IEEES2
Proceedings of the Second International Exergy, Energy and Environment Symposium
3-7 July 2005, Kos, Greece
Paper No.162
DYNAMIC SIMULATION AND OPTIMIZATION OF THE FLUID CATALYTIC CRACKING
PROCESS. APPLICATION TO THE PILOT PLANT OF CPERI.
G.M. Bollas(1), S.A. Papadopoulou(2), A.A. Lappas(3), S.S. Voutetakis(4), I.A. Vasalos(5)
(1,5)
Department of Chemical Engineering, Aristotle University of Thessaloniki, P.O. Box 361, GR 57001,
Thessaloniki, Greece.
(2) Automation Department, Technological Educational Institute of Thessaloniki, P.O. Box 14561, GR 54101,
Thessaloniki, Greece
(3,4) Chemical Process Engineering Research Institute, Centre for Research and Technology Hellas, P.O. Box 361,
GR 57001, Thessaloniki, Greece.
(1)gbollas@cperi.certh.gr, (2)shmira@teithe.gr, (3)angel@cperi.certh.gr, (4)paris@cperi.certh.gr, (5)vasalos@certh.gr
ABSTRACT
The dynamic simulation of the Fluid Catalytic Cracking
(FCC) process is a challenging research subject of high
economic and environmental importance. Optimization of
this complex process demands the development of
accurate models able to describe the process in detail.
FCC technology is consecutively evolving during the last
half century, though the steadiness in the operation of
industrial FCC units restricts the potentiality of obtaining
accurate models through experimentation. Thus, FCC
pilot plants are often used for the simulation of the
commercial units under different operating conditions,
feed properties and catalyst activity and selectivity. The
operation of a pilot unit provides the ability to examine the
process under steady feed and/or catalyst properties, in
order to isolate their respective effects and develop
correlations for each subset of process variables. In this
paper a dynamic simulator of the FCC pilot plant of
Chemical Process Engineering Research Institute
(CPERI) is presented. The simulator was developed and
verified on the basis of steady-state and dynamic
experiments, performed in the pilot unit of CPERI. The
simulation results revealed the ability of the simulator to
predict accurately the operation of the FCC unit, as well
as the potential of optimizing the process operation. The
dynamic simulator can serve as a tool for process
optimization studies and as the basis for the development
of a model based control structure for the pilot plant.
INTRODUCTION
The research interest in dynamic simulation of the fluid
catalytic cracking process has been consecutively
increasing during the last years. Lee and Groves [1]
proposed a dynamic model which treats the riser as a
pseudo-steady state adiabatic plug flow reactor and the
regenerator as a continuous stirred tank reactor with no
dilute phase. Elnashaie et al. [2] developed a dynamic
model for an industrial type IV FCC unit and investigated
the sensitivity and stability of the system. They used twophase models for both the reactor and the regenerator
and included unsteady state dynamic terms for the
thermal behavior and for the carbon mass balance
throughout the entire unit. Lopez-Isunza [3] presented a
dynamic model for mass and energy balance, but their
model neglects the hydrodynamic aspects of the FCC
unit. McFarlane et al. [4] presented a comprehensive
model for the simulation of a type IV FCC unit, in which
they included the reactor, regenerator, bowers, U-bends,
compressors, furnace, and valves, as to be able to
compute the pressure balance and catalyst circulation
rate of this type of FCC units. The regenerator model
includes a dilute phase to account post combustion, but
the riser part used oversimplified computations for the
heat balance. Arbel et al. [5] developed a model that can
describe both the steady-state and dynamic behavior of
an FCC unit. Their riser model was based on the widely
known 10-lump model [6], assuming pseudo-steady state
conditions, while the regenerator model included a
complete description of both full and partial combustion
kinetics. They extensively studied the steady state
multiplicities of an FCC unit and the effect of combustion
mode on the controllability of the unit. Ali and Rohani [7]
presented a dynamic model that consists of a lumped
model for the riser and a two-phase model for the
regenerator with no freeboard region. In-Su Han et al. [8]
presented a detailed dynamic simulator of the FCC
process, in which they included the simulation of catalyst
lift lines, stripper, feed preheater and cyclones. They
applied a distributed parameter 4-lump model for the riser
reactor and a two-regime, two-phase model for the
regenerator.
In this paper a dynamic simulator, developed and
verified on the basis of actual experimental data of the
FCC pilot plant of Chemical Process Engineering
Research Institute (CPERI), is presented. The dynamic
behavior of the simulator was validated against dynamic
experiments, performed in the pilot plant. The term
“dynamic experiments” is used to express experiments,
in which a step change is imposed to a manipulated
process variable, while recording the transient of a
number of process variables from the current steady
state to the new steady state the system will eventually
reach. The development of the dynamic simulator of the
pilot plant serves two main goals: a) the study of the
dynamic behavior of the pilot process that includes
validating the performance of the model against the
steady state results and the dynamic responses of the
unit, identifying the process dependencies and
uncertainties, and performing case studies to examine
the similarities of the pilot plant with commercial units,
and b) the use of the simulator for the development of a
model-based optimizer and control scheme of the entire
unit. This paper deals with the first of the aforementioned
goals and examines the ability of the simulator to provide
an accurate representation of the unit qualitatively and
quantitatively, as well as the ability of the pilot plant to
simulate the main dynamic characteristics of a typical
commercial FCC process.
EXPERIMENTAL SETUP
The FCC pilot plant of CPERI (Fig.1) operates in a fully
circulating mode and consists of a riser reactor, a fluid
bed regenerator, a stripper and lift lines. In the riser the
cracking reactions take place and at the riser exit the
mixture enters the stripper vessel for the separation
(stripping) of gas from catalyst. The reaction product,
from the stripper exit, flows through a heat exchanger for
the condensation of heavier compounds. Thereupon, the
mixture is led to a stabilizer column for better separation
of the liquid and gaseous products. The mixture of
gasoline, light cycle oil (LCO) and heavy cycle oil (HCO)
is obtained through the bottom of the stabilizer. The yield
to liquid products is measured with the ASTM D-2887
simulated distillation method. The fluid bed regenerator is
used to burn-off the carbon, deposited on the catalyst
surface. Two wet test meters and two gas
chromatographers determine the volumetric flow rates
and the composition of the flue and cracked gas,
respectively. An on-line oxygen analyzer always monitors
the excess of oxygen to obtain good catalyst
regeneration. The properties of the feedstock used are
measured according to ASTM standards.
Fig.1. Schematic diagram of the FCC pilot plant of CPERI.
MODEL DESCRIPTION
The simulator includes two main sections: A steady-state
model of the riser reactor and a dynamic model of the
regenerator of the unit. The riser residence times are
much shorter compared to the response times of the
regenerator, hence one can at any instance describe the
riser reactor by a set of steady state relations, which
simplifies the dynamic analysis. Therefore, the behavior
of the regenerator dominates both the dynamic and the
steady state behavior of the system. This is due to the
adiabatic nature of the system in which the need to
balance coke formation and combustion is the overriding
force. The main impact that the riser has on both the
dynamic and steady state behavior of the total system is
on the production of coke and the removal of heat of the
system. Thus, accurate predictions of the pseudo-steady
state conversion, coke yield, heat of cracking and
vaporization are the main concerns for the correct model
integration. The pseudo-steady state and dynamic submodels that constitute the dynamic simulator were
developed in CPERI and presented in the literature [912], and will be briefly discussed in this section.
Simulation of Riser Reactor
The complete model for the steady state simulation of
the FCC riser reactor was assumed to be the product of
the functions describing the influence of operating
conditions, feed properties and catalyst type on the
cracking reactions. The reaction conversion and coke
yield are the only two lumps essential for the riserregenerator models integration, hence a more detailed
lumped model for the prediction of the product
distribution was not included. The general form of the
final correlation for the prediction of the wt% conversion
(x) assumes riser reactor conditions with concurrent plug
flow of gas and solids and second-order rate kinetics for
the total cracking reaction, as presented in eq.(1):
  Ex
x
kx
 C  catalyst  F  feed 
exp 
100  x
WHSV
 RTRX
 nx
 ts

(1)
The same form of correlation was applied for the wt%
catalytic coke yield (ux) for a zeroth order reaction [9], as
presented in eq.(2):
cx  Cc  catalyst  Fc  feed 
  Ec
kc
exp 
WHSV
 RTRX
 nc
 ts

(2)
The parameters (kx, kc, Ex, Ec, nx, nc) in eqs.(1),(2) were
estimated with a dataset of pilot experiments performed
with constant feed and catalyst and at two different
temperatures [9].
For the calculation of the weight hourly space velocity
(WHSV) a hydrodynamic model was developed, in which
the slip between the gas and solids phases was taken
into account and proven to play an important role in small
diameter FCC risers [9]. The proposed model considers
the reactor to be divided in three regions: (a) the mixing
(bottom) region, where the feed evaporates when it
contacts the hot regenerated catalyst; (b) the
intermediate region, where the flow goes from unsteady
to fully developed; and (c) the fully developed flow (top)
region, where the hydrodynamic behavior of the fluid
remains constant with height. The solids space velocity
and the solids residence time were then obtained by
eqs.(3),(4), respectively:
WHSV 
ts 
W Feed
WCat ,bot  WCat ,mid  WCat ,top
3600 W Feed
(3)
(4)
WHSV W Cat
The fully developed flow region of the pilot riser was
simulated under the following assumptions: (a) the flow is
fully developed, thus its hydrodynamic features remain
constant with height; (b) the total volumetric yield of the
reaction is flowing through the whole height of this region;
(c) no particle acceleration is taken into account (it is
considered to be negligible). Hence, eq.(5) holds:
 r ,top 
Qg ,top  p
yr ,top W cat  Qg ,top  p
(5)
In eq.(5) yr,top is the average gas-solids slip factor for the
top section of the riser, used to describe the back-mixing
in the riser. The slip factor represents the ratio of the
catalyst residence time over the gas residence time in the
reactor. The correlation that was applied to the pilot unit
of CPERI for the estimation of the gas-solids slip factor
was the one proposed by Pugsley et al. [13], which
assumes that the “slip phenomenon” is independent of
the gas properties and solids characteristics at gas
velocities much greater than the terminal velocity, but is a
function of the riser diameter, gas volumetric flow and
solids terminal velocity. The complete form of this
correlation is shown in eq.(6), where Frg and Frt are the
Froude numbers for the superficial gas velocity and
solids terminal velocity, respectively:
yr ,top  1 
5.6
 0.47 Frt0.41
,top
Frg2,top
(6)
The voidage of the expanded bottom region, εr,bot, was
related to the superficial gas velocity by means of the
empirical correlation of Richardson and Zaki [14].
Application of this correlation implies a dense-bed
regime, which is a logical assumption, because of the
comparatively large diameter of the bottom region of the
pilot unit and the low superficial gas velocities. The
exponent z in eq.(7) depends on the particle Reynolds
number, and for turbulent flow, it is 2.325.
 r ,bot  z ug ,bot / ut
computational methodology was presented for the
breakdown of an FCC feedstock into pseudocomponents and for the estimation of the properties of
the light and heavy fractions separately. This splitting and
lumping scheme for the total feed fraction was applied to
explore the different extent of contributions to the
catalytic cracking for the heavy and the light fractions.
Fig.2 presents the logical scheme of the proposed
method for the simulation of the effect of feed quality on
conversion the FCC coke yield.
Laboratory measurements
Specific Gravity, Refractive Index, Distillation (ASTM D1160 / TBP)
Carbon, Sulfur, Total Nitrogen Contents, Conradson Carbon Residue
Pseudo-components breakdown
Constant Watson's factor method
Light Fraction Properties
crackable carbon atoms
 NC  NC C A 
(7)
Finally, because of the very small volume of the
intermediate region (15% of the total riser volume), a
simple approximation of averaged (between the top and
bottom regions) hydrodynamic attributes was used.
The regression of eqs.(1),(2) against the pilot data
resulted in catalyst decay constants of -0.75 for the
reaction conversion and -0.88 for the catalytic coke buildup. The cracking reaction activation energy for the pilot
plant of CPERI was calculated at 16000 Btu/lbmol, while
differences in riser temperature do not correspond to
different coke yields, since the activation energy for coke
production is 1600 Btu/lbmol [9].
The second step was to develop accurate functions for
the simulation of the effect of the feedstock properties in
eqs.(1),(2), in order to produce correlations invariable
from the effects of feedstock quality for the prediction of
the reaction conversion and the total coke yield. The
proposed models focus on the needs of the industry,
hence they include bulk properties of an FCC feedstock,
measured with standard analytical procedures accessible
to the average refinery [10]. A large database of
experiments, performed in the FCC pilot plant of CPERI,
with standard catalyst and a large variety of feedstock
qualities was used for the development of what was
called “bulk molecular characterization approach” for the
simulation of FCC feedstocks regarding their relative
(compared to a reference feedstock) potential to enhance
the catalytic cracking (crackability) and the coke
formation (coking tendency). The final models for the
prediction of feedstock crackability and coking tendency
incorporated the specific gravity, the refractive index and
the TBP (or ASTM) distillation of the feedstock, along
with its sulfur, nitrogen and carbon contents. These
properties were combined properly to deliver five
functional groups that accurately characterize the
behavior of FCC feedstocks at cracking conditions, which
involved: the prediction of the catalyst poisoning, the
estimation of the extent of cracking, the estimation of
coke/conversion selectivity, and two coking precursors for
contaminant and residue coke formation. Moreover, a

Operating
Conditions
Function
eq.(1)
Heavy Fraction Properties
nitrogen poisoning
N N 
crackability
coking selectivity
1 k C  
2
A
Operating
Conditions
Function
eq.(2)


A
residue coke
kCCRCCR
Conversion %wt

contaminant coke
k N NT
MWFeed
 NT


exp 

14
 NT  0.437 S 
Coke Yield %wt
Fig.2. Logical scheme of the proposed method for the simulation of the
effect of feed properties on conversion and coke yield.
The proposed functional groups of Fig.2 were
transformed into eqs.(8),(9) for the prediction of the wt%
conversion, non-catalytic and catalytic coke yield:
  Ex 
x
t nx
  w1  NC  NC C A   w2 N N  w3  s
exp 
 (8)
100  x
WHSV
 RTRX 
 NT
2

 
c  kCCRCCR  k N N N exp 
   w4  w5C A  
NT

0.437
S


  Eu 
ts nu
 w1  NC  NC C A   w2  N N   w3  WHSV exp  RT 
 RX 
(9)
Application of the proposed method has shown the ability
of the proposed functional groups to explain the results of
fluid catalytic cracking. The aromaticity and the size of
the average hydrocarbon were shown to dominantly
impact the crackability and the coking tendency, while the
total nitrogen content was proven to be the major catalyst
inhibitor. Finally, the splitting and lumping approach
revealed the strong relation of coke formation with the
heavy components of an FCC feedstock. The catalyst
effect was described with a “catalyst index”. The concept
of describing catalyst activity and selectivity with an index
is a common strategy in industry, in order to validate
catalyst performance in commercial units.
Finally, a pseudo-steady state heat balance of the riser
reactor was performed, which is essential for the
integrated FCC unit heat balancing, since it determines
the catalyst circulation rate in the entire unit. The main
contributors to the overall enthalpy balance in an FCC
plant are: (a) the enthalpy of cracking ΔHcrack, (b) the
enthalpy of vaporization of the gas-oil feedstock, and (c)
the enthalpy content of various process streams (gas-oil,
catalyst, cracked products, inerts). An empirical
correlation was developed to estimate the heat of
cracking in the riser reactor. This correlation was based
on experiments performed at different temperatures, with
various feedstocks and at different conversion levels. The
final correlation estimates the heat of cracking as a
function of conversion, riser temperature and gas-oil
molecular weight, as shown in eq.(10). The enthalpy
content of gas-oil vapors was estimated by using the
empirical correlation of Kesler and Lee [15].
H crack
a T
1 RX
 x 
 ln 

 100  x 
 a2TRX  a3MWFeed    b1TRX  b2TRX  b3MWFeed 
2
(10)
2
Simulation of Regenerator
The structure of the physical model of the regenerator
is shown in Fig.3. The fluidized bed includes two zones:
(a) the dense bed and (b) the freeboard. The dense bed
consists of a bubble and an emulsion phase, while the
freeborad contains the entrained catalyst particles. The
entrained catalyst particles are recycled to the emulsion
phase of the dense zone via cyclones.
the dense phase and the freeboard. The dense bed of
the regenerator was simulated as a pseudo-steady state
PFR (bubble phase) in parallel to a dynamic CSTR
(emulsion phase). The material balance for gas
components in the bubble phase is:
homo
1 dFib
  K Mi  f b  aij K Rjb
A1L1 dl1
j
(11)
The energy balance in the bubble phase is:
homo
1 dQb
  K H  f b   H Rj  K Rjb
A1L1 dl1
j
(12)
In the emulsion phase the material balance equations for
gas and solid components are:
f e e dFie

u ge A1 dt
Fie  Fie,in
A1L1
homo
hete
j
j
(13)
 K Mi  f e e  aij K Rje  f e 1   e   aij K Rje
f e 1   e  dFie

 us  usf  A1 dt
Fie  Fie,in  nc Fif ,out
A1L1
(14)
hete
 f e 1   e   aij K Rje
j
The energy balance equation in the emulsion phase is:
f e 1   e  dQe Qe  Qe,in  Qsf ,out  Qloss


A1L1
us  nusf  A1 dt
(15)
K H  f e e   H Rj  K Rje  f e 1   e    H Rj  K Rje
Fig.3. Structure of physical model of the FCC regenerator.
The assumptions made for the simulation of each
phase shown in Fig.3 are [11, 12]:
 The bubble phase is free of catalyst particles.
 The plug flow regime is used for the bubble phase.
 The emulsion phase components are fully mixed.
 The freeboard is modeled as a plug flow reactor.
 The catalyst particles are hydrodynamically
represented by their average size, density and
porosity. The particle size distribution is used for the
emulsion to freeboard entrainment rate calculation.
 Diffusion in the catalyst particles is neglected.
 Due to the high temperatures, typically occurring in
the FCC regenerator, the ideal gas low is valid.
 The fluidized bed reactor is adiabatic.
The velocity of the gas flowing through the emulsion
phase was considered equal to the minimum bubbling
velocity, which is valid for Geldart type A particles. The
clouds and wakes around the bubbles were assumed to
have zero volume. This assumption is valid for high ratios
of superficial gas velocity over minimum fluidization
velocity (typical for type A particles). The bubbles are
assumed to grow in size with bed height, while the
variation of the fluidizing gas density and superficial
velocity, due to axial temperature gradients and gas
molar rate changes, was also taken into account.
The material and energy balance equations were
formulated separately for gas and solid components in
homo
hete
j
j
The superficial bubble gas velocity for the l1 fraction of
dense bed height is evaluated by differentiating the ideal
gas law in terms of the bubble enthalpy rate term:
dugb
dl1

Rg
dQb
A1PCpg dl1
(16)
The bubble-emulsion mass and heat interchange K Mi ,
K H and the emulsion fraction f e are evaluated by eqs.
(17) - (19), respectively:
1
F
F 1
K Mi   Kti  ib  ie  dl1
 ugb uge  A1
0


(17)
1
K H   H t Tb  Te  dl1
`(18)
0
1
f e   1  fb  dl1
(19)
0
The freeboard is simulated as an ideal two-phase PFR.
The material balances of the gas and solid components
in the freeboard are shown in eqs.(20), (21) respectively:
homo
hete
1 dFif
  f   ij K Rjf  1   f   ij K Rjf
A2 L2 dl2
j
j
(20)
hete
1 dFif
 1   f    ij K Rjf
A2 L2 dl2
j
(21)
conversion and coke yield equations (eqs.(1),(2))
simultaneously, at each solution cycle, as shown in Fig.4.
The energy balance for the freeboard is:
homo
hete
1 dQ f
  f   H Rj  K Rjf  1   f   H Rj  K Rjf
A2 L2 dl2
j
j
(22)
The ideal gas law is differentiated in terms of the gas
enthalpy rate to evaluate the gas superficial velocity:
du gf
dl2

Rg
dQgf
(23)
A2 PCpg dl2
The derivative of the enthalpy of the gas phase is
obtained by eq.(24), assuming that the heat capacity of
the components is constant at each integration step:
dQgf
dl2

Qgf dQ f
(24)
Q f dl2
The chemical species considered to be involved in the
reaction scheme of the regenerator are categorized to
gas components (N2, O2, CO2, CO, H2O) and solid
components (AL2O3, SiO2, C, H, S). A short description of
the kinetics of the heterogeneous and homogeneous
reactions is given in (R1) – (R6).
The intrinsic carbon combustion on the catalyst
surface corresponds to a couple of reactions producing
CO and CO2 with second order kinetics:
K1
1
C  O 2  CO
2
K2
C + O2  CO2
r1  K1 CO 2 
(R1)
r2  K 2 CO2 
(R2)
The homogeneous CO oxidation in the gas phase, at
which water acts catalytically, is:
K3
1
0.5
0.5
CO + O 2  CO 2 r3  K 3 O 2  CO  H 2O 
2
Fig.4. Structure of solution sequence of the integrated FCC simulator.
In Fig.4 the regenerator temperature, the riser
temperature, the coke on regenerated catalyst, the rate
and quality of the feedstock, and the inerts rate are used
for the calculation of the catalyst circulation rate that
satisfies the mass and energy balances in the reactor.
With base the new calculated value for the catalyst
circulation rate and the estimate of the production of coke
the mass flow rate of solids that enter the regenerator is
updated. The iteration loop continues till the convergence
that declares imposition of steady state is achieved.
The responses of the simulator were evaluated for
step changes in the rate and the preheat temperature of
the feed and in the catalyst circulation rate. For the needs
of the particular study, the control loop of reactor
temperature was removed, so that it does not influence
the dynamic behavior of the unit. Accordingly, the routine
of adjustment of catalyst circulation rate for constant riser
temperature was deactivated. The only controllers that
were left in operation in the unit were the one that
regulates the temperature of reactor for the achievement
of pseudo-isothermal conditions, and the one that checks
the regenerator wall temperature for the achievement of
pseudo-adiabatic conditions.
(R3)
The catalytic CO oxidation, at which part of the CO
produced on the catalyst site, is catalytically oxidized on
the catalyst itself, or on an oxidation promoter:
K4
1
CO + O 2  CO 2 r4  K 4 CO
2
(R4)
The hydrogen combustion on the catalyst surface, which
produces a significant amount of heat, is:
K5
1
2H + O 2  H 2O
2
r5  K 5  H O 
(R5)
The coke sulfur combustion on the catalyst, which
produces mainly SO2, is:
K6
S + O2 SO2
r6  K6 SO
(R6)
The reaction of C and CO2 on the catalyst site producing
CO is neglected, as it occurs at a very low rate.
RESULTS AND DISCUSSION
The industrial practice for profitable and constant
operation of the FCC unit is to control the riser exit
temperature. The automatic control of the reactor
temperature was included in the simulator, with the
addition of a routine that adjusts the catalyst circulation
rate. Using the pseudo-steady state model of the reactor,
the catalyst circulation rate is regulated by solving the
system provided by the heat balance (eq.(10)) and the
Fig.5. Dynamic results (observed and simulated) of the FCC pilot plant.
In Fig.5 the comparison of the responses of the unit with
the predictions of the model for the case of 50%
reduction in the feed rate is presented. Increases in the
riser input variables corresponded to aggressive
responses of the system, since the riser has a very small
contribution to the dynamic behavior of the integrated
system. However, after the new riser state was reached,
the regenerator led the system to the new overall steady
state in much greater times. The excellent convergence
between observed and predicted values for reactor and
regenerator temperatures indicate the accurate
formulation of the mass and energy balances, while the
small differences in the prediction of the composition of
regenerator excess gas are owed to small inaccuracies
(within the limits of experimental error) in the prediction of
coke yield. The results of both the simulator and the pilot
plant are in excellent agreement with the experience of
real-time operation of FCC units.
CONCLUSIONS
A dynamic simulator for the FCC integrated system was
presented. The nonlinear dynamic and multivariable
model was verified with experimental data of the pilot
plant of CPERI. The simulator performs satisfactorily, in
describing the complex responses of the unit to typical
disturbances. The accurate simulation of the pilot plant is
significant for process optimization studies. The ultimate
scope of this study is to utilize the simulator as a basis for
model based control of the pilot plant. The purpose of
such a controller would be to provide the operator with
the ability of driving the pilot process to desired states,
such as the maximization of the selectivity of a desired
product or the maximization of the process conversion.
Acknowledgement
Financial support by the Ministry of National Education
and Religious Affairs (program ARCHIMIDES I) and the
General Secretariat of Research and Technology Hellas
(program AKMON 01) is gratefully acknowledged.
NOMENCLATURE
A
cross-sectional area of regenerator section (m2)
c, cx
total coke yield wt%, catalytic coke yield wt%
CA
aromatic carbon content wt% of feed
CCR
conradson carbon residue wt% of feed
Cp
specific heat (kcal/molK)
Ex, Ec
activation energies of reaction to x, c (Btu/lbmol)
fb
bubble phase volume fraction
Fib
molar rate in bubble (mol/s)
Fie
molar rate in emulsion (mols-1)
Fif
molar rate in freeboard (mols-1)
Ht
bubble-emulsion heat interchange (kcalm-3s-1K)
KH
heat interchange rate group (kcalm-3s)
KMi
mass interchange rate group (molm-3s)
KRjb
reaction rate group - bubble phase (molm-3s)
KRje
reaction rate group - emulsion phase (molm-3s)
KRjf
reaction rate group - freeboard (molm-3s)
Kti
bubble-emulsion gas interchange coefficient (s-1)
kx, kc
pre-exponential factor of reaction to x, c
L
height of regenerator section (m)
MWFeed feed molecular weight
NC
carbon number in the average feed molecule
nx, nc
catalyst decay exponent of reaction to x, c
NN
nitrogen number in the average feed molecule
NT
total nitrogen content wt% of feed
Qb
enthalpy rate in bubble phase (kcals-1)
Qe
enthalpy rate in emulsion phase (kcals-1)
Qg
volumetric gas flow in the riser (m3/s)
Qloss
heat loss from the dense bed (kcals-1)
S
sulfur content wt% of feed
TRX
riser reactor temperature (°F)
ts
catalyst residence time in the riser (s)
ug
superficial gas velocity in the riser (m/s)
ut
catalyst particle terminal velocity (m/s)
WHSV weight hourly space velocity (hr-1)
catalyst circulation rate (kg/s)
W Cat
W Feed
gas-oil feed rate (kg/s)
WCat
x
ΔΗcrack
ΔΗRj
riser catalyst inventory (kg)
gas-oil conversion wt%
heat of catalytic cracking (Btu/lb)
heat of reaction j (kcalmol-1)
Greek Letters
εe
dense bed emulsion void fraction
εf
freeboard void fraction
εr
riser void fraction
ρp
catalyst density (kgm-3)
Subscripts
bot
riser bottom section
in
regenerator zone inlet
mid
riser intermediate section
out
regenerator zone exit
top
riser top section
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