Effect of feed atomization on FCC performance:

simulation of entire unit

Ajay Gupta1, D. Subba Rao*
Department of Chemical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

Received 11 June 2002; received in revised form 1 July 2003

Abstract

Entire 4uid catalytic cracking (FCC) unit, comprising of a riser and a regenerator, is simulated by integrating FCC riser model presented
in our earlier work (Chem. Eng. Sci. 56 (2001) 4489) with an FCC regenerator model. The effect of feed atomization (quantified by
average drop size generated by the feed nozzle) on the performance of the unit is evaluated.

Keywords: Fluid catalytic cracking; Atomization; Riser; Regenerator; Selectivity; Simulation

1. Introduction and coke balance between the riser and the regenerator is
maintained by adjusting the catalyst circulation rate between
Fluid catalytic cracking (FCC) unit is a major system in the two. Models of riser and regenerator need to be integrated
a petroleum re8nery. It converts vacuum gas oil (VGO) to to simulate the performance of entire FCC unit.
useful products like LPG, gasoline and cycle oils by catalytic
cracking. Schematic of an FCC unit is shown in Fig. 1. 1.1. Models on riser performance
The unit primarily comprises of two reactors, a riser and
a regenerator. VGO is dispersed into the riser bottom in FCC riser is a complex system to model because of in-
the form of drops through a feed nozzle system. The VGO tricately interrelated hydrodynamics, heat transfer, mass
drops contact hot regenerated catalyst particles entering from transfer and catalytic cracking kinetics. The parameters
the regenerator and get vaporized. The vapor entrains the in4uencing these aspects also change all along the riser
catalyst particles and liquid drops while getting cracked on height:
the catalyst surface along the riser height. In the process the
catalyst progressively gets deactivated due to deposition of • The feed is injected into the riser along with hot catalyst
coke (formed during cracking reactions) on its surface. The particles from the regenerator. The feed vaporizes and
deactivated catalyst leaving the riser top is transferred to the entrains catalyst as well as liquid drops along the riser
regenerator where its activity is restored by burning the coke.
height.
Performance of the riser and regenerator are closely linked.
• Gas velocity increases due to vaporization of liquid feed.
Combustion of the coke on catalyst particles, produced in
• Gas velocity also increases due to molar expansion re-
the riser by cracking reactions, in the regenerator generates
sulting from cracking of VGO to lower molecular weight
the heat needed in the riser for VGO feed vaporization and
products.
endothermic heat of cracking reactions. The intricate heat
• Gas velocity in4uences the axial (and radial) pro8le of
catalyst volume fraction.
• There is considerable slip between gas and catalyst
particles.
• Hydrocarbon vapor gets cracked at the surface of catalyst
particles to produce lighter hydrocarbons as well as coke.
Reactant and product hydrocarbons diffuse to and away
4568 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579

Cracked Products

Flue Gas

FEED NOZZLE

M,,,T1Nl

FEED + STEAM

Fig. 1. Schematic diagram of FCC unit.

from catalyst surface while coke deposits on the catalyst Corella and Frances (1991) considered the riser to con-
surface to progressively deactivate the catalyst. sist of 3-4 well-mixed compartments and used a 8ve lump
• Catalyst temperature falls due to heat transfer for raising kinetic model. Variation of important variables such as slip
sensible heat of feed, its vaporization and endothermic factor, molar expansion factor, temperature dependent ki-
heat of cracking reactions. netics and catalyst deactivation factor from compartment
to compartment were considered while they were assumed
Several FCC riser models with varying degree of sim- to be constant within each compartment. Fligner, Schipper,
pli8cations and assumptions are available in the literature. Sapre, and Krambeck (1994) proposed a cluster model ap-
Most of the reported FCC riser models assume proach to explain experimentally observed high slip factors.
They assumed riser to consist of two phases—a dispersed
• Instantaneous vaporization of feed and thermal equilib- cluster phase containing all the catalyst and a continuous
rium between catalyst and hydrocarbons. phase containing only gas. Reactions take place in clus-
• Plug 4ow for gas and catalyst. ter phase with consumption of reactants and generation of
• Slip factor, ratio between gas velocity and catalyst veloc- products. The resulting concentration gradients between gas
ity, equal to 1. phase and cluster phase provide the driving force for mass
• Reactor as either isothermal or adiabatic. transfer between the two phases. Theologos and Markatos
• Lumped kinetics. (1993) and Gao, Xu, Lin and Yang (1999) proposed three
• Catalyst activity varying either with time-on-stream dimensional CFD models for FCC riser based on Eulerian
or coke concentration on catalyst with non-selective approach. All these models assumed instantaneous vapor-
deactivation. ization of feed at riser bottom and hence neglected the effect
• Vapor velocity to be either constant along the riser height of rate of feed vaporization on FCC riser performance. The
or increase due to molar expansion based on ideal gas law. performance of FCC unit (quanti8ed in terms of conversion
• Hydrocarbon concentration on catalyst surface to be same and product selectivity) is affected significantly by the rate
as that in the gas i.e. no resistance to mass transfer between of vaporization of feed in the entry zone of the riser. The
hydrocarbon vapor and catalyst surface. feed in liquid phase cannot react to crack. Slow vaporiza-
 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579 4569

tion of feed leads to very high catalyst to vaporized feed 4ow. Both homogeneous as well as catalytic post combus-
ratio coupled with high temperature and catalytic activity tion reaction of CO with O2 to form CO2 were considered in
in the riser entry zone. These factors can lead to undesir- the dense phase. Arbel, Huang, Rinard, Shinnar, and Sapre
able secondary cracking reactions. Faster vaporization rates (1995) also modeled the dense bed region on lines of
can be realized by effective feed atomization into fine drops. Krishna and Parkin's model however they assumed gas
A feed nozzle system which could atomize the liquid feed 4ow as three compartments (each well mixed with in itself)
into very minute drops is therefore of prime importance for in series instead of plug 4ow. Sapre, Leib, and Anderson
achieving higher conversion and better product yield dis- (1990) proposed a CFD model for the FCC regenerator to
tribution. Several re8neries across the world have replaced study the effect of catalyst entry and exit geometries.
older FCC feed injection systems with newer designs and
observed improvement in conversions and yield patterns. 1.3. Simulation of entire FCC unit
Theologos, Nikou, Lygeros, and Markatos (1996, 1997)
extended the CFD model of FCC riser proposed by There are many attempts to simulate entire FCC unit
Theologos and Markatos (1993) to include feed vaporiza- (Arbel et al., 1995; Kumar, Chadha, Gupta, & Sharma, 1995;
tion. The model could predict effect of geometrical place- Ali, Rohani, & Corriou, 1997; Malay, Milne, & Rohani,
ment of feed nozzles on the riser performance. In their later 1999; Arandes, Azkoiti, Bilbao, & de Lasa, 2000; Han &
work Theologos, Lygeros, and Markatos (1999) accounted Chung, 2001 a,b). These simulations were based on the as-
for the effect of feed atomization (quantified by average ini- sumption of instantaneous vaporization of feed at riser en-
tial drop size produced by the feed nozzle) on overall reac- try. In the present work, entire FCC unit is simulated by
tor performance. Gao, Xu, Lin, and Yang (2001) extended integrating the riser model of Gupta and Subbarao (2001)
the two phase gas-solid CFD model proposed by Gao et al. (which considered vaporization of feed drops in the riser)
(1999) to include vaporization of liquid feed in the form of with a regenerator model to study the effect of feed atom-
spray in the entry zone of the FCC riser. Recently Gupta ization on FCC unit performance.
and Subbarao (2001) developed a three phase model for
FCC riser taking into account effect of feed atomization on
conversion and yield patterns achievable in a riser reactor. 2. Modeling approach and assumptions
The model could predict pro8les of overall conversion,
product yields, temperature, axial solid holdup, catalyst ac- 2.1. Riser
tivity besides several other parameters. The model results
compared well with the industrial observations. The riser model presented in our earlier work (Gupta &
Subbarao, 2001) is used. The riser is conceptually con-
sidered to consist of a number of equal sized compart-
1.2. Models on regenerator performance ments along the axis as shown in Fig. 2. In the entry zone
each compartment consists of three phases—solid phase
Most of the earlier regenerator models were based on (catalyst particles), gas phase (atomizing/dispersion steam,
the two phase bubbling bed models (Davidson & Harrison, vaporized feed, products) and liquid phase (drops). The cat-
1963; Kunii & Levenspiel, 1969). These models assumed alyst particles and liquid drops are accelerated upwards due
that most of the gas 4ows as bubbles through the dense to drag exerted by the gas phase. The gas velocity also in-
phase, with dense phase in well mixed state and bubble creases continuously along the riser height because of feed
phase in plug flow. To account for the effect of distributor vaporization as well as decrease in vapor density due to for-
design on the performance of regenerator, Behie and Kehoe mation of lower molecular weight products on cracking of
(1973) and Errazu, de Lasa, and Sarti (1979) developed a VGO. Catalyst particles are assumed to move as clusters to
Grid Model by considering the regenerator bed to consist account for the observed high slip velocities. The size of the
of grid region and bubbling bed region axially. de Lasa, cluster is assumed to be 6 mm (Fligner et al., 1994). The
Errazu, Barreiro, and Solioz (1981) analyzed industrial FCC vapor density is calculated by using ideal gas law. A simple
regenerators using five different models. They concluded that hydrodynamic model is proposed for the axial solid holdup
A CSTR model predicted results within 2% of Grid model and liquid drop holdup considering the local force balance.
predictions. The pure bubble model predictions were found The liquid fraction of feed, which is 1 at the riser en-
to be at large deviation from Grid model. It was also con- trance, decreases progressively along the riser height due to
cluded that one need not consider freeboard in combination vaporization. It is assumed that the liquid drops do not break
with grid models. or coalesce along the riser height and their size changes be-
All the models discussed above did not consider post cause of vaporization only. The liquid phase disappears as
combustion reaction of CO to CO2 and modeled the CO2/CO the feed is completely vaporized leaving only gas phase and
ratio as a function of temperature only. Krishna and Parkin solid phase in subsequent compartments.
(1985) modeled the regenerator dense bed assuming the In the heat transfer model, the riser is assumed to be adia-
catalyst to be well mixed and gas to 4ow through it in plug batic. The heat in the catalyst particles provides for heating
4570 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579

Model equations are formulated for each phase in ith

GAS compartment for each jth lump in terms of material and
SOLIDS
energy balances considering hydrodynamics, heat transfer,
mass transfer and reaction kinetics while accounting for
f, =
1 gas phase properties and catalyst activity. Computations are
performed for each compartment starting from the 8rst
(bottommost) to generate values of variables shown for
LIQUID GAS SOLIDS ith compartment in Fig. 2. The inlet conditions at the riser
bottom are known. Within a compartment, each phase is
t assumed to be well mixed. In general outlet conditions for
(i — 1 )th compartment serve as inlet conditions for ith com-
partment. The solution procedure within a compartment is
iterative. Size of each compartment is considered to be equal
to size of cluster. The 4ow of computations is shown in
•1st; Fig. 3. Salient FCC riser model equations are summarized
in Appendix A.

Km-
2.2. Regenerator

T T i-l
Spent catalyst from the riser outlet, after steam stripping,
enters the regenerator and is 4uidized by air entering through
a distributor. Most of the modern regenerators operate in
turbulent 4uidization regime with a dense region at the bot-
tom containing most of the catalyst inventory and a dilute
region on top.
T The oxygen in air reacts with coke on catalyst to form
carbon monoxide and carbon dioxide. Carbon monoxide fur-
^l.T^ M st ,T gill ,p W,Ts i n ) P p ther reacts with oxygen to form carbon dioxide. Catalytic
gin
d
d0 > as well as homogeneous oxidation of carbon monoxide is
considered. Most of these combustion reactions take place
Fig. 2. Conceptual riser model.
in the bottom dense region of the regenerator. The dense
region of the regenerator is modeled on the lines of Arbel
et al. (1995). In the dilute region, the catalyst inventory
of liquid, its vaporization, heating of vapor and endothermic and oxygen concentration is very low and it is assumed that
heat of reaction. The heat transfer and vaporization of feed coke combustion is essentially complete in the dense region.
droplets in the riser is modeled on the lines of Buchanan The heat generated due to combustion of coke and oxida-
(1994). The heat transfer is assumed to be predominantly tion of CO is used to raise sensible heat of catalyst and gas.
convective. For heat transfer between 4uidized bed and liq- Heat losses from the regenerator to the surroundings are
uid drops heat transfer coeNcients are corrected for enhance- considered.
ment due to presence of solids as well as reduction due to The conceptual model of regenerator dense bed is shown
vapors emanating from the surface of a droplet. in Fig. 4. The regenerator dense region is considered to con-
The vaporized VGO diffuses to solid phase and gets sist of two phases—gas phase (N2, O2, CO, CO2 and H2O)
cracked at the catalyst surface. While gaseous products dif- and cluster phase (catalyst particles). The gas phase keeps
fuse back to gas phase, the coke produced gets deposited clusters in a 4uidized state. The bed voidage is estimated
on the catalyst surface. A four lump model for kinetics using King's (1989) correlation. It is assumed that molar
of cracking reactions is used. The four lumps considered 4ow rate of gas does not change due to combustion reac-
are feed, gasoline, gases and coke. The primary crack- tions. This assumption is justi8ed due to presence of large
ing of gas-oil is assumed to follow second order kinetics quantity of inert N2.
whereas secondary cracking of gasoline is assumed to fol- The cluster phase is assumed to be well mixed. The gas
low 8rst order kinetics. The catalyst deactivation model phase is conceptualized as 8ve equal sized well-mixed com-
is based on coke deposited on the catalyst. The kinetic partments in series, which approximate to plug 4ow. The
model used in the present model can be easily substi- gas phase and the cluster phase are assumed to be in thermal
tuted by a more complex kinetic model with more number equilibrium. It is also assumed that there is no resistance
of lumps (corresponding to industrial FCC products) in to mass transfer of gaseous components between gas phase
future work. and cluster phase.
 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579 4571

Perform material
balance to compute

From hydrodynamic
model compute
8cj)8gj and 5^
ij); = fyf F.Err
Compute

Perform enthalpy
balance to recompute
fi,,T gi andT si

Fig. 3. Computation 4ow diagram of FCC riser model.

The inlet conditions for the 8rst gas phase compart- 3. Simulation of entire FCC unit
ment are known. For subsequent gas phase compartments
the inlet conditions are same as the outlet conditions of The riser' and the regenerator of FCC unit are highly
compartment below. The values of coke on regenerated coupled. The interaction between the two and the connect-
catalyst (CRC) and regenerator temperature (Trg) are uni- ing variables are shown in Fig. 6. The catalyst enters the
form everywhere in the regenerator and an initial guess riser from the regenerator at temperature Trg (regenerator
is provided. The material balance equations are solved dense bed temperature), coke concentration CRC (coke on
for each gas phase compartment considering regeneration regenerated catalyst) and at a circulation rate of W. CRC de-
kinetics and hydrodynamics. Overall material balance clo- termines the initial activity of the catalyst entering the riser.
sure and energy balance equations are solved to calculate Along the riser height, the catalyst temperature decreases
new values of CRC and Trg. The solution procedure is while coke on catalyst increases. The deactivated/spent cat-
iterative. The 4ow of computations is shown in Fig. 5. alyst leaves the riser outlet, at temperature Trxo and coke on
Salient FCC regenerator model equations are summarized in spent catalyst CSC, and enters the regenerator at a circula-
Appendix B. tion rate W. At a given steady state the entire heat generated
4572 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579

Cracked products
GAS SOLIDS Flue Gas W, 1 CSC
I
W, T m ,C [ l p

1-B

y, j= O,,CO,CO 2 ,H 2 O
Regenerator Riser

TIg, CRC

FA, Y O ^ O . H J T ^ 1 e

Air Feed
Fig. 4. Conceptual regenerator model. F A ,T ain W,T tg ,CRC Q.<W

Independent variables to riser model: Q,d,

Independent variables to regenerator model: FA.-
Variable adjusted to achieve heat and coke balance : W
Dependent variables : (o ,CSC,T ra ,CRC

Fig. 6. Riser regenerator connectivity.

Input

Guess T_ and C__

in the regenerator shall be consumed in the riser. Similarly

the entire coke generated in the riser shall be consumed
in the regenerator. These two conditions are achieved by
adjusting catalyst circulation rate W. Other associated vari-
ables Trg, CRC, Trxo and CSC settle to steady state values
accordingly.
The feed rate Q, feed inlet temperature T\m and drop size
ddo are independent inputs to the riser model whereas air
4ow rate FA and air inlet temperature T^m are independent
inputs to the regenerator model.
For simulating entire FCC a steady state base case
(assuming 50 urn drop) with exact heat balance and coke
balance between riser and regenerator was established.
Thereafter parametric study on effect of feed atomization
(quanti8ed by average drop size produced by the feed noz-
zle) on performance of entire FCC unit was carried out.
The objective was to evaluate product yields, regenera-
tor temperature Trg, Catalyst circulation rate W and CSC
on varying the drop size dd while maintaining a constant
coke yield at riser outlet and constant CRC (at base case
levels).
The riser and regenerator models were simulated itera-
tively to attain the above objective. The procedure for simu-
Fig. 5. Computation 4ow diagram for regenerator model. lation is summarized in Fig. 7. On simulating the riser for a
 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579 4573

Change base case inputs to riser model Table 1

new drop size Industrial FCC riser data reported by Ali et al. (1997)
and guess value of TIC
Variable Value

Riser I.D. 0:8 m

Adjust W till you get coke make
at base case level Catalyst 4ow rate 144 kg=s
Regenerator dense bed temperature 960 K
Riser pressure 2:9 atm
Input Riser outlet temperature 795 K
new W, corresponding CSC and Tftl
to the regenerator simulator Riser height 33 m
Feed 4ow rate 20 kg=s
Feed inlet temperature 494 K
Air to regenerator 16 kg=s
Adjust air until you get CRC
at base case level and get T

the regenerator. This increases regenerator bed temperature

(Fig. 8b). The trend is in line with observations in FCC units
8tted with improved nozzle systems where drop in regener-
ator temperature is observed. Kako (1991) reported a drop
of 15°C in the regenerator temperature on replacing the old
feed injection system with a new one. In our studies, since
coke yield is 8xed at the base case, CSC corresponding
to lower catalyst circulation rate (for bigger drop size) in-
creases as shown in Fig. 8c. On the riser side it is predicted
that with increase in feed drop size the conversion, gasoline
Fig. 7. Flow sequence for simulation of entire FCC unit.
yield and gas yield exhibit a falling trend (Fig. 8d-f). Re-
garding behavior of gas yield versus feed drop size it shall
be noted that the gas lump considered in the kinetic model
comprise of dry gas (C1-C2) + LPG (C3-C4). In industry
feed drop size bigger than that of base case, keeping all the generally dry gas yield decreases with improved feed atom-
other variables unchanged, higher coke yield at the riser out- ization, while LPG increases. Combined gas yield (C1-C4)
let was predicted. To bring the predicted coke yield to base increases with improved feed atomization. The model pre-
case level, catalyst circulation rate W was adjusted. The ad- dictions are in line with the observations in industry. Table
justed W and coke on spent catalyst (CSC), calculated for 2 presents the improvements in FCC unit performance re-
base case coke yield, were given as inputs to the regenerator ported by Goelzer (1986) and Bienstock, Draemel, Shaw,
model. The regenerator was then simulated while adjusting and Terry (1991), on replacing old feed nozzle systems with
air 4ow rate to obtain CRC same as the base case (assumed new improved ones. The delta changes reported are at a 8xed
to be 0.1%). The new Trg and W were fed back to riser coke make.
model and predicted coke yield observed. The above proce-
dure was repeated till we got coke make in the riser at the
base case level.
5. Conclusions

4. Results and discussions Entire FCC unit comprising of a riser and a regenerator
has been simulated. Effect of feed atomization (quantified by
Data on FCC unit reported by Ali et al. (1997), pre- initial drop size produced by the feed nozzle) on the perfor-
sented in Table 1, were used for simulations assuming mance of the unit at a constant coke yield, has been studied
an initial drop size of 50 urn as the base case. Properties through simulations. It is observed that catalyst circulation
and kinetic constants used for simulations are provided in rate has to be adjusted to lower levels for bigger drop size to
Appendix C. achieve heat and coke balance between the riser and the re-
After establishing the base case, simulations for the entire generator. Predicted values of overall conversion, gasoline
unit were carried out for bigger drop sizes up to 500 urn. yield and gas (C1-C4) yield increase with decreasing drop
Results normalized with respect to the corresponding base size. On the regenerator side, lower regenerator tempera-
case values are shown in Fig. 8a. It is predicted that for a tures are predicted for smaller drop sizes. The predictions
bigger drop size, catalyst circulation rate has to be decreased are in line with the improvements reported in industry on
(Fig. 8a) to achieve base case level coke yield. Lower cata- replacing a multi-pipe feed nozzle (poor atomization) with
lyst circulation rate amounts to lower heat withdrawal from an improved spray feed nozzle.
4574 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579

50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550
(a) Drop size (microns) (b) Drop size (microns)

1.14

/
1.12

1.1

/
S 1-08

1 /

8 1.06
J /

1.04
/

1.02

1
50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550
(c) Drop size (microns) (d) Drop size (microns)

\
\
\
\
\
\

\
\
£ 0.92 \
o \ \

JS \
\
!ai 0.9 \
c \ •

"5 \
\

\ \

50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550
(e) Drop size (microns) (f) Drop size (microns)

Fig. 8. (a) Effect of feed atomization of catalyst circulation rate; (b) effect of feed atomization on regenerator temperature; (c) effect of feed atomization
of carbon on spent catalyst; (d) effect of feed atomization on conversion; (e) effect of feed atomization on gasoline yield; (f) effect of feed atomization
on gas yield.
 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579 4575

Table 2 rj rate of production of component j: in riser,

Improvements in FCC unit performance on replacing old feed nozzle with kg=s m3 cat; in regenerator, kmol=s m3
new atomizing feed nozzle R gas constant, kcal=kmol K
Product yields/conversion Delta change on replacing feed nozzle R! gas constant, atm m3=kmol K
Goelzer (1986) Bienstock et al. (1991)
S slip factor
t time, s
Dry gas, C1-C2 (wt%) -0.90 -0.10
TAin air temperature at regenerator inlet, K
LPG, C3-C4 +6 : 60 vol% + 1:3 wt%
Gasoline (vol%) +5.1 +4.2 Te equilibrium temperature of gas and solid after
Cycle oil (vol%) -5.2 -3.3 complete vaporization, K
Bottoms (vol%) -3.3 -1 Tg temperature of gas, K
Coke 0 0 T\m liquid feed temperature at riser inlet, K
Overall conversion (vol%) +8.5 +4.4
Tls liquid boiling temperature, K
Ts temperature of solids (catalyst), K
Notation Tsin temperature of solids at riser inlet (=Trg), K
Trg regenerator dense bed temperature, K
heat transfer area between gas-liquid, m2 Trxo temperature of catalyst at riser outlet, K
heat transfer area between gas-solid, m2 u gas super8cial velocity, m/s
A cross sectional area of riser, m2 uc cluster velocity, m/s
cc coke concentration on catalyst, wt:=wt: cat ud drop velocity, m/s
coke on spent catalyst (CSC), wt:=wt: cat ug gas actual velocity, m/s
coke on regenerated catalyst (CRC), wt:=wt: cat Vc volume of cluster, m 3
speci8c heat of air, kJ=kg K Vp volume of particle, m 3
speci8c heat of gas W mass 4ow rate of solids, kg/s
cPs yj mole fraction of component j (regenerator), j =
phase, kJ=kg K
speci8c heat of component j in gas phase, O2;CO;CO2;H2O
cPsi ycj mass fraction of component j in cluster phase
kJ=kgK
CT. speci8c heat of vaporized feed (riser), j = 1 ; 2 ; 3 ; 4 ( V G O , gasoline, gas, coke)
ygj mass fraction of component j in gas phase
Cpl speci8c heat of liquid feed, kJ=kg K (riser), j = 1 ; 2 ; 3 ; 4 ( V G O , gasoline, gas, coke)
CP, speci8c heat of solid, kJ=kg K yld j yield of component j, wt% of feed
Cd drag coeNcient, z axial height, m
cluster diameter, m Zd total dense bed height, m
dd drop diameter, m Az height of compartment, m
dp particle diameter, m Greek letters
Ej activation energy for jth reaction, kcal/kmol bc cluster holdup fraction
fl liquid mass fraction of feed bg gas holdup fraction
FA 4ow rate of air to regenerator, kmol/s (l liquid holdup fraction
g gravitational acceleration, m=s2 s voidage
hl gas-liquid convective heat transfer coeNcient, sc cluster phase voidage
kW=m2 K 4> catalyst activity factor
hs gas-solid convective heat transfer coeNcient, X latent heat of vaporization, kJ/kg
kW=m2 K pc cluster density, kg=m 3
Hf heat of formation, kJ/kmol pg gas phase density, kg=m 3
Hr heat of reaction, kJ/kg Pgo V G O vapor density, kg=m 3
heat generated in regenerator, kJ/s pi liquid density, kg=m 3
mass transfer coeNcient of component j, 1/s pp particle density, kg=m 3
Krj reaction kinetic constant for jth Hg gas phase viscosity, kg=m s
reaction, mr3=mcat3 s
Mst mass 4ow rate of steam, kg/s
MWa molecular weight of air, g/mol Appendix A. Riser equations
MWc molecular weight of coke, g/mol
A.1. Liquid phase material balance
MWj molecular weight of component j, g/mol
P pressure, atm Mass in from (i — 1 )th compartment—Mass out from ith
qgl heat transfer from gas to liquid phase, kW compartment = Mass vaporized in the ith compartment:
qsg heat transfer from solid to gas phase, kW
Q mass 4owrate of hydrocarbon feed, kg/s
4576 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579

A.2. Gas phase material balance Liquid phase

Heat transferred from gas to liquid phase = Latent heat
For VGO Mass vaporized in ith compartment + Mass in for vaporization:
from (i — 1 )th compartment — Mass out from ith compart-
ment = Mass transfer to cluster phase:
li) + (Q(1 - //,_,) +M A.6. Energy balance after complete vaporization
fli) + Mst)ygj;i = mji: (A.2)
Sensible heat lost by catalyst and gas mixture = Endother-
For gasoline and gas mic heat of reaction:
Mass in from (i — 1 )th compartment — Mass out from ith (WCps + (Q + Mst)Cpgi )(Tei - Tei_,) = Hri: (A.11)
compartment = Mass transfer to cluster phase:
(Q(1 - f - fli)+Mst)ygj;i A. 7. Heat transfer rates
=mji (A.3) Solid to gas heat transfer rate

3. Cluster phase material balance qsgi =hsiapi(Tsi -Tgi). (A.12)

Gas to liquid heat transfer rate
For VGO, gasoline and gas
qgli = hliali(Tgi - Tls): (A.13)
Mass transferred from gas phase = Mass consumed in
cluster phase:
A.8. Solid to gas heat transfer coefficient
mji = (-rjj)VPl. (A.4)

For coke Nu = 2 + 0:60Re1=2Pr1=3: (A.14)

Mass out of ith compartment — Mass in from (i — 1 )th
compartment = Mass produced: A. 9. Gas to liquid heat transfer coefficient
(Q(1 " fl i ) +Mst)ycJj - (Q(1 - /,,_,) +Mst)ycj;i
=rj;iVpi: (A.5) Nu =
[1:0 + CPg(Tg-Tls)/l]01
A.4. Energy balance for sensible heat transfer in the first Buchanan (1994): (A.15)
compartment
A.10. Mass transfer rates
Sensible heat lost by solids = Sensible heat gained by
liquid:
(A.16)
WCPs(Tsm -TS1) = QCpl(Tls - Tlin); (A.6)
QCpl(Tls - Tlin) A.11. Mass transfer coefficients
T
1
— T• — (A.7)
s = T sin WCp
Sh = 2 + 0:60Re1=2 Sc1= (A.17)
A. 5. Energy balance in ith compartment before complete
vaporization A. 12. Reaction kinetics

Solid phase
VGO -• Gasoline + Gas + Coke; (A.18)
Sensible heat lost by solids = Heat transferred from solid
phase to gas phase + Endothermic heat of reaction:
Gasoline —> Gas + Coke: (A.19)
WCpfT^ - TSi) = qsgi + Hri: (A.8) Reaction rate
Gas phase C n

Heat transferred from solid phase to gas phase = Change

in sensible heat of gas + Heat transferred from gas to liquid W
phase: (Pachovsky & Wojciechowski, 1971); (A.20)

sgi = (Q(1 " A _ i ) +Mst)Cpgi(Tgi - Tg,_,) where, Cj is concentration of component j, Cjo is initial
concentration of pure component j, n=1 for VGO cracking,
, ~ fli)Cphv(Tgi - Tls) + qgli (A.9) n = 0 for gasoline cracking.
 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579 4577

A. 13. Kinetic constants B.2. Overall material balance closure

Number of moles of coke consumed = Number of moles

(A.21) of CO + CO2 produced:
W(cco-cc)
= FA(y CO+ yCO2): (B.2)
MWc
A. 14. Catalyst activity
B.3. Energy balance
B+1
A (A.22)
B + exp(Acci) Heat generated in regenerator=Heat of formation of
(CO + CO2 + H 2 O):
Assuming ideal gas behavior, Hreg = Fa(yCOHfCO + yCO2HfCO2 + yH2OHfH2O): (B.3)
Heat generated in regenerator = Gain in sensible heat of
A. 15. Gas phase density air 4owing through+Gain in sensible heat of catalyst 4owing
through + Heat Loss:
P
P:(A.23) Hreg = FAMWa Cpa(Trg - TAin)

+ WCPs(TTg-TTXo)+HL. (B.4)
A. 16. Gas phase specific heat Regenerator temperature
T = Hreg -HL+FA MWa Cpa TAin + WCps Trxo
rg :
(A.24) FA MWa Cpa + WCps
2.^1
B.4. Dense bed voidage
A.17. Drop size
u
+1 (King; 1989): (B.6)
=3 M+2
ddi = (fli)1 dd0: (A.25)
B.5. Combustion kinetics
A. 18. Momentum balance
Intrinsic combustion of coke can be represented by
Clusters
Net force on cluster=Drag force on cluster—Gravitational
force:
du c 1 2 (B.7)
m c — = QAdjPgiug -uc) )- mcg: (A.26)
Rate of consumption of coke
Liquid drops PpCc
Net force on liquid drop=Drag force on liquid drop- -rc=KcPyo2MCc=KcPyO2 (B.8)
MWC
Gravitational force:
(B.9)
dW^ /I ON
C
dutd = dAd {jPg(Ug - udy) - mdg: (A.27)
Besides intrinsic combustion of coke there is catalytic and
homogeneous oxidation of CO:

Appendix B. Regenerator equations

The kinetic rate expression for catalytic oxidation is
B.1. Gas phase material balance for ith compartment -r3c=K3P2ycoyOl. (B.11)
The kinetic rate expression for homogeneous oxidation is
Moles in from (i — 1)th compartment—Moles out from
ith compartment =Moles consumed in ith compartment: -r3k =K3hP2yCOyO2: (B.12)
Kinetic constants
E
= O 2; CO ; CO 2; H 2 O : (B.1) Kj=KJexp\- j (B.13)
4578 A. Gupta, D. Subba Rao / Chemical Engineering Science 58 (2003) 4567-4579

Table 3 Table 7
Properties of hydrocarbon feed/products at operating conditions Activation energy for cracking reactions

Property Value Cracking reaction Activation energy Ej

(kcal=kmol)
Sp. ht. of liquid VGO 3:56 kJ=kg K
Sp. ht. of gas, gasoline and vapor VGO 3:0-3:5 kJ=kg K VGO -> Gasoline 16 328
Latent heat of feed vaporization 96 kJ=kg VGO -> Gas 21344
Vaporization temperature 700 K VGO -> Coke 15 449
Liquid VGO density 650 kg=m3 Gasoline —» Gas 12612
Gas phase viscosity 1:3 x 10~ 5 kg=m s Gasoline —> Coke 27 621
Gas phase conductivity 3:15 x 10~ 5 kW=m K
Diffusivity 1.0 x 10~ 5 m2=s
Heat of reaction 525 kJ=kg of VGO cracked
Table 8
Deactivation constants
Table 4
Catalyst properties Deactivation parameter Value

Property Value A 4.29

B 10.24
Particle density 1200 kg=m3
Average particle diameter 75 urn
Coke on regenerated catalyst 0:1 wt%

CO2=CO ratio :
Table 5
Molecular weights of components in riser

Lump Molecular wt.

VGO
The heats of formation (kJ=kg mol) of CO, CO2 and H2O
382
Gasoline 120 at temperature T(K) are
Gas 45
Steam 18
HfCO = -111120 : 3 + 11:54T - 0:334 x 10~ 3 r 2

7:82 x 105
;
Table 6 T
Kinetic constants
HfCO2 = -401490.7 + 48:24T - 2:0 x 10~ 3 r 2
Kinetic constant Value (I=mcat3: s) at 756 K
0:334 x 105
68.30 ;
17.15 T
2.32
Kr4 0.20
HfH2O = -243046.1 + 3:26T + 3:51 x 10~ 3 r 2
0.55
0:50 x 105
+ :
T
Appendix C. Numerical values of properties/parameters
used for simulation
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