[petroleum] - uop fluid catalytic cracking unit

Simulation and model predictive control of a UOP fluid catalyticcracking unit

Mircea V. Cristea a,*, Serban P. Agachi a, Vasile Marinoiu b,1

a Faculty of Chemistry and Chemical Engineering, ‘‘Babes-Bolyai’’ University, 11 Arany Janos Street, 3400 Cluj-Napoca, Romaniab Control and Computers Department, ‘‘Petrol-Gaze’’ University, 39 Bucuresti Blvd., 2000 Ploiesti, Romania

Received 14 March 2001; received in revised form 9 March 2002; accepted 9 March 2002

Abstract

Based on a newly developed mathematical model, the complex dynamic simulator of an industrial Universal Oil Products (UOP)

fluid catalytic cracking unit was used to implement the model predictive control (MPC) algorithm. The simulator revealed the

multivariable, nonlinear and strong interacting feature of the process. Combined with equipment and operating constraints they put

severe limits on control performance. Different MPC schemes for the reactor and regenerator’s most important process variables

were tested and the most favorable have been presented. The constrained MPC approach using scheduled linearization to account

for non-linear behavior and a larger number of manipulated than controlled variables proved successful. Comparison with

traditional control using decentralized PID controllers revealed incentives for the multivariable model based predictive control in

maintaining controlled variables very close to their constrained limits where usually the optimum is situated.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: FCCU dynamic simulator; Complex nonlinear behavior; PID control; Model predictive control

1. Introduction

Over 60 years catalytic cracking has been one of the

main processes in petroleum refining supporting a

spectacular development [1]. The fluid catalytic cracking

unit (FCCU) became in the last decades the testing

bench of every advanced control method. Both acade-

mia and industry are interested in developing new

control algorithms and their efficient industrial FCC

implementation, as successful results are usually of large

economic benefits [2]. The catalytic cracking process is

complex both from the modeling and from the control

point of view [3,4].

The dynamic mathematical model development im-

plies some assumptions taking into account specific

aspects of the process. The complex nature of the feed

oil assumes a lumped kinetic mechanism for the treat-

ment of the cracking process. Both reactor and regen-

erator mass and heat transfer are complex. The

adiabatic plug flow reactor model is usually used for

the riser. Two zones frequently describe regenerator

model: a dense bed zone (with dense phase as a CSTR

model but gaseous phase as a plug flow reactor model)

and an entrained catalyst zone (plug flow model) [5].

The control system design and implementation have

to solve challenging tasks. The multivariable character

of the process presenting strong interactions, the non-

linear behavior leading to the need for nonlinear control

and the demand to operate the unit in the presence of

material and operating constraints, are the main ones.

Additionally, the control system has to cope with both

large and short time constants and to face the changing

operating conditions, in the presence of usually unmea-

sured disturbances. As a consequence, model predictive

control (MPC) proves to be a good candidate for

implementing FCCU advanced control due to its multi-

variable structure, direct approach of constraints and

optimal character [6,7].

Based on these preliminary aspects the paper presents

the development of a mathematical model for a UOP

type FCCU and the associated dynamic simulator.

Different MPC schemes are investigated and tested by

* Corresponding author. Fax: �/40-64-193-833.

E-mail address: [email protected] (M.V. Cristea).1 Fax: �/40-44-175-847.

Chemical Engineering and Processing 42 (2003) 67�/91

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dynamic simulation revealing interesting aspects from

the perspective of the industrial implementation.

2. FCCU dynamic model

The FCCU, for which the mathematical model has

been developed and then performed the MPC study, is

presented in Fig. 1.

The newly developed mathematical model for the

UOP type FCCU is based on the mechanistic Amoco

Model IV FCCU [5]. Compared with Amoco Model IV

the new mathematical model describes a different

FCCU type, both from the operation and from theconstruction point of view. The main new model

characteristics are related to the following aspects:

. Different geometric dimensions and relative position

define the reactor and regenerator, compared with

the Model IV case.

. The reactor model uses a Weekman kinetic scheme [9]

for describing the cracking process.

. The regenerator of the UOP FCCU operates in

partial combustion mode.

. Catalyst circulation is described including spent andcatalyst valves on catalyst circulation lines. These

valves are used as main manipulated variables for

FCCU control.

The FCCU dynamic model has been developed on the

basis of reference construction and operation data from

an industrial unit. The described model is rather

complex succeeding to capture the major dynamic

behavior of UOP type FCCU [8]. The model includes

the main reactor�/regenerator subsystems: feed and

preheat system, reactor, regenerator, air blower, wet

gas compressor and catalyst circulation lines.

Main aspects of the new model are outlined in the

following.

2.1. Reactor model

Developing the new mathematical model for the

reactor implied a thorough survey, selection and then

synthesis, based on a large variety of models presented

in literature. The three-lump model has been considered

to be adequate for the global description of the

phenomena taking place in the reactor. Reactor is

divided in two parts: riser and stripper. The riser model

is built on the following assumptions: ideal plug flow

and very short transient time (the residence time in the

riser is very short compared with other time constants,

especially with the regenerator time constants [1,5,8,10]).

It is modeled by mass balance describing the gasoline

and coke�/gases production based on Weekman’s

triangular kinetic model [9]. The mixed nonlinear

differential and algebraic system of equations also

accounts for the amount of coke deposited on catalyst

and for the cracking temperature dynamics [13]. The

reactor is presented in Fig. 2.

Detailed description of the reactor model is presented

in the following.

Fig. 1. Scheme of UOP type FCCU.

M.V. Cristea et al. / Chemical Engineering and Processing 42 (2003) 67�/9168

2.1.1. Mass balance for the riser

Mass balance for the feed is described by the equation

dyf

dza

��K1y2f [COR]F tc: (1)

Mass balance for the gasoline is described by the

equation

dyg

dza

� (a2 K 1y2f �K3yg)[COR]F tc; (2)

where:

K1(u)�kr1 exp�Ef

RT0(1 � u); (3)

K3(u)�kr3 exp�Eg

RT0(1 � u); u�(T�T0)=T ; (4)

F�f0 exp(�atc[COR]za); (5)

f0�1�m�Crgc: (6)

Inlet temperature in the riser T0 is determined by the

heat balance equation [3]

T0�FrgcCpcTreg � FfCpf T2 � DHevpFf

FrgcCpc � FfCpfv

: (7)

The term K1yf2[COR] represents the kinetics of the

feed, K3yg[COR] the kinetics of the gasoline; F is a

function of catalyst deactivation due to coke deposition;

f0 the reduction of catalyst activity due to the coke

resident on the catalyst after regeneration; tc residence

time in the riser; and a2�/k1/k2 fraction of feed oil that

cracks to gasoline. This model develops the models

presented by Lee and Groves [24], Shah et al. [25] andHovd and Skogestad [13]. The amount of coke produced

is described by the following correlation taken from

Voorhies and Kurihara [26]:

C cat�K c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitc

CNrgc

exp�Ecf

RTr

s: (8)

The fraction of coke on the spent catalyst leaving the

riser is:

Csc1�Crgc�Ccat: (9)

The constant values m* and N have been used to

perform a good fit of the mathematical model with

operating data from the industrial unit.

2.1.2. Heat balance for the riser

du

dza

�DHfFf

T0(FscCpc � FfCpf � lFf Cpd)

dyf

dza

: (10)

The amount of gases produced by cracking is

described by the equation:

Fwg �(F3�F4)[C1�C2(Tr�Tref )]: (11)

Constants C1and C2 have been fitted based on data

from the industrial unit.

The stripper model is of CSTR type (mass and heat

balance) evaluating the temperature in the stripper and

the fraction of coke on spent catalyst.

2.1.3. Mass and heat balance for the stripper

dTs

dt�

Frgc

Wr

(Tr�Ts); (12)

dCsc

dt�

�Frgc(Crgc�Ccat)�FscCsc�Csc

dWr

dt

�1

Wr

; (13)

dWr

dt�Frgc�Fsc: (14)

2.1.4. Pressure balance for riser bottom pressure

determination

Prb�P4�rrishris

144; (15)

rris�F3 � F4 � Frgc

nris

; (16)

nris�F3 � F4

rv

�Frgc

rpart

: (17)

The amount of catalyst in the riser is determined by

the equation

Wris�FrgcArishris

nris

: (18)

Fig. 2. Scheme of the FCCU reactor.

M.V. Cristea et al. / Chemical Engineering and Processing 42 (2003) 67�/91 69

2.1.5. Momentum balance for reactor and main

fractionator pressure determination

dP5

dt�0:833(Fwg�FV11

�FV12�FV13

) (19)

FV12�k12V12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP5�Patm

p: (20)

A constant pressure drop, DPfrac, between reactor andmain fractionator is considered; according to this, the

reactor pressure is computed by the equation

P4�P5�DPfrac: (21)

2.2. Regenerator model

The mathematical model for the regenerator presents

a higher complexity due to the importance of this system

in determining the time constant for the entire FCCU.

The regenerator is considered divided in two zones: a

dense bed zone and a zone of entrained catalyst (the

disengaging zone) (Fig. 3).

The dense bed zone consists of two phases: a bubblephase of gaseous reactants and products moving up the

bed in plug flow and a perfectly mixed dense phase

containing gases and solid catalyst.

Mass transfer occurs between the two phases but at

regenerator temperatures the reaction rates are control-

ling, rather than mass transfer between the two phases.

Since the dense phase is considered perfectly mixed, the

temperature is assumed uniform in the bed and thegaseous phase in equilibrium with dense phase. Catalyst

is present in the zone above dense bed due to entrain-

ment. The amount of catalyst decreases with the

regenerator height. In the entrained catalyst zone the

CO combustion is dominant (the amount of catalyst is

diminished) having an important heat contribution.

The operating conditions are corresponding to CO

partial combustion mode.

The regenerator model consists in mass and heat

balance equations for O2, CO, CO2 and coke, but also inheat balance equations for solid and gaseous phase.

These balance equations are correlated with equations

describing entrained catalyst (bed characteristics) in the

zone above dense bed, catalyst flow and pressure in the

regenerator.

2.3. Model of the catalyst circulation lines

For the catalyst flow in the spent and regeneratedcatalyst circulation lines (piping), a steady state behavior

is assumed. It is considered that dynamics of the lines

are very fast compared to the time constants of other

subsystems of the FCCU.

Spent and regenerated catalyst circulation considers a

single-phase flow, based on force balance [14]. For the

regenerated catalyst line the equation is:

144(P6�Prb)�zbedrc�(Etap�Eoil)rc�DPsv;rgc

�DPelb;rgc�FrgcLrgcFrgc

A2rgcrc

�0; (22)

and for the spent catalyst line the force balance is given

by:

144(P4�P6)�(Estr�Elift)rc�Wr

Astr

�DPsv;sc�DPelb;sc�FscLscFsc

A2scrc

�0: (23)

The pressure drop on the slide valves is described by

the following equation:

DPsv��

50Fcat

KAsvsv

�2 144

rc

: (24)

Pressure drop on other pipe restrictions are given by

equations of the type:

DPelb�1

2N�rcv

2: (25)

Detailed presentation of models for the feed and

preheat system, regenerator, air blower, and wet gas

compressor are presented in Appendix B.

3. Results and discussion

3.1. Dynamic simulation results

A set of FCCU dynamic simulations have beenperformed and studied as response to different upsets

in manipulated variables and disturbances. From this

set, the dynamic response to the coking rate disturbanceFig. 3. Scheme of the FCCU regenerator.


KC is presented. A step coking rate disturbance KC

(3.2% step increase) has been applied at time t�/500 s

from the beginning of the simulation. This type of

disturbance simulates changes in properties of the feedoil residing in the increase of the amount of coke

deposited on the catalyst. For the industrial unit, this

kind of coking rate change is possible to appear due to

the fresh feed composition change or to the recycle

flowrate upset. The evolutions of the most representa-

tive process variables are presented in Fig. 4. The

dynamic responses are interpreted over two periods

corresponding to the time sequence of the phenomena.

3.1.1. First period

The increase of coke amount deposited on spent

catalyst evacuated from the reactor is rapid (Fig. 4(j)).

The increased amount of coke entered in the regenerator

induces, in the first time sequence, the small temperature

rise in the regenerator (Fig. 4(c)), and then in the reactor

(Fig. 4(e)), leading to the intensification of cracking

reactions, with direct effect on reactor pressure rise (Fig.4(b)). As a consequence of the reactor pressure rise, the

flowrate of spent catalyst increases (Fig. 4(f)). As spent

catalyst flowrate becomes higher than regenerated

catalyst flowrate (Fig. 4(g)), the reactor catalyst inven-

tory decreases (Fig. 4(a)). The small increase in regen-

erator pressure and then in regenerator catalyst

inventory determines a small decrease in the air entering

the regenerator (due to the increased counter-pressure)(Fig. 4(l)). The regenerator temperature begins to

decline (after a first low-amplitude peak), as a conse-

quence of the increased contribution of spent catalyst

(with lower temperature) entering the regenerator.

3.1.2. Second period

The regenerator temperature decrease induces the

temperature decrease in the reactor followed by apressure decrease in the reactor (Fig. 4(b)). The reactor

pressure reduction determines the decrease of spent

catalyst flowrate (Fig. 4(f)), and the increase of regen-

erated catalyst flowrate (Fig. 4(g)). For the reactor, the

consequence is the increase in catalyst inventory (Fig.

4(a)). The regenerator temperature decrease continues

due to the fact that net coke contribution is increased

(the combustion air flowrate has a negligible increase).The explanation of this net coke contribution increase is

the following: both spent and regenerated catalyst

flowrates increase (small growth), but mainly, the

fraction of coke on spent (Fig. 4(j)) and on regenerated

catalyst (Fig. 4(k)), are also increasing. As a result, the

difference of these two fractions increases. For this

reason, combustion in the regenerator is performed in a

diminished excess of oxygen (Fig. 4(h)), with directimplication on the heat balance of the regenerator. The

equilibrium of carbon combustion is shifted to an

increased amount of CO formation (Fig. 4(m)), and to

a diminished amount of CO2 production (Fig. 4(n)).

Taking into account the fact that heat generated by CO

formation is about three times less than CO2 heat

formation, the global effect is the reduction of net heatcontribution in the regenerator with direct consequence

on temperature decrease (Fig. 4(c)). The cyclone tem-

perature follows this decrease (Fig. 4(i)). New equili-

brium is reached at lower reactor and regenerator

temperatures compared to temperature values before

disturbance occurrence (Fig. 4(c,e)). Catalyst flowrates

and coke fraction on spent and regenerated catalyst are

also increased (Fig. 4(f,g)). The CO fraction is increased(Fig. 4(m)), but CO2 and O2 fractions are decreased.

Results obtained by dynamic simulation present a

good fit with industrial operating data, simulated

variables being situated in a range corresponding to

industrial unit behavior (Table 1). Comparison between

industrial operating data and dynamic simulation results

has been performed for a set of data (1 month period),

confirming the main trends of the dynamic behaviorboth on short and large time scales. Obtaining a better

fit is still possible by increasing the complexity of the

model, but also necessary, as properties of the raw

material is subject to changes.

Dynamic simulations reveal the multivariable and

nonlinear behavior of the process presenting strong

interactions. Inverse response has been noticed denoting

multiple paths with opposing effect transmission. Singleloop decentralized control has to face strong impedi-

ments for such challenging interacting behavior.

The newly developed dynamic simulator offers the

possibility to study different operating regimes induced

both by design changes and by changing operation

strategies. It also proves to be a valuable tool for

investigating the way that different control strategies

may be implemented and predict their results. Advancedcontrol systems, as MPC algorithms, are based on

mathematical models and rely on the dynamic simula-

tor.

3.2. Model predictive control results and interpretations

3.2.1. Control scheme selection

MPC, also referred as moving (receding) horizon

control, has become an attractive control strategyespecially for linear but also for nonlinear systems

subject to input, state and output constraints.

There are some features that individualize MPC in the

field of control design, making it attractive. In contrast

to other feedback controllers that calculate the control

action based on present or past information, MPC

determines the control action based on the prediction of

future dynamics of the system. Due to the futureprediction, early control action can be taken accounting

for future behavior. In practice, most of the systems

have to satisfy input, state or output constraints,


resulting in limitations on achievable control perfor-

mance (in the extreme case affecting the stability). MPC

is able to obtain better control performance in the

presence of constraints since it is able to determine the

current control action for minimizing the errors caused

by constraints that are predicted to become active in the

future. The objective function specifying the desired

control performance is optimized (minimized) on-line at

each time step. The number of computed values in the

manipulated variable sequence is finite (finite input

Fig. 4. Simulation of FCCU dynamic behavior in the presence of a coking rate KC disturbance (3.2% step increase). (a) Reactor catalyst inventory

Wr [t], (b) reactor pressure P4 [bar], (c) regenerator temperature Treg [8C], (d) regenerator pressure P6 [bar], (e) reactor temperature Tr [8C], (f) spent

catalyst flowrate [kg/s], (g) regenerated catalyst flowrate frgc [kg/s], (h) oxygen to air molar fraction in stack gas xO2sg, (i) cyclone stack gas

temperature Tcyc [8C], (j) mass fraction of coke on spent catalyst csc [kg coke/kg catalyst], (k) mass fraction of coke on regenerated catalyst crgc [kg

coke/kg catalyst], (l) regenerator inlet air flowrate Ft [Nm3/h], (m) CO to air molar fraction in stack gas xCOsg, (n) CO to air molar fraction in stack

gas xCO2sg.


horizon) and discrete in time , accounting for the fact

that the involved optimization problem can be solved

with numerical methods. A time-continuous approach

can lead to extremely demanding numerical problems.

Multivariable controllers are often the only solution able

to provide desired control performance in the presence

of interactions and MPC can successfully handle such

cases. For the present study the Dynamic Matrix

Control form of MPC has been employed.

Based on literature survey and analysis of the current

industrial FCCU operation, a set of process variables

has been selected and considered to have first role

importance in efficient and safe operation of the unit

[11�/15].

Fig. 4 (Continued)


The controlled variables have been selected to provide,

through control, a safe and economic operation. Con-

trol of reactor catalyst inventory (reactor level) Wr,

provides stabilization of catalyst circulation. It also sets

up a buffer for diminishing upsets in coke concentration

deposited on the catalyst and for temperature change

progressing from the reactor toward the regenerator.

Regenerator temperature, Treg, has to be maintained at

a certain value to allow a stable removal of coke from

the catalyst. Overriding a high temperature limit pro-

duces a permanent catalyst deactivation; a reduction

under a lower limit leads to coke accumulation on the

regenerated catalyst. The reactor temperature, Tr, has to

be maintained at a certain level to provide a desired

maximum conversion of the feed oil. The stack gas

oxygen concentration, xO2sg, has to be controlled in

order to provide a desired coke combustion, preventing

both a thermal increase and an inefficient load of the

combustion air blower. Maintaining the cyclone tem-

perature, Tcyc, under a maximum limit, provides safe

thermal operation for the regenerator and for the

downstream units (piping and CO boiler).

The manipulated variables have been chosen from the

set of independent variables possible to be changed from

a practical point of view. The main manipulated

variables are the spent and regenerated catalyst flow-

rates that may be changed by regenerated svrgc and

spent svsc slide valve position. The preheating furnace

fuel flow, F5, is an important manipulated variable with

effective action on the thermal balance of the entire unit.

The stack gas flowrate from the regenerator, changed by

stack gas valve position V14 and the air vent flowrate,

changed by air vent valve position V7, are other two

manipulated variables. The wet gas suction flowrate,

changed by suction valve position V11, is another

manipulated variable considered in the control schemes.The selected disturbances reflect main upsets possible

to affect the normal operation of the unit: main

fractionator pressure upset, feed oil coking character-

istics (coking rate) upset and ambient temperature upset

Fig. 4 (Continued)

Table 1

Typical operating conditions and values obtained with the simulator

Process variable Measuring unit Minimum value Maximum value Nominal value Value in the simulator

Air flowrate entering regenerator Nm3/h 85 00 147 000 98 500 102 514

Air vent flowrate Nm3/h 0 5500 2500 2510

Regenerator temperature 8C 650 700 682 685.06

Cyclone temperature 8C 677 710 705 708.5

Reactor temperature 8C 490 525 515 516.99

Reactor pressure Bar 1.2 1.9 1.3 1.279

Regenerator pressure Bar 1.2 2.8 1.5 1.495

Coke on spent catalyst Mass fraction 0.009 0.014 0.012 0.01165

Coke on regenerated catalyst Mass fraction 0.002 0.0045 0.0035 0.00393

CO2 concentration in flue gas Volume fraction 0.08 0.16 0.13 0.141

O2 concentration in flue gas Volume fraction 0.001 0.008 0.0035 0.00288

CO concentration in flue gas Volume fraction 0.03 0.08 0.05 0.042

Catalyst inventory in the reactor Tons 30 60 50 55.7


[5,13]. The main fractionator pressure disturbance has

been included in the simulation by the term DPfrac,

representing the reactor�/main fractionator pressure

drop. This disturbance reveals the effect of upsets in

main fractionator operation, acting on reactor�/regen-

erator system. Such main fractionator pressure upsets

may appear when: vapor flow is changed as a result of

suction flowrate change of wet gas compressor, internal

liquid�/vapor traffic of the main fractionator is changed

due to reboiler and condenser load upset or by pressure

changes induced from downstream gas recovery unit.

An increasing step disturbance has been selected (having

�/37% amplitude increase and applied at time t�/500 s).

The coking characteristic of the feed oil, coking rate KC,

was included as a disturbance to study the effect of

changes in raw material properties. It was noticed that

this unmeasured disturbance has a strong effect on the

heat balance of the entire unit. A positive step change

has been selected for this disturbance (having �/3.2%

amplitude increase and applied at time t�/500 s). The

ambient temperature change is a continuous disturbance

affecting FCCU on a day-time basis. It consists in

combustion air flowrate change, introducing low ampli-

tude upsets in the unit. This disturbance was included as

a descending ramp, with negative slope (�/16 8C/8 h),

applied for 1 hour between t�/300 s and t�/3900 s.

The MPC of the FCCU was designed in a two-level

control structure, acting at the top level of the hierarchic

control system by cascading the low-level regulatory

control loops (usually flowrate control loops).A controllability study, based on relative gain array

(RGA), has been performed for selecting both the most

efficient manipulated variables for changing the con-

trolled variables but also for determining the best MPC

control scheme, among a set of schemes of the same

dimensions. The RGA is a measure of interaction

between controlled variables, each of the RGA elements

denoting the ratio between open loop and closed loop

gain in decentralized control. This controllability in-

dicator, as a first filter for selecting the best control

scheme, proved to be useful not only for decen-

tralized control but also for the multivariable approach

[13,17].

Based on this approach, a set of control schemes has

been investigated [16,17]. They have a different number

of controlled/manipulated variables: 3�/3, 4�/4, 5�/5,

5�/6 schemes, presented briefly in Table 2. The set of

MPC schemes presented in Table 2 have been tested in

the presence of the three typical described disturbances.

Different values have been investigated for the error

diagonal weighting matrix, ywt (Gy), and for the

manipulated-variable move diagonal weighting matrix,

uwt (Gu), from the MPC quadratic optimization objec-

tive.

3.2.2. Different MPC control schemes results

Following the results obtained by dynamic simula-

tion, the most favorable MPC control schemes, from

each category, are: S1: 3�/3, S5: 4�/4, S10: 5�/5. Fromthis large set of MPC dynamic simulations of FCCU,

the representative S5: 4�/4 control scheme results are

presented in Figs. 5 and 6.

As can be noticed, the S5: 4�/4 control scheme

succeeds to counteract the disturbance effects, present-

ing small overshoot and short settling time. This

behavior demonstrates good setpoint following capa-

city.The superior behavior of S5: 4�/4 control scheme,

predicted by the controllability analysis based on RGA

values presented in Table 3, has been confirmed by the

dynamic simulation results.

Compared to S5: 4�/4, the S6: 4�/4 control scheme

has inferior control performance showing higher over-

shoot and longer response time (especially for the case

of KC disturbance). The S7: 4�/4 control schemepresented unsatisfactory control performance (offset)

for all controlled variables in the case of KC disturbance.

For the case of the other investigated disturbances the

control performances of S6: 4�/4 and S7: 4�/4 control

schemes are not essentially affected.

Compared to S1: 3�/3 control scheme, S5: 4�/4

scheme has an unimportant increase of the overshoot

(for the case of KC performance), but a small decrease ofthe response time can be noticed. The ability to maintain

the stack gas oxygen concentration at a predefined value

allows a more efficient FCCU operation due to better

use of air blower capacity and to safer operation by the

control of ‘‘afterburning’’ phenomenon. Having an

additional variable, compared to the 3�/3 control

schemes, it may be concluded that S5: 4�/4 scheme is

preferable.Compared to lower dimension schemes presented

before, the 5�/5 control schemes are characterized by

the existence of higher overshoot and a longer response

time, possibly coupled with small offset, but the control

performances are not considerably affected.

S12: 5�/6 MPC scheme did not reveal improvements

compared to S10: 5�/5 scheme. The advantage of using

a control scheme with a higher number of manipulatedthan controlled variables will become operative when

constraints on manipulated variables are imposed. The

number of manipulated variable surplus may serve as a

supply for the case of operating conditions when one or

more of the manipulated variables become restricted.

3.2.3. Considerations on MPC tuning

It is a well-known fact that model predictive con-

troller tuning, especially for the MIMO case, is difficult[18,19,21]. This aspect is unexpected if taking into

consideration the relatively large number of parameters

possible to be tuned for obtaining desired control


performance. These possible tuning parameters are:

sampling time T , model horizon n , prediction horizon

p , input horizon m , error weighting matrix ywt (Gy ) and

manipulated variable move weighting matrix uwt (Gu).

The tuning difficulties are tied to the MIMO character-

istics of the problem and to the insufficient control of

the tuning effect of parameter changes on the control

performance. These difficulties become more important

when nonlinear behavior of the model is present [20].

Due to these aspects, the model predictive controller

tuning has an iterative character and the control

performance enhancement may be performed, in a great

extent, by recursive simulations. A set of recommenda-

tions for MPC tuning has been specified and may be

regarded as a tuning MPC guide [7,19,20]. The sampling

time T is established as a trade-off between losing

important dynamic information and overloading the

computing system; a value of T�/100 s has been chosen.

Table 2

Tested control schemes

Control scheme (name/dimension) Controlled variables Manipulated variables MPC tuning parameters uwt and ywt

S1 3�/3 Wr Treg Tr svrgc svsc F5 uwt�/[120 120 0.8], ywt�/[0.1 0.2 1]

S2: 3�/3 Wr Treg Tr svrgc svsc V14 uwt�/[120120480], ywt�/[0.1 0.2 1]



S5: 4�/4 Wr Treg Tr xO2sg svrgc svsc V14 V7 uwt�/[3030120120], ywt�/[0.1 0.2 1 0.5]

S6: 4�/4 Wr Treg Tr xO2sg svrgc svsc F5 V7 uwt�/[1501501600], ywt�/[0.1 0.2 1 0.5]

S7: 4�/4 Wr Treg Tr xO2sg svrg, svsc V11 V7 uwt�/[150150300600], ywt�/[0.1 0.2 1 0.5]

S8: 5�/5 Wr Treg Tr xO2sg Tcyc svrgc svsc F5 V7 V11 uwt�/[1501501600300], ywt�/[0.1 0.2 1 0.5 0.5]

S9: 5�/5 Wr Treg Tr xO2sg Tcyc svrgc svsc F5 V7 V11 uwt�/[30 30 0.2 120 60], ywt�/[0.1 0.2 1 0.5 0.5]

S10: 5�/5 Wr Treg Tr xO2sg Tcyc svrgc svsc F5 V7 V14 uwt�/[1501501600600], ywt�/[0.1 0.2 1 0.5 0.5]

S11: 5�/5 Wr Treg Tr xO2sg Tcyc svrgc svsc V11 V7 V14 uwt�/[150150300600600], ywt�/[0.1 0.2 1 0.5 0.5]

S12: 5�/6 Wr Treg Tr xO2sg Tcyc svrgc svsc F5 V7 V11 V14 uwt�/[1501501600300600], ywt�/[0.1 0.2 1 0.5 0.5]

Fig. 5. MPC simulation results (solid) in the presence of KC disturbance (step increase of coking rate), for S5: 4�/4 control scheme; disturbed process

without control (dashed).


The model horizon n is established such as Tn should

extend over the open loop response time (smaller values

can lead to undesired peaks appearing at Tn time

horizon, when the model error first becomes significant);

a value of n�/400 has been taken.

Both prediction horizon p and control horizon m

have been established based on the assumptions that

large values lead to increased computational effort and

short values produce ‘‘short-sighted’’ control policy.

The value of p�/100, i.e. one fourth of the settling time,

was selected for the prediction horizon. The choice of a

smaller p leads to short-sighted control associated with

more aggressive control action. An additional conse-

quence of reducing p is that the constraint violations are

only checked over a short horizon, leading to a dead-

zone with inefficient control effect. The prediction

horizon p is not established very long (relative to open

loop settling time) in order to prevent sluggish control

action (having in fact a stabilization effect) and raising

the computational load. For the control horizon the

value of m�/10 has been taken. The control horizon m

is established not too long, to prevent aggressive control

action, but also not too short, to determine an inefficient

control and to provide a sufficient number of degrees of

freedom.

The diagonal error weighting matrix ywt (Gy) was

determined such as the elements on the main diagonal be

equal to the inverse of the maximum allowed offset of

the particular controlled variable; these values are

weighted again after dynamic simulation tests (Table

2). The diagonal manipulated variable move weighting

matrix uwt (Gu) was determined such as the elements on

the main diagonal be equal to the inverse of the

maximum allowed variation of the manipulated vari-

able; these values are weighted again after dynamic

simulation tests (Table 2).It is meaningful to mention that tuning was per-

formed to obtain good control performance for all cases

of the three applied disturbances resulting in a more

Fig. 6. MPC simulation results (solid) in the presence of DPfrac disturbance (step increase of reactor�/main fractionator pressure drop), for S5: 4�/4

control scheme; disturbed process without control (dashed).

Table 3

RGA for S5: 4�/4 control scheme

svrgc svsc V14 V7

Wr 0.3634 1.3981 �/0.8004 0.0390

Treg 2.0118 �/0.6095 �/0.2298 �/0.1725

Tr 0.3946 0.3969 �/0.9546 1.1631

xO2sg �/1.7698 �/0.1855 2.9848 �/0.0296


conservative tuning than would have been necessary for

each of them considered individually.

3.2.4. MPC versus decentralized PID control

To make a comparison between MPC and traditional

decentralized PID control, simulations have been per-

formed involving the set of controlled and manipulated

variables of S5: 4�/4 control scheme. The pairing of

controlled and manipulated variables used for the PID

decentralized control have been suggested by the RGA

(Table 3): Wr�/svsc, Treg�/svrgc, Tr�/V7 and xO2sg�/V14.Anti-windup PID digital controllers have been applied

[22].

Tuning of the PID controllers has been made by

repeated simulations using an ‘‘experimental’’ type

method based on bringing first the system at the stability

limit. Again, the tuning has been made in a way to

obtain good control performance for all of the three test

disturbances taken into consideration. Comparativeresults of MPC and PID control are presented in Fig.

7. Results presented in Fig. 7 reveal the superior

behavior for the case of MPC, both with respect to

overshoot and response time. Following the performed

simulations it may be concluded that, as the number of

controlled variables is high and the interactions between

them are strong, a multivariable control strategy can be

successful and MPC proves to be an effective one.

3.2.5. MPC using model scheduling approach

The model used for computation of manipulated

variables is a linear one, obtained by the linearization

of the nonlinear model around the operating point [23].

Results presented in previous paragraphs use such a

unique model. For the elimination of errors caused by

nonlinearities the authors proposed and investigated the

behavior of a control scheme using scheduled lineariza-tion. The FCCU linearized model is periodically up-

dated at time moments multiple of 3000 s, starting from

t�/1500 s. The changing model case has a roughly better

control performance, particularly for Wr controlled

variable (affected by the lowest value in the error-

weighting matrix) (Fig. 8). The scheduled linearization

using a higher frequency did not reveal significant

improvement for the cases of MPC control in thepresence of the investigated disturbances. This may be

determined by keeping the operating point relatively

close to the setpoint values. As disturbance effects are

more important, the updating of the linearized model, at

higher and possibly variable frequency, may become

necessary. Further results are under investigations.

Fig. 7. Comparative results between MPC, S5: 4�/4 (solid) and PID control (dash�/dotted) in the presence of KC disturbance; disturbed process

without control (dashed).


3.2.6. Constrained MPC

Among the most attractive MPC characteristics is the

possibility of considering constraints in a direct way.

This attribute offers, while specifying FCCU operating

and material constraints, the best (in an optimal sense)

solution for the control problem. For the SISO case,

requiring and conforming to constraints is frequently

not very difficult. But for the MIMO case, where

interactions are present, the aim of obtaining desired

control performance is usually a difficult task. Accord-

ing to this aspect, the interest and success MPC

algorithm has gained in a large number of reported

industrial applications may be explained [24]. The case

of MPC with constraints on manipulated variables is

investigated.

To test this ability, the following potential FCCU

malfunction event is simulated. One of the slide valves,

the spent catalyst slide valve svsc, presents a malfunc-

tion consisting in the impossibility of opening it over the

upper limit specified by the value svrgcsup�/0.4 and

Fig. 8. MPC comparative representation for: MPC adaptive model case (dashed�/dotted), MPC with unique linearized model case (solid) and case of

disturbed process without control (dashed); S10: 5�/5 control scheme in the presence of KC disturbance.


closing it under the lower limit specified by svrgcinf�/0.3

value. The position of the slide valve during nominal

operation is given by svrgc�/0.35 value. This accidental

situation raises special problems for the operating

personnel in an industrial unit having traditional

(classical) control system. For the case of MPC system

it is sufficient to specify this constraint and keep closed

the feedback control loops until the normal operation

regime is restored.

The simulation of MPC behavior for this special

operating condition is presented in Fig. 9, but only for

reactor catalyst inventory Wr, controlled variable; other

variables exhibit similar behavior with the uncon-

strained case. The coking rate disturbance KC has been

applied and the MPC with adaptive model has been

simulated. The investigated control scheme is S12: 5�/6.

Vector of constraint limits imposed to the manipulated

variables is given by ulim�/[0 0.3 0 0 0 0 1 0.4 1.98 0.5 1

0.8]. The first six values fix the minimum limits and

the last six the maximum limits allowed for the

manipulated variables (in the order they are specified

in Table 2).

As may be observed in Fig. 9, the control perfor-

mance with MPC is not substantially affected by the

occurred constraint. Two of the manipulated variables

(svsc and V7) reached the lower limit values. These

limitations do not seem to have a negative impact on the

controlled variables due to the fact that optimal strategy

succeeds to change the other manipulated variables in a

way to provide good control performance.The possibility may also be observed to involve a

higher number of manipulated variables than controlled

variables and the potential use of this ‘‘excess’’ of

command for the cases when constraints on manipu-

lated variables are present.

Based on the present study it may be considered that

this way of MPC application is revealing and sustaining

the incentives of MPC algorithm from the perspective of

its industrial implementation.

4. Conclusions

The paper presents a new model and dynamic

simulator for the FCCU aggregate systems: reactor,

regenerator, catalyst circulation lines, preheating sys-

tem, air blower and wet gas compressor. The nonlinear,dynamic and multivariable model has been fitted and

then verified with a set of representative operating data

originating from an industrial FCCU, showing its

complex behavior as response to typical disturbances.

It may be observed that the disturbance most difficult to

reject proved to be the coking rate factor, KC, although

the disturbance considered with the highest amplitude

change was the reactor�/main fractionator pressuredrop, DPfrac.

Investigations have been performed by simulation to

reveal incentives and limitations for implementing MPC.

The most favorable MPC control schemes, for each

investigated category, are: S1: 3�/3, S5: 4�/4, S10: 5�/

5. The last one is the most profitable, due to the large

number of controlled variables. It is interesting to notice

that S12: 5�/6 control scheme (containing an extra-manipulated variable), in its unconstrained form, does

not bring additional quality to MPC. But when con-

straints on manipulated variables are present, this

approach proves real improvements due to the ‘‘sur-

plus’’ of command able to compensate for those

manipulated variables limited by constraints. Compared

with the traditional decentralized PID control, MPC

presents better control performance based on its multi-variable feature, inherent prediction ability and capacity

to directly handle constraints using an even larger

number of manipulated than controlled variables. A

nonlinear MPC method has been proposed and inves-

tigated to account for process non-linearity based on

periodic updating of the linearized model used for

control action computation. This nonlinear MPC im-

plementation may lead to potential improvement by theuse of dynamic sensitivity analysis.

In practice, the MPC implementation is intended to

be performed in a two-layer structure: the layer of

decentralized PID loops stabilizing the main process

variables and the MPC layer adjusting the setpoints of

the underlying regulatory loops.

Benefits of better control performance in FCCU

operation mainly consist in the achievement of safe-keeping the controlled variables very close to the

constrained limits, where optimum operating conditions

usually lie.

Fig. 9. Controlled variables for constrained MPC (svscinf�/0.3,

svscsup�/0.4), scheme S12: 5�/6 in the presence of KC disturbance;

unconstrained MPC (solid), constrained MPC (dashed�/dotted), dis-

turbed process without control (dashed).


Detailed mathematical model of the UOP FCCU may

be found in Appendix B.

Appendix A: Nomenclature

Argc cross sectional area of regenerated catalyst

pipe (ft2)

Aris cross sectional area of reactor riser (ft2)

Asc cross sectional area of spent catalyst pipe

(ft2)

Astr cross sectional area of reactor stripper (ft2)

Asv cross sectional area of regenerated/spentcatalyst slide valve at completely open

position (in2)

[COR] catalyst to oil ratio

Ccat mass fraction of coke produces in the riser

Cpc heat capacity of catalyst (Btu/lb/F, J/kg/K)

Cpd heat capacity of steam (Btu/lb/F, J/kg/K)

Cpf heat capacity of the feed (Btu/lb/F, J/kg/K)

Cpfv heat capacity of feed vapor (Btu/lb/F, J/kg/K)

Crgc

(crgc)

coke fraction on regenerated catalyst (lb

coke/lb catalyst, kg coke/kg catalyst)

Csc (csc) coke fraction on spent catalyst in the stripper

(lb coke/lb catalyst, kg coke/kg catalyst)

Csc1 coke fraction on spent catalyst at riser outlet

(lb coke/lb catalyst, kg coke/kg catalyst)

C1 wet gas production constant (mol/lb feed,mol/kg feed)

C2 wet gas production constant (mol/lb feed/F,

mol/kg feed/K)

Ecf activation energy for coke formation (Btu/

mol, kJ/mol)

Ef activation energy for cracking the feed (Btu/

mol, kJ/mol)

Eg activation energy for cracking gasoline (Btu/mol, kJ/mol)

Elift elevation of the pipe for spent catalyst, inlet

in the regenerator (ft, m)

Eoil elevation of feed inlet in the riser (ft, m)

Estr elevation of the pipe for spent catalyst outlet

from the reactor (ft, m)

Etap elevation of the pipe for regenerated catalyst,

outlet from the regenerator (ft, m)Fcat flowrate of spent or regenerated catalyst

(t/min)

Ff total feed flowrate (lb/s, kg/s)

Frgc (frgc) regenerated catalyst flowrate (lb/s, kg/s)

Fsc (fsc) spent catalyst flowrate (lb/s, kg/s)

FV11

flow through wet gas compressor suction

valve V11 (mol/s, molg/s)

FV12

flow through valve V12 (mol/s, molg/s)FV

13flow through valve V13 (mol/s, molg/s)

Fwg wet gas production in the reactor (mol/s,

molg/s)

Ft air flowrate into regenerator (Nm3/h)

F3 fresh feed flowrate (lb/s, kg/s)

F4 slurry recycle flowrate (lb/s, kg/s)

hris height of the riser (ft, m)K flow coefficient for the slide valve (0.7)

Kc reaction rate constant for coke production

(s�1)

kr1 reaction rate constant for the total rate of

cracking of the feed oil (s�1)

kr3 reaction rate constant for the rate of

cracking gasoline to light gases and coke

(s�1)k12 wet gas V12 valve flow rating (mol/s psia1/2,

kg/s (N/m2)1/2)

Lrgc length of regenerated catalyst pipe (ft, m)

Lsc length of spent catalyst pipe (ft, m)

m manipulated variable (input) horizon

m* factor for the dependence of the initial

catalyst activity on Crgc

n model horizonN exponent for the dependence of Ccat on Crgc

N* integer value representing a constant for

pressure drop on catalyst pipes

p prediction horizon

Patm atmospheric pressure (psia, N/m2)

Prb pressure at the bottom of the riser (psia, N/

m2)

P4 reactor pressure (psia, N/m2)P5 main fractionator pressure (psia, N/m2)

P6 regenerator pressure (psia, N/m2)

R universal gas constant (ft3 psia/lb mol/R, J/

mol/K)

sv spent/regenerated catalyst slide valve posi-

tion (0�/1)

svsc spent catalyst slide valve position (0�/1)

svscinf spent catalyst slide valve lower limit con-straint (0.3)

svscsup spent catalyst slide valve higher limit con-

straint (0.4)

svrgc regenerated catalyst slide valve position

(0�/1)

t time (s)

tc catalyst residence time in the riser (s)

T sampling time (s)Tcyc regenerator stack gas temperature at cyclone

(F, K)

Tr temperature of reactor riser outlet (F, K)

Tref base temperature for energy balance (F, K)

Treg temperature of regenerator bed (F, K)

Ts temperature of stripper outlet (F, K)

T0 temperature of the feed entering the riser

after mixing with the catalyst (F, K)T2 furnace outlet temperature of the feed (F, K)

ulim vector of constraints imposed to the manip-

ulated variables ([0 0.3 0 0 0 0 1 0.4 1.98 0.5 1

0.8])


uwt (Gu) diagonal weighting matrix for the manipu-

lated variable move, in the optimization

index

v catalyst velocity in spent/regenerated pipe (ft/s, m/s)

vris volumetric flowrate in the riser

(ft3/s, m3/s)

V14 position of the stack gas valve (0�/1)

V7 position of the air vent valve (0�/1)

V11 position of the wet gas compressor suction

valve (0�/1)

V12 position of the flare valve (0�/1)Wr inventory of catalyst in the reactor (stripper)

(lb, kg)

Wris inventory of catalyst in the riser (lb, kg)

xO2,sg molar ratio of O2 to air in stack gas (mol O2/

mol air)

xCOsg molar ratio of CO to air in stack gas (mol

CO/mol air)

xCO2,sg molar ratio of CO2 to air in stack gas (molCO2/mol air)

yf mass fraction of feed oil

yg mass fraction of gasoline

ywt (Gy) diagonal weighting matrix for the error, in

the optimization index

za dimensionless distance along riser

zbed dense bed height (ft, m)

a catalyst deactivation constant (s�1)DHevp heat of vaporizing the feed oil (Btu/lb,

kJ/kg)

DHf heat of cracking (Btu/lb, kJ/kg)

DPelb,sc pressure drop on different elements of spent

catalyst pipe (psia, N/m2)

DPelb,rgc pressure drop on different elements

of regenerated catalyst pipe (psia,

N/m2)DPfrac pressure drop across reactor main fractio-

nator (psi, N/m2)

DPsv pressure drop on regenerated/spent catalyst

slide valve (psi)

DPsv,sc pressure drop on spent catalyst slide valve

(psia, N/m2)

DPsv,rgc pressure drop on regenerated catalyst slide

valve (psia, N/m2)f0 initial catalyst activity at riser inlet

l ratio of mass flowrate of dispersion steam to

mass flowrate of feed oil

rc density of catalyst in the dense phase (lb/ft3,

kg/m3)

rpart settled density of catalyst (lb/ft3, kg/m3)

rris average density of material in the riser (lb/ft3,

kg/m3)rv vapor density at riser conditions (lb/ft3, kg/

m3)

u dimensionless temperature in the riser

Appendix B: FCCU model description

The newly developed mathematical model for the

UOP type FCCU is based on the mechanistic AmocoModel IV FCCU [5]. Compared with Amoco Model IV,

the new mathematical model describes a different

FCCU type, both from the operation and from the

construction point of view. Different geometric dimen-

sions and relative position define the reactor and

regenerator in this case, compared with the Model IV

case. The regenerator of the presented UOP FCCU

operates in partial combustion mode. The reactor modeluses a Weekman kinetic model [9]. Catalyst circulation

is described including spent and catalyst valves on

catalyst circulation lines. These valves are used as

main manipulated variables for FCCU control.

The FCCU dynamic model has been developed on the

basis of reference construction and operation data from

an industrial unit. The described model is rather

complex succeeding to capture the major dynamicbehavior of UOP type FCCU [8]. The unit consists of

the following parts: feed and preheat system, reactor,

regenerator, air blower, wet gas compressor and catalyst

circulation lines [5,14].

B.1. Feed and preheat system

The feed and preheat system is presented in Fig. A1.

The total feed flow F3 enters the preheat furnace at T1

temperature and is heated by means of the gaseous fuelhaving F5 flowrate. The feed preheat dynamic behavior

is described by the following mass and energy balance

equations:

dT3

dt�

1

tfb

(F5DHfu�UAfTlm�Qloss) ; (A1)

Tlm�(T3 � T1) � (T3 � T2)

ln

�T3 � T1

T3 � T2

� ; (A2)

Qloss�a1F5T3�a2 ; (A3)

Fig. A1. Feed and preheat system.


dT2

dt�

1

tfo

(T2;ss�T2) ; (A4)

T2;ss�T1�UAfTlm

F3Cpf

: (A5)

B.2. Reactor and main fractionator model

Developing the new mathematical model for the

reactor implied a thorough survey, selection and thensynthesis, based on a large variety of models presented

in literature. The three-lump model has been considered

to be adequate for the global description of the

phenomena taking place in the reactor. Reactor is

divided in two parts: riser and stripper. The riser model

is built on the following assumptions: ideal plug flow

and very short transient time (the residence time in the

riser is very short compared with other time constants,especially with the regenerator time constants

[1,5,8,10].). It is modeled by mass balance describing

the gasoline and coke�/gases production based on

Weekman’s triangular kinetic model [9]. The mixed

nonlinear differential and algebraic system of equations

also accounts for the amount of coke deposited on

catalyst and for the cracking temperature dynamics [13].

The reactor is presented in Fig. A2.

B.2.1. Mass balance for the riser

Mass balance for the feed is described by the equation

dyf

dza

��K1y2f [COR]Ftc: (A6)

Mass balance for the gasoline is described by theequation

dyg

dza

� (a2K1y2f �K3yg)[COR]Ftc (A7)

where:

K1(u)�kr1 exp�Ef

RT0(1 � u); (A8)

K3(u)�kr3 exp�Eg

RT0(1 � u); (A9)

u� (T�T0)=T0;

F�f0 exp(�atc[COR]za); (A10)

f0�1�m�Crgc: (A11)

Inlet temperature in the riser T0 is determined by the

heat balance equation [3]

T0�FrgcCpcTreg � FfCpf T2 � DHevpFf

FrgcCpc � FfCpfv

: (A12)

The term K1yf2[COR] represents the kinetics of the

feed, K3yg[COR] the kinetics of the gasoline; F is a

function of catalyst deactivation due to coke deposition;

f0 the reduction of catalyst activity due to the cokeresident on the catalyst after regeneration; tc residence

time in the riser; a2�/k1/k2 fraction of feed oil that

cracks to gasoline. This model develops the models

presented by Lee and Groves [24], Shah et al. [25] and

Hovd and Skogestad [13]. The amount of coke produced

is described by the following correlation taken from

Voorhies and Kurihara [26]:

C cat�K c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitc

CNrgc

exp�Ecf

RTr

s: (A13)

The fraction of coke on the spent catalyst leaving the

riser is:

Csc1�Crgc�Ccat: (A14)

The constant values m* and N have been used to

perform a good fit of the mathematical model with

operating data from the industrial unit.

B.2.2. Heat balance for the riser

du

dza

�DHfFf

T0(FscCpc � FfCpf � lFf Cpd)

dyf

dza

: (A15)

The amount of gases produced by cracking is

described by the equation:

Fwg�(F3�F4)[C1�C2(Tr�Tref )]:: (A16)

Constants C1and C2 have been fitted based on data

from the industrial unit.

Fig. A2. FCCU reactor.


The stripper model is of CSTR type (mass and heat

balance) evaluating the temperature in the stripper and

the fraction of coke on spent catalyst.

B.2.3. Mass and heat balance for the stripper

dTs

dt�

Frgc

Wr

(Tr�Ts); (A17)

dCsc

dt�

�Frgc(Crgc�Ccat)�FscCsc�Csc

dWr

dt

�1

Wr

; (A18)

dWr

dt�Frgc�Fsc: (A19)

B.2.4. Pressure balance for riser bottom pressure

determination

Prb�P4�rrishris

144; (A20)

rris�F3 � F4 � Frgc

nris

; (A21)

nris�F3 � F4

rv

�Frgc

rpart

: (A22)

The amount of catalyst in the riser is determined by

the equation

Wris�FrgcArishris

nris

: (A23)

B.2.5. Momentum balance for reactor and main

fractionator pressure determination

dP5

dt�0:833(Fwg�FV11

�FV12�FV13

) (A24)

FV12�k12V12


p: (A25)

A constant pressure drop, DPfrac, between reactor and

main fractionator is considered; according to this, the

reactor pressure is computed by the equation

P4�P5�DPfrac: (A26)

B.3. Regenerator model

The mathematical model for the regenerator presents

a higher complexity due to the importance of this system

in determining the time constant for the entire FCCU.

The regenerator is considered divided in two zones: a

dense bed zone and a zone of entrained catalyst (the

disengaging zone) (Fig. A3).

The dense bed zone consists of two phases: a bubblephase of gaseous reactants and products moving up the

bed in plug flow and a perfectly mixed dense phase

containing gases and solid catalyst.

Mass transfer occurs between the two phases but at

regenerator temperatures the reaction rates are control-

ling, rather than mass transfer between the two phases.

Since the dense phase is considered perfectly mixed, the

temperature is assumed uniform in the bed and thegaseous phase in equilibrium with dense phase. Catalyst

is present in the zone above dense bed due to entrain-

ment. The amount of catalyst decreases with the

regenerator height. In the entrained catalyst zone the

CO combustion is dominant (the amount of catalyst is

diminished) having an important heat contribution. The

operating conditions are corresponding to CO partial

combustion mode.The model consists in mass and heat balance equa-

tions for O2, CO, CO2 and coke, but also in heat balance

equations for solid and gaseous phase. These balance

equations are correlated with equations describing

entrained catalyst (bed characteristics) in the zone above

dense bed, catalyst flow and pressure in the regenerator.

B.3.1. Heat balance

The dense phase of the bed is assumed perfectly mixed

due to the intense circulation of the catalyst. It is also

considered that the entire amount of hydrogen depositedon the catalyst is burned in the regenerator. Partial

combustion mode is considered compared to Model IV

FCCU [5].

Fig. A3. FCCU regenerator.


The heat balance of the dense bed is described by the

equations:

[WregCpc�M1]dTreg

dt�Qin�Qout; (A28)

Qin�Qair�QH�QC�Qsc

Qout�Qfg�Qrgc�Qe;(A29)

Qair�FairCpair(Tair�Tbase); QH�FHDHH; (A30)

QC�Fair(XCO;sgDH1�XCO2;sgDH2); (A31)

Qsc�FscCpc(Tsc�Tbase); (A32)

Qfg� [Fair(XO2;sgCpO2�XCO;sgCpCO�XCO2 ;sgCpCO2

�0:79CpN2)�0:5FHCpH2O](Tcyc�Tbase); (A33)

Qrgc�FrgcCpc(Treg�Tbase); (A34)

FH�Fsc(Csc�Crgc)CH: (A35)

The heat balance in the disengaging zone is described

by:

Cp(z)�0:79CpN2�XCO(z)CpCO�XCO2

(z)CpCO2

�XO2(z)CpO2

� [0:5CpH2OFH�dzCpcMe]

� 1

Fair

; dz�0 z]zcyc;

�dz�1 zBzcyc: (A37)

Carbon balance:

dCrgc

dt�

1

Wreg

�dWc

dt�Crgc

dWreg

dt

�; (A38)

dWreg

dt�Fsc�Frgc; (A39)

dWc

dt�(FscCsc�FH)

� [FrgcCrgc�12Fair(XCO;sg�XCO2;sg)]: (A40)

Mass balance on oxygen, carbon monoxide and

carbon dioxide are given by:

dXO2

dz� [100(�0:5k1�k2)rB(z)Crgc�k3XCO(z)]

� XO2(z)

ns

; (A41)

dXCO(z)

dz� [100k1rB(z)Crgc�2k3XCO(z)]

XO2(z)

ns

; (A42)

dXCO2(z)

dz��

dXO2(z)

dz�0:5

dXCO(z)

dz; (A43)

XCO2(z)�XO2

(0)�XO2(z)�0:5XCO(z); (A44)

XO2(0)�

1

Fair

(0:21Fair�0:25FH); (A45)

CO2 ;sg�100FairXO2

Fsg

; (A46)

CCO;sg�106 � 28XCO

28XCO � 44XCO2� 32XO2

� 22:12: (A47)

Volume fraction of catalyst is given by the following

equations:

drB(z)

dz�0; rB(z)�1�oe 05z5zbed; (A48)

drB(z)

dz�

�1000FairrB(z)

Aregnsrc;dilute

zbedBz5zcyc; (A49)

oe�min

�1; max

�of ; of

�1:904 � 0:363ns � 0:048n2

s

zbed

��; (A50)

of �0:332�0:06ns: (A51)

The mass flow of entrained catalyst leaving the dense

bed is described empirically by the following equations:

Me�Aregnsrc;dilute (A52)

where:

rc;dilute�1�0:582ns; (A53)

dTreg(z)

dz�0 05z5zbed;

dTreg(z)

dz�

�DH1

dXCO(z)

dz�DH2

dXCO2(z)

dz

�1

Cp(z)zbedBz5zcyc;

(A36)


ns�Fsg � Fair

2

1

rgAreg

; (A54)

rg�520P6

379 � 14:7(Treg � 459:6): (A55)

B.3.2. Pressure balance

It is assumed an ideal gas behavior for regenerator

gases. The regenerator pressure is described by the

equations given below:

dP6

dt�

R

Vreg;g

�n

dTreg

dt�(Treg�459:6)

dn

dt

�; (A56)

dn

dt�Fair�Fsg ; (A57)

Vreg;g�Aregzcyc�Aregzbed(1�oe); (A58)

Prgb�P6�Wreg

144Areg

; (A59)

DPRR�P6�P4: (A60)

The bed height is described by the empirical equation

zbed�min

�zcyc;

�2:85�0:8ns�

Wreg � rc;diluteAregzcyc

Aregrc;dense

�

��

rc;dense

rc;dense � rc;dilute

��;

�rc;dense�rpart(1�of ): (61)

B.4. Air blower model

The air blower is a centrifugal compressor driven by a

steam turbine (Fig. A4). A head-capacity performance

equation describes suction flowrate as a function of

discharge pressure with suction at normal atmospheric

pressure:

Fsucn;comb�48 000

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:581�109�1:249�106P2

base

q; (A62)

Pbase�14:7P2

P1

; (A63)

F7�kcomb

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP2�Prgb

q�Fair; (A64)

FV6�k6fpp(V6)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPatm�P1

p; (A65)

FV7�k7fpp(V7)


p: (A66)

B.5. Wet gas compressor

Wet gas compressor is of centrifugal type (Fig. A5). It

is driven by an electric motor. It is assumed that the wet

gas compressor is pumping against a constant pressure

in the downstream vapor recovery unit.

Wet gas compressor equation is described below:

Fsucn;wg�4353:5�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:366�108�0:1057H 2

wg

q; (A67)

Hwg�182:922(C 0:0942rw �1) ; (A68)

Crw�Pvru

P7

: (A69)

The suction pressure of the wet gas compressor is

described by the equations:

dP7

dt�5(FV11

�F11); (A70)

FV11�k11fpp(V11)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP5�P7

p; (A71)

fpp(x)�e2ln[(0:15)�(1�x)] x�0:5fpp(x)�0:3x x50:5

; (A72)

FV13�k13V13Pvru: (A73)

Fig. A4. Regenerator combustion air blower. Fig. A5. Wet gas compressor.


B.6. Model of the catalyst circulation lines

For the catalyst flow in the spent and regenerated

catalyst circulation lines (piping), a steady state behavioris assumed. It is considered that dynamics of the lines is

very fast compared to the time constants of other

subsystems of the FCCU. Equations such as Eq. (A77)

have been used to fit the pressure drops in the model

with data from the industrial unit.

Spent and regenerated catalyst circulation considers a

single-phase flow, based on force balance [14]. For the

regenerated catalyst line the equation is:

144(P6�Prb)�zbedrc�(Etap�Eoil)rc�DPsv;rgc

�DPelb;rgc�FrgcLrgcfrgc

A2rgcrc

�0; (A74)

and for the spent catalyst line the force balance is given

by:

144(P4�P6)�(Estr�Elift)rc�Wr

Astr

�DPsv;sc�DPelb;sc�FscLscfsc

A2scrc

�0: (A75)

The pressure drop on the slide valves is described by

the following equation:

DPsv��

50Fcat

KAsvsv

�2 144

rc

: (A76)

Pressure drop on other pipe restrictions are given by

equations of the type:

DPelb�1

2N�rcv

2: (A77)

Appendix C: Nomenclature

Areg cross sectional area of regenerator

(ft2, m2)

Aris cross sectional area of reactor

riser (ft2, m2)Astr cross sectional area of reactor

stripper (ft2, m2)

Argc cross sectional area of regener-

ated catalyst pipe (ft2, m2)

Asc cross sectional area of spent

catalyst pipe (ft2, m2)

Asv cross sectional area of regener-

ated/spent catalyst slide valve atcompletely open position (in2/m2)

a1 furnace heat lost parameter (Btu/

ft3/F, J/m3/K)

a2 furnace heat lost parameter (Btu/

s, J/s)

Ccat mass fraction of coke produces in

the riserCCO,sg concentration of carbon monox-

ide in stack gas (ppm)

CH mass fraction of hydrogen in coke

[COR] catalyst to oil ratio

CO2,sg concentration of oxygen in stack

gas (% mol)

Cp (z ) average heat capacity (Btu/mol/F,

J/mol/K)Cpair heat capacity of air (Btu/mol/F, J/

mol/K)

Cpc heat capacity of catalyst (Btu/lb/

F, J/kg/K)

CpCO heat capacity of carbon monoxide

(Btu/mol/F, J/mol/K)

CpCO2

heat capacity of carbon dioxide

(Btu/mol/F, J/mol/K)Cpf heat capacity of the feed (Btu/lb/

F, J/kg/K)

Cpfv heat capacity of feed vapor (Btu/

lb/F, J/kg/K)

Cpd heat capacity of steam (Btu/lb/F,

J/kg/K)

CpN heat capacity of nitrogen (Btu/

mol/F, J/mol/K)CpO

2heat capacity of oxygen (Btu/mol/

F, J/mol/K)

Csc coke fraction on spent catalyst in

the stripper (lb coke/lb catalyst,

kg coke/kg catalyst)

Csc1 coke fraction on spent catalyst at

riser outlet (lb coke/lb catalyst, kg

coke/kg catalyst)Crgc coke fraction on regenerated cat-

alyst (lb coke/lb catalyst, kg coke/

kg catalyst)

Crw wet gas compressor compression

ratio

C1 wet gas production constant (

mol/lb feed, mol/kg feed)

C2 wet gas production constant(mol/lb feed/F, mol/kg feed/K)

Ecf activation energy for coke for-

mation (Btu/mol, KJ/mol)

Ef activation energy for cracking the

feed (Btu/mol, KJ/mol)

Eg activation energy for cracking

gasoline (Btu/mol, KJ/mol)

Elift elevation of the pipe for spentcatalyst, inlet in the regenerator

(ft, m)

Eoil elevation of feed inlet in the riser

(ft, m)


Estr elevation of the pipe for spent

catalyst outlet from the reactor

(ft, m)

Etap elevation of the pipe for regener-ated catalyst, outlet from the

regenerator (ft, m)

Fair air flowrate into regenerator

(mol/s, molg/s)

Fcat flowrate of spent or regenerated

catalyst (lb/s, kg/s)

Fcoke production of coke in the riser (lb/

s, kg/s)Ff total feed flowrate (lb/s, kg/s)

FH burning rate of hydrogen (lb/s,

kg/s)

fpp(x) nonlinear valve flowrate function

Frgc regenerated catalyst flowrate (lb/

s, kg/s)

Fsc spent catalyst flowrate (lb/s, kg/s)

Fsg stack gas flowrate (mol/s, molg/s)Fsucn,comb combustion air blower suction

flow (ICFM, m3/s)

Fsucn,wg wet gas compressor inlet suction

flow (ICFM, m3/s)

ffrgc friction constant for pipe-regen-

erated catalyst flow (lbf s/ft2, N s/

m2)

ffsc friction constant for pipe-spentcatalyst flow (lbf s/ft2, N s/m2)

FV6

flow through combustion air

blower suction valve V6 (lb/s, kg/

s)

FV7

flow through combustion air

blower vent valve V7 (lb/s, kg/s)

FV11

flow through wet gas compressor

suction valve V11 (mol/s, molg/s)FV

12flow through valve V12 (mol/s,

molg/s)

FV13

flow through valve V13 (mol/s,

molg/s)

Fwg wet gas production in the reactor

(mol/s, molg/s)

F1 oil flowrate (lb/s, kg/s)

F2 oil flow rate (lb/s, kg/s)F3 fresh feed flowrate (lb/s, kg/s)

F4 slurry recycle flowrate (lb/s, kg/s)

F5 furnace fuel flowrate (scf/s, m3/s)

F6 combustion air blower through-

put (lb/s, kg/s)

F7 combustion air flow to the re-

generator (lb/s, kg/s)

F11 wet gas flow to vapor recoveryunit (mol/s, molg/s)

hris height of the riser (ft, m)

K flow coefficient for the slide valve

(0.7)

Kc reaction rate constant for coke

production (s�1)

k1 reaction rate constant (s�1)

kr1 reaction rate constant for thetotal rate of cracking of the feed

oil (s�1)

k2 reaction rate constant (s�1)

kr2 reaction rate constant for the rate

of cracking of feed oil to gasoline

(s�1)

k3 reaction rate constant (mol air/s

mol CO)kr3 reaction rate constant for the rate

of cracking gasoline to light gases

and coke (s�1)

k6 combustion air blower suction

valve flow rating (lb/s psia1/2, kg/s

(N/m2)1/2)

k7 combustion air blower vent valve

flow rating (lb/s psia1/2, kg/s (N/m2)1/2)

k11 wet gas compressor suction valve

flow rating (mol/s psia1/2, kg/s (N/

m2)1/2)

k12 wet gas V12 valve flow rating

(mol/s psia1/2, kg/s (N/m2)1/2)

k13 wet gas V13 valve flow rating

(mol/s psia1/2, kg/s (N/m2)1/2)k14 regenerator stack gas valve flow

rating (mol/s psia1/2, kg/s (N/

m2)1/2)

Lrgc length of regenerated catalyst

pipe (ft, m)

Lsc length of spent catalyst pipe (ft,

m)

M polytropic exponentm* factor for the dependence of

the initial catalyst activity on Crgc

MI effective heat capacity of regen-

erator mass (Btu/F, KJ/K)

Me flowrate of entrained catalyst

from dense bed (lb/s, Kg/s)

N exponent for the dependence of

Ccat on Crgc

N* integer value representing a con-

stant for pressure drop on cata-

lyst pipes

n quantity of gas (mol)

Patm atmospheric pressure (psia, N/m2)

Prb pressure at the bottom of the riser

(psia, N/m2)

Prgb pressure at the bottom of theregenerator (psia, N/m2)

Pvru discharge pressure of wet gas

compressor in vapor recovery

unit (psia, N/m2)


P1 combustion air blower suction

pressure (psia, N/m2)

P2 combustion air blower discharge

pressure (psia, N/m2)P4 reactor pressure (psia, N/m2)

P5 main fractionator pressure (psia,

N/m2)

P6 regenerator pressure (psia,

N/m2)

P7 wet gas compressor suction pres-

sure (psia, N/m2)

Qair enthalpy of air to regenerator(Btu/s, J/s)

QC total heat of burning coke (Btu/s,

J/s)

Qcatout enthalpy of catalyst out of the

riser (Btu/s, J/s)

Qe total heat lost from regenerator to

environment (Btu/s, KJ/s)

Qfg enthalpy of stack gas exiting theregenerator (Btu/s, J/s)

QH enthalpy of hydrogen to regen-

erator (Btu/s, J/s)

Qin enthalpy into regenerator, reac-

tor(Btu/s, J/s)

Qout enthalpy out of regenerator, re-

actor(Btu/s, J/s)

Qloss heat loss from furnace (Btu/s, J/s)Qrgc enthalpy of regenerated catalyst

(Btu/s, J/s)

Qsc enthalpy of spent catalyst (Btu/s,

J/s)

R universal gas constant (ft3 psia/lb

mol 8R, J/mol 0K)

svsc spent catalyst slide valve position

svrgc regenerated catalyst slide valveposition

Tair temperature of air entering re-

generator (F, K)

Tatm atmospheric temperature (F, K)

Tbase base temperature (F, K)

Tcomb,d combustion air blower discharge

temperature (F, K)

Tcyc regenerator stack gas temperatureat cyclone (F, K)

Tdiff temperature difference between

cyclone and regenerator bed

temperature (F, K)

Tlm furnace logarithmic mean tem-

perature (F, K)

Tr temperature of reactor riser outlet

(F, K)Tref base temperature for energy bal-

ance (F, K)

Treg temperature of regenerator bed

(F, K)

Ts temperature of stripper outlet (F,

K)

Tsc temperature of spent catalyst en-

tering regenerator (F, K)T0 temperature of the feed entering

the riser after mixing with the

catalyst (F, K)

T1 temperature of the fresh feed

entering the furnace (F, K)

T2 furnace outlet temperature of the

feed (F, K)

T2,ss steady state furnace outlet tem-perature of the feed (F, K)

T3 furnace firebox temperature (F,

K)

tc catalyst residence time in the riser

(s)

UAf furnace overall heat transfer

coefficient (Btu/s/F, J/s/K)

Vcomb,d combustion air blower dischargesystem volume (ft3, m3)

Vcomb,s combustion air blower suction

system volume (ft3, m3)

Vreg,g regenerator volume occupied by

gas (ft3, m3)

v catalyst velocity in spent/regener-

ated pipe (ft/s, m/s)

vrgc velocity of regenerated catalyst(ft/s, m/s)

vris volumetric flowrate in the riser

(ft3/s, m3/s)

vs superficial velocity in the regen-

erator (ft/s, m/s)

vsc velocity of spent catalyst (ft/s, m/

s)

vslip slip velocity (ft/s, m/s)V6, V7, V8, V9, V11,

V12, V13, V14

position of the corresponding

valves (0�/1)

Wc inventory of carbon in the regen-

erator (lb, kg)

Wr inventory of catalyst in the reac-

tor (stripper) (lb, kg)

Wreg inventory of catalyst in the re-

generator (lb, kg)Wris inventory of catalyst in the riser

(lb, kg)

XCO molar ratio of CO to air (mol CO/

mol air)

XCO,sg molar ratio of CO to air in stack

gas (mol CO/ mol air)

XCO2

molar ratio of CO 2 to air (mol

CO2/mol air)XCO

2,sg molar ratio of CO2 to air in stack

gas (mol CO2/ mol air)

XN molar ratio of N2 to air (mol N2/

mol air)


XO2

molar ratio of O2 to air(mol O2/

mol air)

XO2,sg molar ratio of O2 to air in stack

gas (mol O2/ mol air)yf mass fraction of feed oil

yg mass fraction of gasoline

z distance along riser (ft, m)

za dimensionless distance along

riser

zbed dense bed height (ft, m)

zcyc height of cyclone inlet (ft, m)

ztop height of O2 and CO measure-ment point (ft, m)

a catalyst deactivation constant

(s�1)

DHf heat of cracking (Btu/lb, KJ/kg)

DHevp heat of vaporizing the feed oil

(Btu/lb, KJ/kg)

DHfu heat of combustion of furnace

fuel (Btu/SCF, KJ/m3)DHH heat of combustion of hydrogen

(Btu/lb, KJ/kg)

DH1 heat of formation of CO (Btu/

mol, J/mol)

DH2 heat of formation of CO2 (Btu/

mol, J/mol)

DPfrac pressure drop across reactor main

fractionator (psi, N/m2)DPRR pressure difference between re-

generator and reactor (psi, N/m2)

DPsv pressure drop on regenerated/

spent catalyst slide valve (psi)

DPsv,rgc pressure drop on regenerated

catalyst slide valve (psia, N/m2)

DPelb,rgc pressure drop on different ele-

ments of regenerated catalyst pipe(psia, N/m2)

DPsv,sc pressure drop on spent catalyst

slide valve (psia, N/m2)

DPelb,sc pressure drop on different ele-

ments of spent catalyst pipe (psia,

N/m2)

oe effective void fraction in regen-

erator dense phase bedof apparent void fraction in regen-

erator dense phase bed

f0 initial catalyst activity at riser

inlet

u dimensionless temperature in the

riser

l ratio of mass flowrate of disper-

sion steam to mass flowrate offeed oil

hp polytropic efficiency

rairg density of air at regenerator con-

ditions (lb/ft3, kg/m3)

rB volume fraction of catalyst (lb/ft3,

kg/m3)

rc,dilute density of catalyst in the dilute

(disengaging) phase (lb/ft3, kg/m3)rc,dense density of catalyst in the dense

phase (lb/ft3, kg/m3)

rg density of exit gas (lb/ft3,

kg/m3)

rpart settled density of catalyst (lb/ft3,

kg/m3)

rris average density of material in the

riser (lb/ft3, kg/m3)rv vapor density at riser conditions

(lb/ft3, kg/m3)

tfb furnace firebox constant (Btu/F,

J/K)

tfo furnace time constant (s)

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[petroleum] - uop fluid catalytic cracking unit

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