants for the three lump, four lump and five lump

kinetic models that decreases the number of parameters to be estimatedsimultaneously; a modeling study (Wallenstein and Alkemade, 1996) on FCC

catalyst selectivity using the experimental data from a microactivity test reactor; a

rate constants sensitivity analysis by Pareek et al. (2002) by grouping 20 rate

constants of Weekmans kinetic model (Weekman, 1979) in five categories byusing CATCRACK developed by Kumar et al. (1995); a new approach by Ng et

al. (2002) for determining product selectivity in gas oil cracking using a four lump

kinetic model; a study (Hagelberg et al., 2002) of the kinetics of gas oil crackingon a FCC equilibrium catalyst with short contact times using a novel isothermal

pulse reactor; a bulk molecular characterization approach (Bollas and Vasalos,2004) for the simulation of the effect of bulk properties of FCC feedstocks on thecrackability and coking tendency; an eight-lump kinetic model for secondary

reactions of FCC gasoline proposed by Wang et al. (2005); a study on the effect

of catalyst to oil ratio, temperature, residence time, and feed composition on

products selectivities and product distribution by Dupain et al. (2006); and anapproach (Hernandez-Barajas et al., 2009) based on representing rate constantswith a continuous probability distribution function for the estimation of kinetic

parameters in lumped catalytic cracking reaction models.

2.4 Interphase heat transfer and mass transfer

After the complete vaporization of feed droplets, a vapor phase (hydrocarbons andsteam) and a solid phase (catalyst particles) exist in the riser. There is

considerable temperature difference in these phases near the bottom of the riser.

Since, the temperature influences the reaction rates the prediction of interphase

heat transfer becomes important.From heat transfer point of view, very early models assumed isothermal

riser. Most of the riser models assume instantaneous thermal equilibrium between

the vapor and solid phases at the riser inlet. There have been very fewexperimental measurements of heat-transfer rate between gases and suspended

fine particles, and only limited correlations are available (Bandrowski and

Kaczmarzyk 1978; Kato et al. 1983).Generally the experimental observations on heat transfer coefficients

between gas and particles are expressed as Nusselt number as a function ofReynolds number based on single particle diameter (Kunii and Levenspiel, 1991):



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3/1

3/203.0

g

gpg

p

g

p

VU

d

kh

(3)

Theologos et al. (1999) developed a 3-D mathematical model that predicts

the two-phase flow, heat transfer and chemical reaction in catalytic cracking riser

reactor. They used a correlation of Nusselt number as a function of Reynoldsnumber. The model was used to assess the effects of interphase heat transfer in

the overall performance of the riser. Gupta and Subba Rao (2001) used modified

Nusselts number proposed by Buchanan (1994). Wu et al. (2010) used acorrelation for Nusselt number that is proposed by Ranz and Marshall (1952).

Jepson (1986) has developed a non-isothermal transport reactor model

incorporating an empirical gas-particle heat-transfer correlation.

External mass transfer resistances in the riser are neglected in most of theworks on FCC riser modeling (Corella and Frances, 1991a; Martin et al., 1992;

Ali et al., 1997; Derouin et al., 1997; Theologos et al., 1999; Das et al., 2003,

Berry et al., 2004; Gupta et al., 2007). However, considering mass transferresistance between the phases helps in predicting the concentration of the reacting

species at the catalyst surface. Flinger et al. (1994) in their model considered mass

transfer to occur between the two phases. Authors obtained the mass-transfercoefficient as a fitting parameter based on the conversion profile in a commercial

FCCU. Like external heat transfer, mass transfer may be expressed as Sherwood

number as a function of the Reynolds number based on single particle diameter.Gupta and Subba Rao (2001) and Nayak et al. (2005) modeled the interphase

mass transfer using the correlation for Sherwood number proposed by Ranz and

Marshall (1952). Han and Chung (2001b) calculated the diffusion coefficients

using the correlation proposed by Baird and Rice (1975):

3/43/1)(35.0 DgUD gf (4)

Intrapellet mass transfer has the effect of decreasing the reactant

concentration within the pellet. Consequently, the average rate will be less thanwhat it would be in the absence of internal concentration gradient (Smith, 1981).Pruski et al. (1996) determined adsorption coefficients for four lumps, while

cracking gas oil. Bidabehere and Sedran (2001) developed a model to study the

effects of diffusion, adsorption, and reaction at high temperature inside theparticles of commercial FCC catalysts and experimentally studied the relative

importance of these phenomena using two equilibrium catalysts and n-hexadecaneas a test reactant in a riser simulator reactor. Al-Khattaf and de Lasa (2001)

described the effects of diffusion on activity and selectivity of FCC catalysts.



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Atias and de Lasa (2004) studied adsorption and diffusion under reaction

conditions similar to those of fluid catalytic cracking (FCC) by performing

experiments in a novel fluidized CREC riser simulator using FCC catalysts of

various crystallite sizes. The CREC riser simulator, used by the authors,facilitated the assessment of adsorption parameters on FCC catalysts under

reaction conditions and the decoupling in their evaluation from that of intrinsickinetic parameters. Their study is more close to the FCC conditions as compared

to the earlier studies that are done at low temperatures under low or no reactivity

conditions. Dupian et al. (2006) have discussed the external and internal mass

transfer correlations used for modeling the FCC riser.

2.5 Catalyst deactivation

During the cracking reactions, FCC catalyst gets deactivated due to the deposition

of coke on the catalyst surface. Most of the popular theories on deactivation arebased on the time-on stream concept. Many researchers (Voorhies, 1945;Wojciechowski, 1968, 1974; Nace, 1970; Gross et al., 1974) have used this

concept to formulate various empirical functions for accounting the effect of

catalyst decay on the cracking kinetics.

Various models for time dependent catalyst decay have been proposed fordifferent lengths of contact time. Models of Weekman (1968) and Nace et al.

(1971) used relatively high contact times (1.2 to 40 min), and Models of Paraskos

et al. (1976) and Shah et al. (1977) used relatively low contact times (0.1 to 10 s).Froment and Bischoff (1990) proposed a mechanistic based model considering

catalyst decay rate as a function of the fraction of active sites and the

concentration of the reactants.Corella et al. (1985) studied the catalyst decay for a wide range of contact

times (2 to 200 s) considering homogeneous and non homogeneous catalystsurfaces. Authors showed that the order of deactivation kinetics decreases with

the contact time, taking values 3, 2, and 1, successively. They further justified the

change of order of deactivation with the different contact times by showing thediscrepancy in the values of these constants obtained by Weekman (1968) and

Nace et al. (1971) for relatively large contact times, and Paraskos et al. (1976) and

Shah et al. (1977) for short contact times. The deactivation equations proposed byvarious authors are listed in Table 3.



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Table 3. Empirical equations proposed for the catalyst deactivation (Source:Gupta, 2006)

Author Kinetic equation of activity d

differential integrated

Weekman (1968) -da/dt = a a = e-t

1

Weekman and Nace

(1970)

-da/dt =

A-1/

(+1/)

a = A-

A-1/

(+1)/

(if d 1)

Wojciechowski

(1968)

-da/dt = Aag a = [1+(g-1)At]

-

1/(g-1)

A g

(if g 1)

Corella et al. (1985) -d(k0a)/dt =

k0(1-d)

( k0a)d

integrated ford=1

d=2

d=3

12

3

a = average activity of catalyst

t = time= average deactivation functiond = order of deactivation

k0= cracking kinetic constant, average value for all the reactants present in feed

Corella et al. (1986) determined the kinetic parameters of cracking and of

deactivation for a given feed-catalyst system. Corella and Menendez (1986)developed a model in which the catalyst surface was assumed to be non-

homogeneous with acidic sites of varying strength. Corella and Monzon (1988)

developed a model for deactivation and coking kinetic relations between activity,concentration of coke and time on stream for four different mechanisms of coke

formation and growth. Corella and Frances (1991b) correlated the deactivation

kinetic constant with the commercial feedstock and commercial catalysts andproposed overall deactivation orders ranging from 1.4 to 2.7.

There is no specific function that can be used for the deactivation.

Different empirical equations have been used by various researchers to fit their

experimental data. However, there are two functions that fit the experimental data

quite well: power function and exponential function. The exponential function ismore widely used. Larocca et al. (1990) reported that the catalyst deactivation can

be represented by both an exponential decay function and a power decay functionwith an average exponent of 0.1to 0.2. Kraemer et al. (1991) used the data from

two different experimental reactors and showed that exponential decay function or



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power law function could equally represent the data; however, the power law

assumes the unrealistic limits of infinite catalyst activity at zero time-on-stream

and requires two parameters to describe deactivation. They further concluded that

the simple first order decay function is an effective equation for describing thecatalyst activity decay for short reaction times (less than 20 seconds).

Al-Khattaf and de Lasa (1999) have estimated the effective gas oildiffusivity in Y-zeolites. The effectiveness factor for gas oil cracking was

calculated for 1 m and 0.1m zeolite. Authors showed that diffusional

constraints have a major impact on primary cracking reactions and on gasoline

composition. Den Hollander et al. (2001)determined the performance of coked(0.56wt% coke on catalyst) and fully regenerated FCC catalyst by cracking a

hydrowax feedstock in a micro-riser equipment. Authors predicted that the

activity of coked catalyst was lower but was still significant, and the selectivitywas similar to the regenerated catalyst.

Lopez-Isunza (2001) presented a mechanistic model to study thedeactivation of FCC catalyst by combining interphase and intraparticle masstransfer interactions with the cracking reactions in an isothermal, ideally mixed

fluidized bed in which reactions occur inside the cylindrical pore in a single pellet

(microsphere) cracking catalyst. The deactivation of the catalyst is modeled using

Langmuir-Hinshelwood expression. Corella (2004) developed a selectivedeactivation kinetic model for the commercial FCC catalysts and feedstocks.

3.

Conclusions

Feed atomization into small droplets of uniform size is desired as it helps inavoiding side reactions thereby improving the yields of desirable products. The

smaller feed diameter leads to faster evaporation rates, a better mixing with

catalyst, and uniform cooling of the catalyst. This leads to reduction in undesiredthermal cracking.

Also, it is desired that the feed is distributed evenly throughout

the entire cross section of the riser so that the temperature distribution in the riser

entry zone is improved.The three phase, 3-D models can capture the real hydrodynamic in the

riser, especially in the feed entry zone. Computational fluid dynamics is a

powerful tool that may be used to model the complex phenomena in the riser

entry zone. Also, in FCC riser models, incorporating the effect of cracking on thehydrodynamics helps in better predictions of the physical phenomena.

There are a number of kinetic models/schemes available in the literature.

However, in most of the FCC riser simulation studies either four lump or ten lumpkinetic schemes are used. Use of detailed kinetic models by the researchers is

limited in order to avoid the mathematical complexity. CFD models may be used

to incorporate more detailed kinetics with complex hydrodynamics.



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Considering Interphase heat transfer resistance and mass transfer

resistances in the model gives realistic phase temperature and concentration

profiles and influences the kinetic constants and rate of the cracking reactions

eventually leading to better prediction of product yields.In most of the models of FCC risers, a very simplified deactivation model

(assuming first order deactivation for all the reactions) is used. However, Corella(2004) have shown that the deactivation orders are not same for all the reactions.

The use of variable deactivation order may be explored in future models.

Nomenclature

A parameter in correlation of Xu and KatoAr Archimedes number, ds

3g(s-g)g/

2

CD effective drag coefficientCD,0 standard drag coefficient

D riser diameter (m)Df effective diffusion coefficient (m

2/s)

dcl cluster diameter (m)

dp particle diameter (m)Fr Froude number, u0/(gD)

0.5

Frt Froude number based on the terminal settling velocity of single

particle, Vt/(gD)0.5

f drag force correction factor

g gravitational acceleration (m/s2)

hp interface heat transfer coefficient between catalyst and gas phases[kJ/(s m2K)]

kg thermal conductivity of gas [kJ/(s m K)]M2 parameter in correlation of Xu and Kato

m parameter in correlation of Mostoufi and Chaouki

Q1 parameter in correlation of Xu and Kato

Rep particle Reynolds number, dpgVp/Ret particle Reynolds number based on terminal velocity, dpgUt/

Us solid superficial velocity (m/s)

Ug gas velocity (m/s)Umf gas velocity at incipient of fluidization (m/s)

Uo superficial gas velocity (m/s)Ut terminal velocity (m/s)Vp average particle velocity (m/s)



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Greek letters

average axial voidage

mf voidage at incipient of fluidizations solid volume fraction

cl cluster density (kg/m3)

g gas density(kg/m3)

p particle density(kg/m3)

g gas viscosity (Pa.s)s particulate viscosity

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