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K. K. Dagde, Y. T. Puyate / International Journal of Engineering Research and Applications(IJERA) ISSN: 2248-9622 www.ijera.com

Vol. 2, Issue 5, September- October 2012, pp.698-714

698 | P a g e

Modelling And Simulation Of Industrial FCC Unit: AnalysisBased On Five-Lump Kinetic Scheme For Gas-Oil Cracking

K. K. Dagde * and Y. T. Puyate**

*(Department of Chemical/Petrochemical Engineering, Rivers State University of Science and Technology, PortHarcourt, P. M. B. 5080, Port Harcourt, Nigeria)**(Department of Chemical/Petrochemical Engineering, Rivers State University of Science and Technology,

Port Harcourt, P. M. B. 5080, Port Harcourt, Nigeria)

AbstractModels which describe the performance

of the riser and regenerator reactors of fluidcatalytic cracking (FCC) unit are presented. Theriser-reactor is modelled as a plug-flow reactoroperating adiabatically, using five-lump kineticsfor the cracking reactions. The regenerator-

reactor is divided into a dilute region and a denseregion, with the dense region divided into abubble-phase and an emulsion phase. The bubble-phase of the regenerator is modelled as a plug-flow reactor, while the emulsion phase is modelledas a continuous stirred tank reactor. The modelsare validated using plant data obtained from afunctional industrial FCC unit. It is shown thatpredictions of the models compare very well withplant data for both reactors. Simulation resultsindicate that catalyst-to-gas oil ratio and inlet-air

velocity have significant effects on theperformance of the riser and regenerator reactorsrespectively. The yield of gasoline and otherproducts of the catalytic cracking process increaseas the height of riser-reactor increases, withmaximum yield of gasoline (of about 0.45 massfraction) occurring about half-way up the riser-height. Both the amount of coke on spent catalystand the riser-temperature decrease with time,while the regenerator-temperature increases withtime. The riser-temperature varies from about650K to 800K, while the regenerator-temperatureranges from about 650K to 1080K. The optimumvalues of process variables obtained for effectiveoperation of FCC are inlet-air velocity of 14m/s,riser-temperature of about 653K, and catalyst-gasoil ratio of 3.

Keywords: Riser, regenerator, kinetics, catalyticcracking, simulation.

1. IntroductionFluid catalytic cracking (FCC) is one of the

most important processes in the petroleum refinery;employed for the conversion of straight-runatmospheric gas-oil, vacuum residues, and other

related heavy stocks, into a broad spectrum of products in the presence of a catalyst. The productsof catalytic cracking include fuel gases, liquefiedpetroleum gas, high-octane gasoline, light fuel oil,diesel fuel, heavy fuel oil, etc. FCC unit consists of areaction section and a fractionating section thatoperates together as an integrated process unit. The

reaction section has two reactors: (i) the riser-reactorwhere almost all the endothermic cracking reactionsand coke deposition on the catalyst occur, and (ii) theregenerator-reactor, where air is used to burn-off theaccumulated coke on the catalyst. The catalyst-regeneration process also provides the heat requiredfor the endothermic cracking reactions in the riser-reactor.

In the FCC unit, the catalyst enters the riser-reactor as a dense bed and is pneumatically conveyedupwards by the dispersing steam and vapourizinggas-oil feed. It is during this period of conveying thecatalyst that catalytic cracking of gas-oil takes place

through efficient catalyst and gas-oil contact. Thecatalyst later becomes deactivated due to cokedeposition on it, and the deactivated catalyst thenpasses through the spent-catalyst slide-valve in theriser-reactor and enters the top of the regenerator.The major purpose of the regenerator is to oxidize thecoke on the spent catalyst with oxygen to form CO,CO2, and H2O, thereby reactivating the catalyst.Compressed combustion-air enters the regeneratorfrom the bottom through a grid distribution patterndesigned to provide efficient mixing of air withdeactivated catalyst, resulting in a fluidized-bedcatalyst-regeneration operation. The regeneratedcatalyst passes through the regenerated-catalyst slide-valve and is mixed with gas-oil at the riser- reactor‟s base and the cycle is repeated. Provisions are madefor adding fresh catalyst makeup to maintaininventory and for withdrawal of aged andcontaminated catalyst. The FCC unit is quite complexfrom both the process modelling/simulation andcontrol points of view. The complexity of the FCCunit is attributed to the strong interaction between theriser and the regenerator reactors, and the uncertaintyin the cracking reactions, coke deposition, and cokeburning kinetics. The objective of FCC is tomaximize the yield of high octane gasoline andminimize coke formation to make it economicallyattractive.

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Lee and Grooves [1] developed a mathematicalmodel for fluid catalytic cracking using the three-lump kinetic model of Weekman and Nace [2] for thecracking reactions in the riser-reactor, where (1) gas-oil (the feed and taken as one lump) is converted into(2) light gases plus coke lump, and (3) gasoline. The

major disadvantage of this model is that it lumpedcoke and light hydrocarbon gases together despite thedifferent characteristics of these components.However, the three-lump scheme is simple indescribing the cracking reactions and is able todetermine gas-oil conversion and gasoline yieldindependently.

Several workers [3, 4, 5, 6] later used thefour-lump kinetic scheme of Lee et al. [7] whichaccounts for coke formation on the catalyst, to modeland simulate fluid catalytic cracking process. In thefour-lump scheme, (1) gas-oil is converted into (2)light gases (C1-C4), (3) coke, and (4) gasoline. Themajor disadvantage of this model is that it lumped thehydrocarbon light gases and fuel gases (C1-C2)together, making it impossible to predict the yield of these gases independently.

Dagde et al. [8] applied five-lump kineticmodel for the cracking of vacuum gas-oil in which(1) gas-oil is converted into (2) liquefied petroleumgas (LPG, i.e. C3-C4), (3) gasoline, (4) coke, and (5)fuel gases (dry gases, i.e. C1-C2). The riser-reactorwas modelled as a two-phase fluidized-bed reactorassumed to operate isothermally, but the energybalance for the riser-reactor and analysis for catalyst-regeneration in the regenerator-reactor were notconsidered. Such a five-lump kinetic scheme allowsindependent predictions of LPG and fuel gases whichare very significant and desirable in view of thedomestic, commercial, industrial, and laboratoryapplications of these gases [9].

Other workers [10, 11, 12, 13] have alsopresented models for fluid catalytic cracking usingten-lump and eleven-lump kinetic schemes for thecracking reactions in the riser-reactor, where thevarious lumps are based on the molecular structure of the components. The feed was lumped into paraffins,naphthenes, and aromatics, in both its heavy and lightfractions. The products were divided into two lumps,with the first lump comprising products in thegasoline range, while the second lump consists of coke and light hydrocarbon gases. The drawbacks of these models include mathematical complications inthe modelling procedures and lack of experimentaldata to validate the models.

In the present paper, models for the riser andregenerator reactors during catalytic cracking of gas-oil are presented. The coke combustion kinetics of Morley and de Lasa [14] is employed in theregenerator, while a five-lump kinetic scheme isadopted for the catalytic cracking reactions where theriser-reactor is modelled as a plug-flow reactoroperating adiabatically.

2. The FCC modelThe fluid catalytic cracking (FCC) model equationspresented in this study are based on the schematicflow diagram of the process depicted in Fig. 1. Thefeed (gas-oil) enters the riser-reactor from thebottom, and is cracked into various products in the

presence of a catalyst. The particle-separator vesselimmediately above the riser acts as a disengagingchamber where vapour products and heavycomponents are separated from the catalyst usingstripping steam.

It is assumed that the stripping process completelyremoves the hydrocarbon gases adsorbed inside thecatalyst pellets before the spent catalyst is sent to theregenerator.

Figure 1: Schematic diagram of fluid catalyticcracking unit.

The regenerator operates as a fluidized-bedand consists of two regions, namely an upper “diluteregion ” and a lower “dense region.” The dilute regionis the section between the top of the regenerator andthe boundary between the two regions, while thedense region extends from the boundary between thetwo regions to the exit of the regenerator vessel (seeFig. 1). The amount of solids entrained in the diluteregion is usually very small compared to the totalamount of catalyst retained in the regenerator vessel.Most of the coke on the catalyst pellets is combustedin the dense region, and full combustion of coke to

Flue Gas

Spentcatalyst

Hydrocarbon Products

FreshCatalyst

Gas Oil

REGENERATOR

RISERRegeneratedcatalyst

Particleseparator Dilute Region

Dense Region

Heat

O2

CO 2

CO

EmulsionPhase

BubblePhase

Air

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2CO is assumed in this region. Thus, the effect of the dilute region on the overall performance of theregenerator is ignored [4].

3. The riser-reactor

3.1. The five-lump kinetic schemeFigure 2 shows the five-lump kinetic schemeused in this study, where (1) gas-oil is converted into(2) gasoline, (3) liquefied petroleum gas (LPG), (4)fuel gases, and (5) coke. This kinetic scheme does notaccount for secondary cracking of products into cokebecause the kinetic rate constants for such secondarycracking reactions are of order of magnitudes smallerthan the ones for primary cracking reactions. For thisreason, all secondary cracking reactions are neglectedin this analysis [15, 16, 17].

Fig. 2: Schematic diagram of five-lump reacti onscheme.

The following rate equations areformulated for the various components of thefive-lump kinetic model shown in Fig. 2

ss yK K K K r 21151413121 )()(

(1)

ss yK yK K r ])[()( 2112224232

(2)ss yK yK yK r )()( 2

1132233343 (3)

ss yK yK yK r )()( 21143342244

(4)

ss yK r )()( 21155

(5)

where ijK are the rate constants for the cracking of

lumps i to ; j )( ir are the reaction rates with

respect to lumps ,i with ,1i 2, 3, 4, 5;

T ii y / are the mass fractions of the various

lumps, with i as the mass densities of the different

lumps, and T is the total mass density of all the

five lumps; ss is the effectiveness factor; and isthe catalyst deactivation function. Since the overallcracking rate is affected by the catalyst activity, itseffect should be incorporated into the above rate

equations which is represented by . Thedeactivation kinetic model of Weekman and Nace [2]is chosen in this study because of its simplicity andpopularity in FCC modelling, and is expressed in theform

cd t K exp (6)

where ct is the catalyst residence time which iscalculated as

cat

Rc

V t (7)

where RV is the volume of the riser-reactor, cat is

the volumetric flow rate of catalyst into the riser-

reactor, and d K is the catalyst decay coefficient

which is related to the reaction temperature in theArrhenius form

) / exp( RT E K K dod (8)

where doK is the catalyst decay pre-exponential

factor, E is the activation energy, R is the

universal gas constant, and T is the absolutetemperature. But

.

)(

cat

ocat

CTOF

(9)which when substituted into eq. (7) noting that

, R R R L AV yields

CTOF

L At

o

Rcat R

c

(10)and then into eq. (6), gives

)(exp CTOF

L AK

o

R Rcat d

(11)

where CTO is the catalyst-to-gas oil ratio, R L is the

height of the riser-reactor, R A is the cross-sectional

area of the riser-reactor, oF is the mass flowrate of

gas-oil, and cat is the mass density of catalyst. The

effectiveness factor ( ssη ) for the catalytic

cracking of vacuum gas-oil is evaluated as [18]

i

i

ss h

htanh

(12)

VGO (1)

Gasoline (2)

LPG (3)

Fuel gas (4)

Coke (5)

K12

K34

K13

K14

K15

K23

K24

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where ih is a modified Thiele modulus given as

eff

niicat

ext i D

C K n

ah

1

2)1(1

(13)

where n is the order of reaction (equal to 2 for gas-

oil cracking); extαis the catalyst-specific external

surface area; iK are the kinetic rate constants of the

respective lumps; eff Dis the effective diffusivity of

gas-oil through the catalyst, and iC is the molar

concentration of the various lumps.

It is important to note that extα

in eq. (13) can be

defined using the characteristic dimension, , Z L of the Zeolite crystallite (i.e. catalyst particle size) sinceall the cracking reactions take place in the Zeolitecrystallite with little influence from the matrix of thecatalyst [19]. Therefore, approximating the crystallitegeometry to be a sphere, gives the catalyst-specificexternal surface area as [17]

Z ext L

6

(14)which when substituted into eq. (13) yields thefollowing expression for gas-oil:

eff

ocat Z o D

C K K K K K Lh

)(

2

3

61615141312

(15)

where the subscript “o” indicates gas -oil. It isexpected that diffusion of gas-oil takes place in aUSY Zeolite, and the effective diffusion coefficient

of gas-oil ( eff D) is given by the Erying equation

[20]. RT E D D D peff / exp

(16)

where p Dis the pre-exponential factor for diffusion,

and D E is the activation energy for diffusion.

Model of the riser-reactorIn the derivation of the mathematical modelof the riser-reactor, the following assumptions aremade:Axial dispersion in the riser-reactor is negligible.Catalyst particles have a uniform size in a givendifferential element, and both gas-oil and gasolinehave identical activity decay function [21]The riser wall is adiabatic.Feed viscosity and heat capacities of all componentsare constant.Adsorption and dispersion inside the catalystsparticles are negligible.

Pressure changes throughout the riser-height are dueto static head of catalyst in the riser.

Coke deposition on the catalyst does not affect thefluid flow.

In each section of the riser-reactor, thecatalyst and gas have the same temperature.The coke has the same specific heat as the catalyst.The riser dynamic is fast enough to justify plug-flow

characteristics and a quasi-steady state model.Instantaneous vaporization occurs at the entrance of the riser-reactor [4].

Cracking reactions are completed in theriser-reactor.Applying the conservation principle to a control

volume ( dL A R ) of a plug-flow riser-reactor based

on the above assumptions, where dL is thedifferential height o f the reactor‟s control volume,gives the mass and energy balances as

ss R

R

yK K K K

r

dL

dyU

dt

dy

2115141312

111

)(

)(

(17)

ss R

R

yK yK K

r dL

dyU

dt

dy

])[(

)(

211222423

222

(18)

ss R

R

yK yK yK

r dL

dyU

dt

dy

)(

)(

2113223334

333

(19)

ss R

R

yK yK yK

r dL

dyU

dt

dy

)(

)(

2

114334224

444

(20)

ss R R yK r dL

dyU

dt

dy )()( 2

115555 (21)

dL

dT R )( pooPcat cat

Ro R

C F C F

A

)(

)()(

)()(

)()(

34343

242423232

15151414

1313121221

H K y

H K H K y

H K H K

H K H K y

(22)

where R is the average void fraction in the riser-

reactor, RT is the temperature of the riser-reactor,

U is the riser superficial velocity, cat F is the mass

flow rate of catalyst, pcat C and poC

are thespecific heat capacities of catalyst and gas-oil

respectively, ij H are the heat of reaction for the

cracking of component i to j , and L is the variableheight of the riser-reactor.Since gas-oil is the feed which is cracked into thevarious products, the mass fraction of gas-oil at the

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inlet ( 0 L ) of the riser-reactor is unity, while themass fractions of the products at the inlet are equal tozero because no product is formed at the inlet of theriser-reactor. Also, at the inlet of the riser-reactor, thefeed temperature is taken to be a reference

temperature ( ref T ) equal to 800K [22]. Theseboundary conditions at the inlet of the riser-reactorare defined mathematically as

ref R

i

T T

y

y

L 0

1

:01

i = 2, 3, 4, 5 (23)

We define the following dimensionless variables

R L L

Z (24)

ref

R R

T

T (25)

where Z is the dimensionless height of the riser-

reactor, and Rθ is the dimensionless riser-temperature. Using eqs. (24) and (25) in eqs. (17) – (22), and noting that

R

o

AU

=

Ro

o

A

F

(26)

gives

0)( 2115141312

1

sso

o R R R yK K K K F

L A

dZ

dy

(27)

0])[( 2112224232 sso

o R R R yK yK K F

L A

dZ

dy

(28)

0)( 2113223334

3ss

o

o R R R yK yK yK F

L A

dZ

dy

(29)

0)( 2114334224

4ss

o

o R R R yK yK yK F

L A

dZ

dy

(30)

0)( 2115

5ss

o

o R R R yK F

L AdZ dy

(31)

ref poo pcat cat

o R R R R

T C F C F

L A

dZ

d

)(

0

)(

)()(

)()()()(

34343

242423232

15151414

1313121221

H K y

H K H K y

H K H K

H K H K y

(32)

and the boundary conditions (23) become

:0 Z 1

0

1

5432

1

R

y y y y

y

(33)

where o

is the volumetric flow rate of gas-oil. Equation (27) – (32) were solved numerically

using a fourth-order Runge-Kutta algorithm using theboundary conditions (33).

4. The regenerator 4.1. Regenerator combustion kinetics

Usually, coke is a mixture of differentcomponents (carbon, hydrogen, nitrogen, sulphur,etc.), but mainly carbon [4] Thus, during catalystregeneration in FCC unit, coke is burnt to producecarbon monoxide and carbon dioxide [11, 13]. Also,

the homogeneous CO combustion reaction takingplace in the bubble-phase is assumed to be negligiblecompared with the catalytic CO combustion in theemulsion phase [23,4]. The following irreversiblecoke combustion reactions occur in the emulsionphase of the regenerator [24].

Heat COOC C K 22 (34)

Heat COOC C K

221

(35) Heat COOCO COK 222

1

(36)

where C K is the reaction rate constant for coke

burning, and COK is the reaction rate constant for

the catalytic CO combustion. Equation (36) is the“after - burning” reaction which takes place in thedense region if sufficient oxygen is supplied tosupport it. The reaction which goes to completion inthe dense region of the regenerator to fully regeneratethe catalyst is called the “controlled -after- burning”

reaction. However, CO burning is usually initiatedby using a promoter, which is a catalyst that speedsup the reaction of carbon monoxide to carbondioxide. The promoter, usually a metal like platinum,is attached to the FCC catalyst during manufacturing.Platinum-based combustion promoters have beenutilized in FCC units to catalyze the oxidation of CO

to 2CO for over 30 years [25, 26, 27]. The betterthe dispersion of platinum, the more effective is thecombustion of coke. The rate expressions for thecomponent gases in the emulsion-phase are obtained

as follows.Coke (C): 2)( COC K r CS C C (37)

Oxygen (O2):2 / 1

2 22)( OCOCOCS O C C K COC K r

(38)Carbon dioxide (CO2):

2 / 12 22

)( OCOCOCS CO C C K COC K r (39)

Carbon monoxide (CO):2 / 1

2 2)( OCS COCS CO C C K COC K r

(40)

where)( C r

is the rate of coke combustion;)( ir

are the rates of combustion of individual components

of the flue gases (i.e. exit gases), with 2Oi , CO,

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;CO 2 CS C is the molar concentration of coke on

spent catalyst; iC are the molar concentrations of the

flue gases; ,K ,K and ,K are the rate constantsin eqs. (37) – (40) defined as follows [4, 5]

C K K

11

for CO balance (41)

C K K

1

for CO2 balance (42)

C K K

22

2

for O2 balance (43)

where COCO / 2 is the intrinsic ratioof carbon dioxide to carbon monoxide. The molefractions of the various flue gases are expressed withrespect to the molar concentration of oxygen in thefeed air, in the form

f O

OO C

C y

2

2

2

(44)

f O

COCO C

C y

2 (45)

f O

COCO C

C y

2

2

2

(46)

where f OC 2 is the molar concentration of

oxygen in the feed air, and the prime indicates molefraction.

4.2. Model of the regenerator-reactorHere, we are concerned with only the dense

region since the effect of the dilute region on thedynamics of the regenerator is ignored as indicatedabove. The dense region is divided into a bubble-phase and an emulsion-phase [28]. The emulsion-phase is assumed to be a bed at minimum fluidizationvelocity, and coke combustion reactions occur in thisphase. The air distributors, spent catalyst, andcyclones recycles pipes in the emulsion-phaseproduce enough turbulence which justifies this phaseto be modelled as a continuous stirred tank reactor.The bubble-phase, on the other hand, is dominated bygases at high velocity compared with the velocity inthe emulsion-phase. Hence, the bubble-phase movesas plug-flow and exchanges mass and heat with theemulsion-phase without coke combustion reactiondue to its deficiency in catalyst particles [6]. In thederivation of the mathematical model for catalystregeneration, the following assumptions are made:

Unsteady state conditions for the energy andcoke combustion balances in the emulsion-phase dueto the high density of catalyst [4], and Steady statecondition for the same operations in the bubble-phasedue to low solid density.

The homogeneous combustion reactiontaking place in the bubble-phase is negligible

compared with the catalytic CO combustion in theemulsion-phase [14, 4]

Mass balance for coke combustion in the emulsion-phaseApplication of the law of conservation of mass tocoke combustion in the emulsion-phase based on theabove assumptions, gives

d

dL

L

y

U

Lr

U A L

y y

d

dy GI

GI

S

a

GSS C

a E GGI

S S R RS

)1( (47)where the dimensionless rate of change of catalyst-bed height is obtained as

a E cat G

RS GI

U Ad

dL

)1(

(48)The dimensionless variables in eqs. (47) and (48),and the volume of the regenerator, are defined as

cat

S S y

;;

cat

R R y

;1 E GGG L AV

;GSS

GGI L

L L

GSS

a

L

t U

(49)

where S yis the mass fraction of spent catalyst, R y

is the mass fraction of regenerated catalyst, S is

the mass density of spent catalyst, R is the mass

density of regenerated catalyst, cat

is the mass

density of catalyst, GV is the volume of the

regenerator, is the dimensionless time, GI Lis the

dimensionless catalyst-bed height, G Lis catalyst-bed

height, G Ais the cross-sectional area of the

regenerator, E is the void fraction in the emulsion-

phase, GSS Lis the steady-state catalyst-bed height,

and S and R are the volumetric flowrates of

spent and regenerated catalyst respectively.

Mass balance for gases in the bubble-phaseIn the bubble-phase, steady-state operation

is assumed because of the high velocity of gases, andit is also assumed that no combustion reaction takesplace in this phase due to low density of catalyst.Application of the law of conservation of mass togases in the bubble-phase, with the assumptions of noaccumulation of gases and without coke combustionreactions, gives the material balance for the fluegases as

ieib Ba

GSS be

GI

ib y yU LK

dLdy

1

(50)

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where beK is the mass-transfer coefficient

between the bubble and emulsion phases, B is the

void fraction in the bubble-phase, ie yand ib y

aremass fractions of gases in the emulsion and bubblephases respectively and are defined as

,TG

ibib y

TG

ieie y

(51)

with 2Oi , CO , ;CO 2 ib and ie

are themass densities of gases in the bubble and emulsion

phases respectively, and TG is the total mass

density of gases in the regenerator.

Mass balance for gases in the emulsion-phase

Application of the law of conservation of mass togases in the emulsion-phase, with accumulation of gases and coke combustion reactions, gives thematerial balance for the flue gases as

a

GSS ieibbe

a

GSS i

a E GI

ieieoieoie

U

L y yK

U

Lr

U L

y yU

d

dy

)1(

)(

(52)

where ieoU is the incipient velocity in the

emulsion-phase, ieo yare the initial mass fractions of

the respective gases in the emulsion-phase, and)( ir are the reaction rates of the flue gases in the

emulsion-phase.

Energy balance in the bubble-phaseApplication of the law of conservation of

energy to gases in the bubble-phase based on theabove assumptions, gives the energy balance in thisphase as

b

GSS Bebbe

GI

b

U

LT T H

dL

T d )1()(

(53)with

,ref

bb T

T T

ref

ee

T

T T

(54)

where, bT and eT

are the dimensionlesstemperatures in the bubble and emulsion phases

respectively, bT is the bubble-phase temperature, eT

is the temperature in the emulsion-phase, ref T is a

reference temperature taken to be 960K [22], be H is

the heat-transfer coefficient between the bubble and

emulsion phases, and bU is the bubble velocity.

Energy balance in the emulsion-phase

Application of the law of conservation of energy to coke on spent and regenerated catalysts aswell as the gases in the emulsion-phase, with cokecombustion reactions, accumulation of gases, andtransfer of heat between the bubble and emulsionphases, gives the energy balance in this phase as

)(

)(

)()1()(

R

RS

R

p R pieieGI Ga

e R p R RS pS

p R pieie E GI Ga

e pieieieaoieo pieoieoe

C C L AU

T C T C

C C L AU T C T C

d T d

)(

))(())((1

2

ref a p R pieie

GSS

n

i RC C Oiie

T U C C

Lr H r H

R

d

dL

L

T

U C C

T T L H GI

GI

e

a p R pieie

ebGSS be

R)(

)((55)

with

ref

aoao T

T T ,ref

R R T

T T (56)

where ieo and ie are the volumetric flow

rates of flue gases at the inlet and outlet of the

emulsion-phase; aoT is the dimensionless inlet air

temperature of the regenerator, ieo and ie

are themass densities of the flue gases at the inlet and outlet

of the emulsion-phase respectively, 2O is the mass

density of gas (oxygen) in the emulsion-phase, pieoC

and pieC are the specific heat capacities of the flue

gases at the inlet and outlet of the emulsion-phase

respectively, S pC and R pC

are the specific heatcapacities of spent catalyst and regenerated catalyst

respectively which are taken to be equal, ie ΔH are

the heat of reaction of the flue gases in the emulsion-

phase, C ΔH is the heat of reaction for coke

combustion, is the specific area for heat transfer

between the bubble and emulsion phases, and RT isthe dimensionless temperature of the riser. Note thatthe inlet temperature of the regenerator is partly thetemperature of the spent catalysts entering theregenerator from the riser, and partly the inlet-airtemperature.

5. Hydrodynamic specifications The interchange mass-transfer coefficients

between the bubble and emulsion phases are relatedin the form [28]

bccebe K K K

111

(57)with

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2 / 1

377.6

b

br mf ce

d

DU K

(58)and

4 / 5

4 / 12 / 185.55.4

bb

mf bc

d

g D

d

U K

(59)

where ceK is the mass-transfer coefficient between

the cloud and emulsion phases, bcK is mass-transfer

coefficient between the bubble and cloud phases, bd

is the effective bubble diameter, D is air diffusivity

through the catalyst, g is the acceleration due to

gravity, mf is the voidage at minimum fluidization,

and br U is the rise-velocity of a single bubble in the

bed and is given by [29]2 / 1)(711.0 bbr gd U (60)

Accordingly, the interchange heat-transfercoefficients between the bubble and emulsion phasesmay be expressed as

bccebe H H H

111

(61)with (Kuni and Levenspiel, 1991)

4 / 5

4 / 12 / 1)(85.55.4

b

pgGoGo

b

pgGomf bc

d

gC K

d

C U H

(62)

where Go is the density of the gas mixture, pgC

is the specific heat capacity of the gas mixture, GoK

is the thermal conductivity of the gas mixture, ce H

is the heat-transfer coefficient between the cloud and

emulsion phases, and bc H is the heat-transfer

coefficient between the bubble and cloud phases. By

comparing the expressions for bcK and bc H

above,

a corresponding expression for ce H may be

obtained through the expression for ceK

as2 / 1

377.6

b

br mf pgGoGoce

d

U C K H

(63)The flow velocities in the analysis are related in theform (Froment and Bischoff, 1990)

br mf ab U U U U (64)

where mf U is the minimum fluidization

velocity in the emulsion-phase of the regenerator, and

aU is the superficial inlet-air velocity into the

regenerator. The exit concentrations of the flue gasesand exit temperatures from the emulsion and bubblephases are given as [30]

eb OOO y y y

2221

(65)

eb COCOCO y y y222

1 (66)

eb COCOCO y y y 1

(67) ebe T T T 1

(68)where

a

mf

U

U 1

(69)

and the subscripts e and b indicate emulsion-phaseand bubble-phase respectively.

6. Estimation of kinetic parameters6.1. Kinetic parameters for cracking reactionsin the riser-reactor

The riser-reactor model equations containunknown kinetic parameters such as the reaction rate

constants ( iK ) for the various reaction paths, and the

catalyst deactivation function ( ). These constantshave to be determined before eqs. (27)-(32) can beintegrated. The kinetic parameters for the crackingreactions based on the five-lump kinetic model arepresented in Table 1.

The reaction rate constants are functions of temperature and are generally given by the Arrheniusrelation [18]

RT

E K K

iioi exp

(70)

where the prime indicates values of iK predicted by

eq. (70), ioK are the preexponential kinetic

constants for the respective lumps, and i E are the

activation energies of the different lumps. The rate

constants ( iK ) and the stoichiometric coefficients

( ijV ) of the various lumps are expressed as [30]

;11 K V K ogg

oog M

M V (71)

;22 K V K oLPG LPG

ooLPG M

M V (72)

;33 K V K od d

ood M

M V (73)

;44 K V K oc c

ooc

M

M V (74)

;55 K V K gLPG LPG

ggLPG M

M V (75)

;66 K V K gd d

ggd M

M V (76)

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;77 K V K LPGd d

LPG LPGd M

M V (77)

where o M is the molecular weight of gas-oil, g M

is

the molecular weight of gasoline, LPG M is the

molecular weight of LPG, c M is the molecular

weight of coke, and d M is the molecular weight of

dry gas.

Table1: Estimated kinetic parameters for crackingreactions in the riser-reactor [30]

REACTIONPATH

ACTIV.ENERGY(kJ/kmol)

PRE-EXPON.FACTOR(s-1)

HEATOFREACT.(kJ/kg)

STOICHIOME.COEFFICIENT(V ij)

Gas-oiltogasoline

0.02 46.24 -60780 3.2767

Gas-oiltoLPG

0.00184 59.75 -2000 8.2655

Gasoline todry gas

0.00184 46.24 149000 20.7527

Gasoline tocoke

0.00581 59.75 107600 20.965

Gasoline to

LPG

0.005566 78.49 200 2.5225

Gasoline todry gas

0.002183 78.49 200 6.4022

LPG todry gas

0.03174 59.75 100 2.5380

Catalystdecay

83806.556 117705

Table 2 shows the average molecular weights of the

five lumps used in the study.

Table 2: Average molecular weights of five-lumpkinetic scheme [*31; ** 32].

LUMP AVERAGE MOLEC.WEIGHT(kg/kmol)

Gas – oil *386o M

Gasoline **8.117g M

LPG **7.46 LPG M

Dry gas**4.18d M

Coke **400c M

6.2. Kinetic parameters for catalystregeneration

Equation (70) remains valid for estimating

the reaction rate constants, cK and ,coK used in the

coke combustion reactions in the regenerator. Table 3

shows the kinetic parameters for coke and carbonmonoxide.

Table 3. Kinetic parameters for coke burning[14]

REACTION PP RR EE --EE XX PPOO NN EE NN TT IIAA LL CC OO NN SSTT AA NN TT

AA CC TT II VV AA TT II OO NN EE NN EE RR GG YY

(( k k JJ / / k k mm oo ll )) Cokecombustion

8104.1 (m 3 / kmol s)

224.99

CO catalyticCombustion

247.75(m 3)1.5 kmol 0.5 /kgs

70.74

7. Reactors dimensions, feedstock andcatalyst propertiesThe dimensions of the riser and regenerator

reactors, as well as properties of the feedstock andproducts of the FCC process, were obtained from theNew Port Harcourt Refinery Company [22] and arepresented in Table 4 – 8.

Table 4. Dimensions of industrial riser andregenerator reactors [22]

REACTOR HEIGHT(m)

DIAMETER(m)

Riser 22.9 2.9

Regenerator 35.45 9.8

Table 5 . FCC feed and products properties [22]

COMPONENT

APIGRAVITY

SPECIFICGRAVITY

COMPOSITION(wt. %)

FLOW-RATE(kg/hr)

Gas oilfeed

21.2 0.927 100 244090

Fuel Gas - - 5.4 13180C3 (LPG)

- - 6.3 15388

C4 (LPG)

- - 10.7 26118

Gasoline 60.0 0.739 45.9 112037Lightcycle oil

14.0 0.973 17.8 43448

Bottoms 0.5 1.072 8.8 21480Coke - - 5.1 12448

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Table 6. Physical properties of gas – oil [22]PARAMETER VALUEVapour density (kg/m 3) 9.52Liquid density at 288 oK (kg/m ) 924.8Specific heat (gas), (kJ/kg K) 3.3Specific heat (liquid), (kJ/kg K) 2.67Heat of vapourization (kJ/kg) 156Vapourization temperature (K) 698Flowrate (kg/s) 68.05Inlet temperature (K) 797

Table 7. Physcial properties of catalyst [33, 22]PARAMETER VALUEParticle size (m) 61075 Specific heat capacity (kJ/kg K) 1.12Mass flowrate from riser toregenerator (kg/hr)

1729750

Bulk density (kg/m 3) 975Mass flowrate (kg/s) 480.49Inlet temperature (K) 975Holdup in the regenerator(kg)

5000 – 70000

Table 8. Physical properties of air [4].PARAMETER VALUEDensity (kg/m 3) 1.03Specifi c heat capacity (kJ/kg K) 1.206Bubble-emulsionmass-transfer coefficient (s – 1)

0.5

Bubble-emulsionheat-transfer coefficient (kJ/m 2sK)

0.84

Flowrate (m 3 /s) 43.2466Inlet temperature (K) 370

8. Results and Discussion Table 9 shows the comparison between

model-predictions and plant data for the riser-reactors, while the comparison between model-predictions and plant data for the regenerator-reactoris shown in Table 10.

Table 9. Comparison between model-predictions andplant data for the riser- reactor

PARAMETER MODELPREDICTION

PLANTDATA

Weight fraction of LPG (C 3-C4)

0.1704 0.17

Weight fraction of hydrocarbon fuelgases (C 1-C2)

0.0546 0.054

Weight fraction of coke 0.0511 0.051

Weight fraction of gas oil 0.2654 0.266

Outlet temperatureof riser (K) 652.7 658.00

Table 10. Comparison between model-predictionsand plant data for the regenerator

PARAMETER MODELPREDICTION

PLANTDATA

Temperature (K) 1015.07 1016.48Coke (wt. %) 0.00686 0.007O2 (mol. %) 0.0312 0.03CO 2 (mol. %) 0.161 0.16CO (mol. %) 0.0568 0.00

It may be seen from Tables 9 and 10 that the model-predictions compare very well with the plant data,indicating that the models presented for the riser andregenerator reactors are adequate. For proper catalystregeneration with low carbon content on theregenerated catalyst and complete burning of CO toCO2, there must be excess oxygen concentration of 1to 4 mol.% [34] in the regenerator which is consistentwith the plant-value of oxygen and model-predictionin Table 10. Although carbon monoxide was notdetected in the flue gases of the plant data, the model-predicted 5.7 mol.% of carbon monoxide in the fluegases is recommended for combustion in the COboiler to generate superheated steam and energy forthe plant.

Figure 3 shows the variations of the massfractions of gas-oil and products of the crackingprocess along the height of the riser-reactor. Themass fraction of gasoline increases with theheight of the riser-reactor to a maximum value of about 0.45 corresponding to dimensionless riser-height of about 0.55, where the totaldimensionless height of the riser-reactor is unity (=1); thereafter, the mass fraction of gasolineremains approximately constant at the maximumvalue as the dimensionless riser-height increasesbeyond 0.55. The mass fractions of LPG, fuelgases, and coke, increase steadily as the height of riser-reactor increases, while the mass fractiongas-oil decreases exponentially along the heightof the riser-reactor as it is cracked into thevarious products.

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Dimensionless Height of Riser-Reactor

M a s s F r a c t i o n

Gas-Oil GasolineLPG Fuel GasesCoke

Figure 3. Variations of mass fractions of gas – oil,gasoline, LPG, fuel gases, and coke, alongdimensionless height of riser-reactor

Figure 4 shows plots of mole fraction of theflue gases against dimensionless time, indicating thatthe concentration of oxygen increases rapidly withtime to a maximum value of 0.0742 at adimensionless time of 0.025, and then decreasescontinuously to 0.0312 at a dimensionless time of unity. We note in Fig. 4 that initial concentrations of oxygen, carbon monoxide, and carbon dioxide were

chosen [5] in order to simulate the models. Thus, theinitial rapid increase in the concentrations of thesesgases in Fig. 4 may indicate that the chosen initialconcentrations of the gases are less than their „actual‟concentrations at the beginning of coke combustionAs the combustion process progresses, oxygen fromthe inlet air reacts with coke on the spent catalyst toproduce carbon monoxide and carbon dioxide, so theconcentration of oxygen in the exit gases decreaseswith time while the concentrations of carbonmonoxide and carbon dioxide increase with time.

Figure 4. Variation of mole percent of flue gases withdimensionless time

In Fig. 4, the concentration of carbondioxide increases continuously with time, while theconcentration of carbon monoxide increases to amaximum value and then decreases from themaximum value with time. Although the decrease inconcentration of carbon monoxide with time from themaximum value may be due to its conversion tocarbon dioxide, this conversion process cannot beattributed to the presence of significant quantity of oxygen in the regenerator since oxygen alsodecreases with time during the period of carbonmonoxide depletion. Hence, the decrease inconcentration of carbon monoxide with time in Fig. 4after attaining the maximum value may be due to thecontribution of combustion promoter which sustainsand speeds up the reaction of carbon monoxide tocarbon dioxide.Figure 5 shows the variations of the amount of cokeburnt in the regenerator, as well as riser andregenerator temperatures, with dimensionless time.The amount of coke burnt in the regeneratordecreases tremendously with time, which is a resultof the decrease in the amount of coke on the spentcatalyst with time..

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0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

0 0.2 0.4 0.6 0.8 1

Dimensionless Time

C o

k e B u r n t

( w t . %

)

200

300

400

500

600

700

800

900

1000

1100

T e m p e r a t u r e

( K )

Coke Burnt

Riser Reactor Temperature

Regenerator Temperature

Figure 5. Variations of amount of coke burnt, riserand regenerator temperatures,

with dimensionless timeThe increase in temperature of the regenerator withtime is due to the exothermic coke combustionreaction taking place in this vessel, while thedecrease in temperature of the riser-reactor with timeis due the endothermic cracking reactions.

8.1 Sensitivity AnalysisA simulation model can be used to optimize

plant performance by choosing the optimal set of operating conditions. However, before optimizingsuch a process, it is important to determine howsensitive a process is with respect to decisionvariables. In this section, the effects of catalyst-to-gasoil ratio (CTO) and inlet-air velocity on theperformance of the FCC unit are investigated.

Figure 6 shows the effect of catalyst-to-gas oil ratio (CTO) on the conversion of gas-oiland yield of products. The mass fraction of all theproducts increases slightly as the CTO increases

to 3, thereafter the mass fraction of each productremains constant for 3.CTO Increasing theCTO means increasing the flowrate of catalystentering the riser-reactor. With more catalystavailable in the riser, the number of active sites of catalyst for the cracking reactions also increasesresulting in increased conversion of gas-oil intoproducts for 3.CTO

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15

Catalyst-to-Gas oil Ratio

M a s s

F r a c t i o n

Gas Oil GasolineLPG Fuel GasCoke

Figure 6. Variation of mass fractions of gas-oil andproducts with catalyst-to-gas oil ratio

Accordingly, the mass fraction of gas-oildecreases slightly as the CTO increases to 3 (seeFig. 6), thereafter the mass fraction of gas-oilremains approximately constant. The slightdecrease in the mass fraction of gas-oil for

3CTO is a result of its conversion toproducts. The catalyst spends less time in theriser-reactor at high CTO than at low CTO, whichat high CTO reduces the contact time of gas-oiland catalyst for effective cracking of gas-oil; thiseffect is evident in Fig. 6 where conversion of gas-oil and yield of products remain practicallyconstant for 3.CTO Thus, an optimum valueof 3CTO is obtained for the catalyticcracking process.

Figure 7 shows the effect of CTO on theriser and regenerator temperatures, indicating that theriser-temperature dropped from an initial value of about 657.5K to about 653K as the CTO increases

from 1 to 3; thereafter, the riser-temperature remainsuniform for CTO > 3. The initial drop in riser-temperature for CTO < 3 is due to increase in theendothermic cracking of gas-oil within this range of CTO. The rate of cracking of gas-oil is maximum atCTO = 3 corresponding to a minimum mass fractionof gas-oil (see Fig. 6), beyond which, the rate of cracking of gas-oil remains constant at the maximumvalue resulting in a constant temperature of the riser-reactor as obtained in Fig. 7 for CTO > 3.

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640

645

650

655

660

665

670

0 5 10 15

Catalyst-to-Gas oil Ratio

R i s e r T e m p e r a t u r e

( K )

0

200

400

600

800

1000

1200

R e g e n e r a t o r

T e m p e r a t u r e

( K )

Riser TemperatureRegenerator Temperature

Figure 7. Variation of riser and regeneratortemperatures with catalyst-to-gas oil ratio

Thus, the optimum riser-temperature formaximum cracking of gas-oil is about 653K. We notethat the optimum temperature of the riser-reactor canvary significantly depending on the processconditions. It is interesting to observe that theoptimum riser-temperature of about 653K obtained inFig. 7 corresponds roughly to the temperature at thepoint of intersection of the riser and regeneratortemperatures in Fig. 5. In other words, maximumconversion of gas-oil and maximum yield of gasolineoccur at the optimum riser-temperature (obtainedhere to be about 653K) which in the present analysiscorresponds to dimensionless riser-height of about0.55 (see Fig. 5), and is consistent with Fig. 3 forgasoline yield. Figure 7 also indicates that theregenerator-temperature remains practically constantat about 1000K for all values of CTO, meaning thatCTO does not have significant effect on thetemperature of the regenerator. This is because CTOmainly influences the catalytic cracking reactions inthe riser-reactor with attendant effect on the riser-temperature for CTO < 3. The spent catalyst entersthe regenerator at a temperature equal to the outlettemperature of the riser-reactor of about 653K(model-estimated value, see Table 9). Thistemperature of spent catalyst is less than theregenerator-temperature of about 1000K; hence, thetemperature of the regenerator is not affected by thetemperature of spent catalyst, and remains constantirrespective of the CTO.

Figure 8 shows the effect of inlet-airvelocity on the regenerator-temperature and theamount of coke burnt. As the inlet-air velocityincreases, the amount of coke burnt in the regeneratorincreases continuously, but the regenerator-temperature initially increases to a maximum value of about 1080K corresponding to inlet-air velocity of

about 14m/s, beyond which, the regenerator-temperature decreases as the inlet-air velocityincreases. The increase in the amount of coke burntand the initial increase in regenerator-temperature asthe inlet-air velocity increases, are due to increase inthe rate of the exothermic coke combustion reactions

resulting from increased rate of supply of oxygenfrom the inlet-air. At the maximum regenerator-temperature (obtained in Fig. 8 to be about 1080K),the operation of the regenerator is said to havereached „total combustion regime‟ and any carbonmonoxide present in the regenerator is converted tocarbon dioxide. For inlet-air velocity above 14m/s,the spent catalyst spends less time (low residencetime of spent catalyst) in the regenerator caused bychannelling and by-passing effect inherent in typicalfluidized-bed reactors [35]

0.00E +00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

12 14 16 18 20

Air Velocity (m/s)

C o k e

B u r n t ( w

t . % )

800

850

900

950

1000

1050

1100

1150

R e g e n e r a t o r t e m p e r a t u r e ( K )

Coke BurntRegenerator Temperature

Figure 8. Variation of coke burnt and regenerator-temperature with air velocity.

Some portion of the spent catalyst alsoescapes with the flue gases without proper contactwith the combustion air. All these factorsassociated with high inlet-air velocity result inheat losses which reduce the temperature of theregenerator and this effect increases as the inlet-air velocity increases beyond 14m/s, as obtainedin Fig. 8. Even though the amount of coke burntand the rate of the exothermic coke combustionreactions increase as the inlet-air velocityincreases, the overall quantity of heat generatedin the regenerator for inlet-air velocity greaterthen 14m/s may be less than the quantity of heatlost from the regenerator to the surrounding;hence, the decrease in regenerator-temperature forinlet-air velocity greater than 14m/s. It is veryessential that the coke be burned off the spent

catalyst at the same rate as it is produced in theriser-reactor. This can be achieved by maintaininga small amount of excess oxygen in the

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regenerator above that which is required to burnthe coke. When all the coke is not burnt, the unitis said to be „behind -in- burning‟ with the resultthat the catalyst turns grey [34] and looses itsactivity thereby decreasing the yield of desiredproducts in the riser. To avoid this, the velocity

of air entering the regenerator should beincreased gradually.

9. ConclusionModels which describe the operations of the

riser and regenerator reactors in an industrial FCCunit have been presented. The five-lump kineticscheme adopted for the cracking reactions in theriser-reactor, and the steady-state and unsteady-statemodels developed from the mass and energy balancesfor the riser and regenerator reactors, give adequatepredictions of the feed and products of gas-oilcracking and catalyst-regeneration processes. It isshown that CTO and inlet-air velocity havesignificant effects on the performance of the riser andregenerator reactors respectively. The riser-temperature varies from about 650K to 800K, whilethe regenerator-temperature ranges from about 650Kto 1080K (see Figs. 5, 7, and 8). The optimum valuesof process variables obtained in the analysis foreffective operation of FCC are inlet-air velocity of about 14m/s, riser-temperature of about 653K, andcatalyst-gas oil ratio of 3.

Notation

G A

cross-sectional area of the regenerator, m2. R A cross-sectional area of the riser reactor, m2

CS C molar concentration of coke on spent

catalyst, kmol/m3.

iC molar concentrations of the flue gases (i.e.

exit gases, i = O2, CO, CO2), kmol/m3.

f OC 2 molar concentration of oxygen in the feed

air used in eqs. (44)-(46),kmol/m3.

ieC

molar concentrations of flue gases in theemulsion-phase, kmol/m3.

ibC molar concentrations of flue gases in the

bubble-phase, kmol/m3.

cat pC specific heat capacity of the catalyst in the

riser-reactor, kJ/kg K

poC specific heat capacity of gas-oil in the riser-

reactor, kJ/kg K

pieoC specific heat capacities of flue gases at the

inlet of the emulsion-phase, kJ/kg K.

pieC specific heat capacities of flue gases at the

outlet of the emulsion-phase, kJ/kg K.

pgC specific heat capacity of gas mixture used in

eq. (62), kJ/kg K

S pC specific heat capacity of spent catalyst,kJ/kg K.

R pC specific heat capacity of regenerated

catalyst, kJ/kg K.CTO catalyst-to-gas oil ratio

bd effective bubble diameter, m.

D air diffusivity through the catalyst in theregenerator used in eq. (59), m2/s.

eff Deffective diffusivity of gas-oil through the

catalyst in the riser-reactor used in eq. (16), m2/s

p Dpre-exponential factor for diffusion used in

eq.(16), m2/s

D E activation energy for diffusion used in eq.(16), kJ/kmol E activation energy used in Eq. (70), kJ/kmol.

oF mass flowrate of gas-oil, kg/s

cat F mass flowrate of catalyst, kg/s

g acceleration due to gravity, m/s2.

ihmodified Thiele modulus used in eq. (12).

ohmodified Thiele modulus for gas-oil used in

eq. (15).

be H heat-transfer coefficient between the bubble

and emulsion phases, kJ/m2s K

bc H heat-transfer coefficient between the bubble

and cloud phases,kJ/m2s K

ce H heat-transfer coefficient between the cloud

and emulsion phases,kJ/m2s K

C K reaction rate constant for coke burning,

m3/kmol s.

COK reaction rate constant for the catalytic CO

combustion, m3/kmol s.

d K catalysts decay coefficient used in eq. (8),

-1s doK

catalyst decay pre-exponential kinetic factor

used in eq. (8), -1s

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beK mass-transfer coefficient between the bubble

and emulsion phases,-1s

ceK mass-transfer coefficient between the cloud

and emulsion phases, s-1.

bcK mass-transfer coefficient between the bubble

and cloud phases, s-1.

iK reaction rate constant used in Eq. (70),

m3/kmol s.

ioK pre-exponential constant used in Eq. (70),

m3/kmol s.

GoK thermal conductivity of gas mixture used in

eq. (62), W/m K,K ,K ,K rate constants used in Eqs. (37) –

(40), m3/kmol s.GI L

dimensionless catalyst-bed height.

G Lcatalyst-bed height, m.

GSS Lsteady-state catalyst-bed height, m.

R L height of riser-reactor, m

z L characteristic dimension of Zeolitecrystallite size used in eq. (14), µm

i M molecular weight of component i used in

eqs. (71)-(77), kg/kmol)( ir reaction rates of flue gases in the emulsion-phase, kmol/s.

)( C r rate of coke combustion reaction; kmol/s.

R universal gas constant, kJ/kmol K.t time, sT absolute temperature, K.

bT dimensionless temperature in the bubble-

phase.

eT

dimensionless temperature in the emulsion-phase.

bT temperature in the bubble-phase, K.

eT temperature in the emulsion-phase, K.

aoT dimensionless inlet air temperature of the

regenerator.

RT temperature of riser-reactor, K

RT dimensionless temperature of the riser-reactor.

RT riser-reactor temperature, K.

mf U minimum fluidization velocity, m/s.

aU superficial inlet air velocity, m/s.

ieoU incipient velocity into the emulsion-phase,

m/s.br U rise velocity of a single bubble, m/s.

bU bubble velocity, m/s.

ijV stoichiometric ratio of component i to

component j used in eqs (71)-(77).

GV volume of the regenerator, m3.

ie ymass fractions of gases in the emulsion-

phase.

ib ymass fractions of gases in the bubble-phase.

S ymass fraction of spent catalyst.

R y mass fraction of regenerated catalyst.

ieo yinitial mass fraction of the respective gases

in the emulsion-phase.

2O ymole fraction of oxygen used in eq. (44).

CO ymole fraction of carbon monoxide used in

eq. (45).

2CO y mole fraction of carbon dioxide used in eq.(46).

i ymass fraction of component i

Z dimensionless height of riser-reactor.

Greek Letters intrinsic ratio of carbon dioxide to carbon

monoxide defined after eq. (43).

ext catalyst-specific external surface area used

in eq. (14), m-1

a dimensionless parameter defined in eq.(69).

R average void fraction in the riser-reactor

E void fraction in the emulsion-phase.

B void fraction in the bubble-phase.

mf voidage at minimum fluidization.

o mass density of gas-oil, kg/m3

i mass density of lump ,i kg/m3

T total mass density of all lumps defined aftereq. (6), kg/m3

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S mass density of spent catalyst, kg/m3.

R mass density of regenerated catalyst, kg/m3.

cat mass density of catalyst, kg/m3.

ib

mass densities of gases in the bubble-phase,kg/m3.

ie mass densities of gases in the emulsion-

phase, kg/m3.

ieo mass densities of flue gases at the inlet of

the emulsion-phase, kg/m3.

ie mass densities of flue gases at the outlet of

the emulsion-phase, kg/m3.

2O mass density of gas (oxygen) in the

emulsion-phase, kg/m3.

TG total mass density of gases in the

regenerator, kg/m3.

Go mass density of gas mixture used in eq. (62),

kg/m3

S volumetric flow rate of spent catalyst, m3/s.

R volumetric flow rate of regenerated catalyst,m3/s.

ieo volumetric flow rates of flue gases at the

inlet of the emulsion-phase, m3/s.

ie volumetric flow rates of flue gases at theoutlet of the emulsion-phase, m3/s.

o volumetric flowrate of gas-oil used in eq.(27), m3/s

ie ΔH heat of reaction of flue gases in the

emulsion-phase, kJ/kmol.

C ΔH heat of reaction for coke combustion,

kJ/kmol.

ij H heat of reaction for cracking lump i to , j

kJ/kmol specific area for heat transfer between the

bubble and emulsionphases, m2/m3.

catalyst deactivation function.

R dimensionless temperature of riser-reactor

ss effectiveness factor dimensionless time.

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the Fluidized Bed Catalytic Cracking Plant,Transaction of the Society of Computer Simulation, 1985, 2, 3, 219-236.

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Reaction Kinetics on the Model Predictionsof an Industrial Fluid Catalytic CrackingUnit, Chemical EngineeringCommunications, 1996, 149: 163-184.

[4] H. Ali, S. Rohani, J. P. Corriou, Modelingand Control of a Riser Type Fluid CatalyticCracking (FCC) Unit, Transactions of the

Institution of Chemical Engineers, 1997, 75 ,

401 – 412. [5] I. S. Han, C.B. Chung, Dynamic Modeling

and Simulation of a Fluidized CatalyticCracking Process. Part 1: Process Modeling,Chemical Engineering Science, 2001, 56,

1951 – 1971.[6] D. Krishnaiah, V. Gopikrishna, B. Awang,

S. Rosalam, “Steady State Simulation of aFluid Catalytic Cracking Unit , Journal of

Applied Science, 2007, 7, 15, 2137-2145. [7] L. S. Lee, V. W. Chen, T. N. Huang, Four-

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