561228

Chemical Engineering Science 56 (2001) 1973}1990

Dynamic modeling and simulation of a #uidized catalytic crackingprocess. Part II: Property estimation and simulation

In-Su Han, Chang-Bock Chung*Faculty of Applied Chemistry, Chonnam National University, Kwangju 500-757, South Korea

Received 16 December 1999; received in revised form 18 August 2000; accepted 5 September 2000

Abstract

A dynamic simulator was developed which implements the detailed dynamic model for an FCC process and the model solverpresented in Part I of this paper. The simulator incorporates the correlation equations developed in this study for the thermodynamicproperties and transport parameters contained in our model. First, the simulator was validated by comparing the overall steady-statebehavior of the system with those in the literature. Then, base case steady-state pro"les were obtained for major process variables inthe reactor riser and regenerator of an industrial scale FCC unit. Next, the issue of multiple steady states in FCC operations wasaddressed and con"rmed by investigating the sensitivity of our model to initial conditions. Finally, the dynamic responses to stepchanges in three major process inputs were presented and discussed with an emphasis on the interaction between the reactor andregenerator dynamics. � 2001 Published by Elsevier Science Ltd.

Keywords: Fluid catalytic cracking; Dynamic simulator; Property estimation; Multiple steady states; Sensitivity

1. Introduction

Dynamic simulations have been widely used in chem-ical process engineering to predict and analyze the dy-namic behavior of chemical processes. An accurate ande$cient dynamic simulator is recognized as a valuabletool for various studies on advanced control, online op-timization, hazard analysis, and operator training. Sincea typical FCC unit processes a large amount of feedstockinto products of additional value, a re"nery can achieveenormous economic bene"ts from such process improve-ment studies.

A detailed dynamic model of an FCC process wasdeveloped in Part I of this paper on the basis of conserva-tion principles. Then an e$cient model solver was con-structed on the basis of a modular approach where themodel equations were grouped into 12 modules eachcorresponding to a speci"c part of the process andtype of equations. The model and numerical algorithmsdeveloped in the previous part are implemented by a

*Corresponding author. Tel.: #82-62-530-1884; fax: #82-62-530-1899.E-mail address: [email protected] (C.-B. Chung).

dynamic simulator written in Fortran. Since our dynamicsimulator for #uid catalytic crackers (called DSim-FCC)takes the structure of Fortran 90 module procedurescomprising versatile subprogram units (Meissner, 1995),it can be easily modi"ed when one wants to extend thesimulator function or to append additional modules.Interested readers can obtain the dynamic simulator bywriting to the authors.

This paper presents the simulation and its results ob-tained using DSim-FCC. First, the estimation techniqueis presented for the thermodynamic properties andtransport parameters contained in our model. Thecorrelation equations for each property estimated onthe basis of data in the various literatures are presentedin detail in the Appendix A. Next, to show the validityof our simulator, the steady-state behavior of thesystem is compared with those in the literature. Then,steady-state pro"les of major process variables alongthe axial position of the riser and regenerator areshown and compared with other information in the liter-ature for an industrial scale FCC unit. The issueof multiple steady states in FCC operations is alsoaddressed and con"rmed by investigating the sensitivityof our model to initial conditions. Finally, the dynamicresponses to step changes in major process inputs arepresented and discussed.

0009-2509/01/$ - see front matter � 2001 Published by Elsevier Science Ltd.PII: S 0 0 0 9 - 2 5 0 9 ( 0 0 ) 0 0 4 9 4 - 2

Fig. 1. Schematic diagram of a side-by-side type FCC unit.

2. Property estimation

The dynamic model upon which our simulator DSim-FCC is based contains numerous property parametersthat have to be speci"ed before carrying out simulationruns. The parameters mainly consist of the thermo-dynamic properties of the substances that are involvedeither in cracking reactions or in coke burning reactionsand the transport parameters between two phases inthe reactor riser and the regenerator. Since thecracking reaction mixture comprising numerous hydro-carbon species is represented by the four lumps (gasoil, gasoline, light gases, and coke) in this study, itis necessary to estimate the properties of each lumpusing an appropriate characterization method forpetroleum fractions. It is also necessary to developcorrelation equations that express the properties asfunctions of system temperature and pressure. Thissection brie#y describes the scheme used in this paperto develop such correlation. The correlation equationsincorporated in our simulator are presented in detail inthe Appendix A.

True boiling point (TBP) or American Society forTesting and Materials D86 (ASTM D86); ASTM Com-mittee D-2, 1991 distillations are two standard methodsto characterize crude oil or petroleum fractions that havea wide range of boiling points. Once either distillationcurve is obtained experimentally, it can be converted intothe other and can be used to calculate average boilingpoints of various types. The average boiling point thusobtained and the speci"c gravity measured in the labtogether form the basis for estimating other physicalproperties of the petroleum fraction such as averagemolecular weight, heat capacity, vapor pressure, and soon. Hence the physical properties of the gas oil andgasoline lumps that are included in our FCC model arecorrelated with the average boiling points and speci"cgravity as well as with the process temperature andpressure. It should be noted that the correlation equa-tions presented in Appendix A include several empiricalequations that were developed in this study by nonlinearregression of literature data.

The heat capacities and viscosities of the light gases(C

�}C

�) and the products of coke burning reactions are

expressed as functions of temperature only. Since thelight gases are treated as a single lump in our model, itsproperty is assumed independent of composition. For thepurpose of property estimation, however, it is assumedthat the light gas lump has typical composition as foundin "eld operations and that its property can be calculatedas a weighted sum of component properties.

Our dynamic model postulates two-phase tubular re-actor models for the reactor riser and as well as the densebed and freeboard of the regenerator. The parametersassociated with the heat and mass transfer between thesetwo phases are thermal conductivities, heat transfer coef-

"cients, di!usivities, and mass transfer coe$cients. Asshown in Appendix A, these parameters are estimatedusing correlation equations either found in the literature(Baird & Rice, 1975; Kunii & Levenspiel, 1991) or ob-tained by nonlinear regression of literature data (Tech-nical Data Committee, 1988).

3. Simulations and discussions

The simulator DSim-FCC was used to investigate thebehavior of a side-by-side type FCC unit shown in Fig. 1.Recall that the dynamic model presented in Part I of thispaper was found to have 13 degrees of freedom that hasto be speci"ed before carrying out an open-loop simula-tion. Table 1 lists 13 variables chosen in this study asspeci"cations of the degrees of freedom as well as eightparameters related to feedstock characteristics and sixparameters related to ambient air characteristics. Fromthe viewpoint of process control, these 27 variables rep-resent either external disturbances to the process or pro-spective manipulated variables in a certain controlcon"guration. From the viewpoint of dynamic simula-tion, they represent process inputs whose values can bealtered during the execution of the simulator in order toobtain dynamic responses to such changes. Table 1 alsolists the assumed values of the 27 inputs at the base caseoperating conditions. Table 2 lists the dimensionsof an 30,000 BPD FCC unit assumed in this study.Table 3 shows the properties of the catalyst and coke,and Table 4 lists the kinetic parameters of crackingreactions and coke burning reactions. The kinetic para-meters of the four-lump cracking reactions in Table 4were reported by Ancheyta-Juarez, Lopez-Isunza,

1974 I.-S. Han, C.-B. Chung / Chemical Engineering Science 56 (2001) 1973}1990

Table 1Process inputs and base case operating conditions

Type Variable Description Base case operatingconditions

F��

Entrance #ow rate of liquid feedstock 49.3 kg/s¹��

Entrance temperature of liquid feedstock 535 KF�

Flow rate of the air entering the regenerator 34.0 kg/s¹�

Temperature of the air entering the regenerator 432 KF��

Flow rate of stripping steam 1.1 kg/s¹��

Temperature of stripping steam 430 KF��

Flow rate of dispersion steam 1.6 kg/sDegrees of freedom ¹

��Temperature of dispersion steam 430 K

P��

Pressure at main-fractionator 185.5 kPaP�

Downstream pressure of the stack gas valve 110.0 kPax��

Stem position of the slide valve on theregenerated catalyst transport line 0.57

x��

Stem position of the slide valve on the spentcatalyst transport line 0.46

x�

Stem position of the regenerator stack gas valve 0.70

¹��

, ¹��

, ¹��

, ¹��

, ¹��

TBP distillation temperatures at distilled vol% 554.3,605.4,equal to 10, 30, 50, 70, and 90, 647.0, 688.2,

Feedstock characteristics respectively. and 744.8 K, respectively.S�

Speci"c gravity of liquid feedstock 0.894 (API: 26.8)R�

Aromatics to naphthenes weight ratio in feedstock 2.1>��

Weight fraction of Conradson carbon residue in feedstock 0.5 wt%

f ��

, f ��

, f ��

, f � ��

, f ��

Composition of ambient air 0.2097, 0, 0.0003, 0, andAmbient air characteristics 0.79, respectively.

¹�

Ambient air temperature 300 K

Table 2Dimensions of the simulated FCC unit

Process unit Dimension

Length (m) Diameter (m)Riser 30.0 1.1Disengaging section 8.5 5.1Stripping section 6.2 3.2Regenerator 18.0 8.2Spent catalyst transport line 10.5 0.8Regenerated catalyst transport line 12.5 0.8

Total no. of cyclones equipped Dimensions of cyclone inlet (m)Reactor cyclones 2 0.8 (H)/0.4 (W)Regenerator cyclones 2 1.0 (H)/0.5 (W)

Table 3Characteristics of catalyst and coke used in simulations

CatalystAverage particle diameter 7�10�� mMinimum particle diameter 2�10�� mSphericity 0.72Density 1410 kg/m�

Speci"c heat 1.15 kJ/(kg K)

CokeDensity The same as catalystSpeci"c heat The same as catalystAtomic ratio of hydrogen to carbon 1.2

Aguila-Rodriguez, and Moreno-Mayorga (1997). Theheats of cracking reactions were roughly estimated bytrial-and-error to match the calculated riser outlet tem-perature with a typical operation temperature reportedby Callahan and Ushiba (1988). The kinetic parametersfor oxidation of coke, homogeneous and catalytic oxida-tions of carbon monoxide were adopted from the papersof Morley and de Lasa (1987), Howard, Williams, andFine (1973), and Ali and Rohani (1997), respectively. Theintrinsic CO

�/CO molar ratio was estimated using the

empirical equations proposed by Errazu, de Lasa, andSarti (1979).

I.-S. Han, C.-B. Chung / Chemical Engineering Science 56 (2001) 1973}1990 1975

Table 4Kinetic parameters of cracking and coke burning reactions

Four-Lump cracking reactionFrequency factor (s��) Activation energy (kJ/kg mol) Heat of reaction (kJ/kg)

Gas oil to gasoline 1457.50 57 359 195Gas oil to C

�}C

�gases 127.59 52 754 670

Gas oil to coke 1.98 31 820 745Gasoline to C

�}C

�gases 256.81 65 733 530

Gasoline to coke 6.29�10�� 66 570 690Catalyst deactivation �

��

"1.1�10�� E��

"49 000 kJ/kg mol �H��

"0.1177

Coke burning reaction and oxidation

Frequency factor Activation energy (kJ/(kg mol)Coke burning reaction 1.4�10� m�/(kg mol s) 125000CO oxidation (non-catalytic) 3.5�10� m�/(kg mol s) 165000CO oxidation (catalytic) 247.75 m��/(kg mol�� kg s) 70 480Intrinsic CO

�/CO molar

ratio �"0.000953 exp(5585/¹)�H

��"!4800.22#16.1¹, kJ/kg mol

�H��

"!10 364.88#34.60¹#0.00055¹�, kJ/kg molHeat of formation �H

��"!118975.04#27.61¹#0.00251¹�, kJ/kg mol

�H��

"!406909.11#43.26¹#0.00575¹�, kJ/kg mol�H

� ��"!252111.38#34.39¹#0.000315¹�, kJ/kg mol

The simulation results presented in this section coverboth the steady state and dynamic responses of the FCCunit described previously. First, steady-state responseswere obtained by executing the simulator for a su$-ciently long time until all the variables lined out. Thesesteady-state simulations were carried out many timeseach with altered values of the two major operatingvariables (the catalyst circulation rate (F

�) and the air

#ow rate into the regenerator (F�)). Then, the simulation

results were compared with those in the literature. Inaddition, the predicted pro"les of several process vari-ables are plotted along the height of reactor riser orregenerator for the base case operating conditions. Next,the multiple steady states in FCC operations were con-"rmed by investigating the sensitivity of our model toinitial conditions. Finally, the dynamic responses of theprocess to step changes in several process input variableswere predicted and analyzed.

3.1. Comparison of steady-state behavior with the previousmodels

In this section we show the validity of our simulatorby comparing our simulation results with thosefrom the previous FCC models. Although direct andqualitative comparison is not feasible due to di!erentkinetics and unavailability of simulation data, weinvestigate the overall steady-state behavior of the FCCunit as functions of the catalyst circulation and the air#ow rate.

Fig. 2 shows the steady-state behavior of majorstate variables as functions of the air-#ow rate when the

catalyst circulation rate is "xed at a speci"ed value of 250or 300 kg/s. Fig. 2a shows that with decreasing air #owrate the oxygen concentration gradually decreases untilalmost all the oxygen is exhausted. In this transition thesystem moves from a so-called full-combustion mode toa partial-combustion mode (Arbel, Huang, Rinard, Shin-nar, & Sapre, 1995a; Arbel, Rinard, Shinnar, & Sapre,1995b). The point of transition in combustion mode canbe easily located at the maximum points of the curves forthe regenerator and reactor temperatures in Fig. 2b.Alternatively, this point corresponds to either the max-imum points of the gas-oil conversion or the minimumpoints of the coke on catalyst in Fig. 2c. The resultsshown in Fig. 2 exhibit good matches with the "eldobservations and simulation results of Arbel et al. (1995a)not only in terms of qualitative trend but also in terms ofthe slopes of the curves.

Fig. 3 shows the steady-state behavior of major statevariables as functions of the catalyst circulation ratewhen the air #ow is "xed at a speci"ed value of 35 or40 kg/s. As the catalyst circulation rate increases, the COcombustion in the regenerator transits from a full com-bustion mode to a partial combustion model with ac-companying changes in the state variables. Again, theseresults are in good agreement with Arbel et al. (1995a).The steady-state behavior of the regenerator temperatureshown in Fig. 3b is also analogous to that of Kumar,Chadha, Gupta, and Sharma (1995). Ali and Rohani(1997) presented similar results for the regenerator tem-perature and the coke on catalyst, but opposite trend inthe reactor temperature to ours as well as Arbel et al.(1995a).


Fig. 2. Steady-state responses to changes in air #ow rate.

Fig. 3. Steady-state responses to changes in catalyst circulation rate.


Fig. 4. Base case steady-state pro"les along the riser.

3.2. Steady-state proxles along the riserand the regenerator

Fig. 4 depicts the predicted steady-state pro"les ofseveral process variables along the reactor riser under thebase case operating conditions. The conversion of gas oilreaches 73 wt% at the riser outlet and 90% of the conver-sion is attained within the "rst 20 m of the riser (Fig. 4a).Most heat exchange between the catalyst phase and thegas phase takes place within the "rst 10 m, thus two-phase temperatures approaching each other within 3.0 Kat the riser outlet (Fig. 4b). After su$cient heat is trans-ferred from the catalyst to the gas phase, the gas temper-ature as well as the catalyst temperature drops withincreasing riser height because of endothermic crackingreactions. Both the catalyst and gas velocities sharply riseto about 7.5 m/s at the riser bottom due to the volumeexpansion accompanying feed vaporization (Fig. 4c).There is signi"cant molar expansion of gaseous sub-stance as large molecules crack to smaller molecules, sothe interstitial velocities of both phases steadily increaseup to 17 m/s at the outlet. The slip velocity between twophases is maintained within 0.25 m/s. It can be inferredfrom the predicted velocity pro"les that assuming con-stant velocity in the riser would result in signi"cant errorin describing cracking reactions. The pressure shows analmost linear decrease along the riser with the total dropof about 16 kPa. This value shows good agreement with

a measured value (16.7 kPa) and a predicted value(13.7 kPa) reported by Theologos, Nikou, Lygeros, andMarkatos (1997) who developed a very rigorous three-dimensional riser model.

Fig. 5 shows the predicted pro"les of several processvariables along the regenerator height at the same steadystate as in Fig. 4. Since the predicted catalyst bulk densityof 448 kg/m� in the dense bed is much larger than31 kg/m� in the freeboard, most coke burning reactionstake place in the dense bed (Fig. 5a). The molar stack-gascomposition was predicted to be 0.2% O

�, 0.6% CO,

14.8% CO�, and 9.2% H

�O, which also agrees well

with the observations obtained for typical promotedcoke burning reactions (Faltsi-Saravelou, Vasalos,& Dimogiorgas, 1991; Zheng, 1994). Since catalyst par-ticles are assumed perfectly mixed in the dense bed, theyhave uniform coke concentration and temperature pro-"les in the dense bed (Figs. 5b and c). As a result of theafter-burning oxidation of CO, CO concentration islower and temperature is higher in the freeboard than inthe dense bed.

3.3. Multiple steady-states and sensitivity toinitial conditions

There has been plethora of literature on the subject ofmultiple steady states and their stability of FCC units inthe past three decades. Since Iscol (1970) proposed the


Fig. 5. Base case steady-state pro"les along the regenerator.

existence of multiple steady states in the normal ranges ofcommercial operation, many papers followed arguingpro and con on the possibility of multiplicity and itsconditions (Lee & Kugelman, 1973; Edwards & Kim,1988; Elshishini & Elnashaie, 1990, Arandes & de Lasa,1992). The dispute and confusion on the issue seems to beclari"ed by Arbel et al. (1995a,b), who performed a sys-tematic analysis based on a relatively detailed model ofmodern FCC units. A part of the authors' conclusionscan be summarized as follows: (1) there are at least threesteady states for "xed inputs to present design units. Incase there is only one, it is a trivial quenched state; (2) theupper (ignited) and the lower (quenched) state are alwaysstable whereas the intermediate one is always unstable.

Most analyses on multiple steady states for a processinvolving exothermic reactions are carried out usinga steady-statemodel to "nd the operating points at whichthe rate of heat generation equals that of heat removal.Dynamicmodels can be also used to con"rm the multiplesteady states by investigating the trajectories of the sys-tem subject to di!erent initial conditions because eachstable steady state has a unique domain of attraction onthe phase plane. Elnashaie and Elshishini (1993) studiedthe sensitivity of their dynamic model to initial condi-tions. The process trajectories starting from several initialconditions were found to drift either to an upper steadystate or to a lower steady state. They found that thedynamic behavior of their FCC model is very sensitive tothe initial catalyst activity in the reactor.

Dynamic simulations were performed starting fromperturbed initial conditions to investigatemultiple steadystates for our FCC model. First, the initial conditionswere set as the values at the base case steady stateobtained previously except the dense bed temperaturewhich was perturbed to 1100, 900, and 820 K, respective-ly. Fig. 6 compares the transient trajectories of reactortemperature, dense-bed temperature, and coke on regen-erated catalyst evolving from each initial condition.When starting from 1100 or 900 K, the process showsdi!erent transient responses (curves 1 and 2) but ulti-mately converges to the original base case steady state.When starting from 820 K, however, both the reactorand dense-bed temperatures keep decreasing until itreaches the point where the regenerated catalyst is notcapable of vaporizing gas oil feed any more. Since thenthe riser will be "lled with liquid gas oil feed, normaloperation of the unit would not be possible any longer.This state of inoperability of an FCC unit is calleda quenched state in the literature (Elshishini & Elnashaie,1990; Arbel et al., 1995b) whereas the normal steady stateobtained above is called an ignited state. It is clear thatthe unstable steady state in the middle cannot be identi-"ed in open-loop dynamic simulations.

It may be interesting to check the sensitivity ofour FCC model to initial conditions of several key vari-ables. It was found in our simulations that the process issensitive to dense bed temperature in that an initialtemperature below 827 K would cause the process to


Fig. 6. Transient responses starting from di!erent initial dense bed temperatures: (1) ¹��

"1100 K, (2) ¹��

"900 K, (3) ¹��

"820 K.

Fig. 7. Multiple steady states in regenerator operation with catalystin#ow conditions "xed.

drift toward the quenched state. On the other hand, theprocess always drifts toward the upper steady state what-ever temperature the reactor initially may assume be-tween 270 and 920 K. The di!erent sensitivity behaviorbetween the two cases can be attributed to much largerthermal holdup of the regenerator compared to the reac-tor. The process also drifts to the upper steady stateswhen the initial coke on spent and regenerated catalyst isless than 0.055 and 0.054, respectively.

It is the regenerator with exothermic reactions andback-mixed thermal dynamics that is responsible for themultiple steady states in FCC operation. Since the riser ismodeled as a tubular reactor with endothermic reactionsand the disengaging-stripping section does not involveany reaction, the reactor does not have dynamic charac-teristics that may lead to multiple steady states (Maya-Yescas & Lopez-Isunza, 1997). To investigate thesteady-state multiplicity inherent in the regenerator dy-namics, dynamic simulations were performed with thescope con"ned to the regenerator. Fig. 7 compares thetransient responses evolving from two di!erent initialtemperatures (1100 and 500 K) of the dense bed when theconditions of spent catalyst entering the regenerator are"xed. It is clear that the high-initial temperature leadsto the upper steady state whereas the low initialtemperature leads to the lower steady state. The upperand lower steady states represent two stable modes of


Table 5Step change scheme for process inputs in dynamic simulation

Step change scheme

Case 1: Changes in gas oil feed rate.Case 2: Changes in air #ow rate.Case 3: Changes in stem positions of the slide valves at both catalyst transport lines.

operation as far as the regenerator is concerned. Whenconnected to a reactor with catalyst circulated in-be-tween, however, the lower steady state would result in thequenching of the whole unit because the regeneratedcatalyst at such low temperature would fail to vaporizegas oil feed.

3.4. Dynamic responses

Dynamic simulation of the FCC process was per-formed according to the simulation scheme shown inTable 5. Gas oil feed rate, air #ow rate, and stem posi-tions of the slide valves at both catalyst transport lineswere chosen as simulation variables to whose changes thedynamic responses are demonstrated. Each simulationrun started from the steady state corresponding to thebase case operating conditions and the subsequent tran-sient response was obtained as each simulation variablewent through a series of step changes shown in Table 5.

3.4.1. Changes in gas-oil feed rateFig. 8 shows the predicted dynamic responses to the

changes in gas oil feed rate. After the gas oil feed rate isincreased by 5% at time equal to 10 min, the reactortemperature drops because of an increase in heat con-sumption to vaporize the gas-oil feed (Fig. 8a). Thelowered riser temperature results in a considerable de-crease in gas oil conversion by about 6.1 wt% (Fig. 8e)while the increased feed rate leads to a sharp rise in cokeon spent catalyst and subsequently on regenerated cata-lyst (Fig. 8f ). Because the increased feed rate also raisesthe density of hydrocarbon gases in the reactor, there isa jump of gas pressure as well as of the pressure at thereactor bottom (Fig. 8c). This jump will also triggera jump of spent catalyst #ow rate but an opposite e!ectupon regenerated catalyst #ow rate (Fig. 8d). Therefore,the catalyst holdup in the reactor steadily decreases untila new steady state is reached where the two catalystcirculation rates are balanced each other (Fig. 8b). Sincedecreasing catalyst holdup means decreasing static head

acting on the reactor bottom, the pressure at the bottomwill descend from the aforementioned initial jump until itsettles down to a new steady-state value which is lowerthan the original steady state (Fig. 8c). This inverse re-sponse behavior of the reactor bottom pressure alsoexplains the similar behavior of the spent catalyst #owrate which is directly in#uenced by the reactor bottompressure (Fig. 8d). Regenerator temperatures start to de-crease in both the dense bed and freeboard regions sincethe increased spent catalyst in#ow from the reactorcooler than before implies an enhanced heat removal ratein energy balance (Fig. 8a). Since the "xed air #ow doesnot supply enough oxygen to burn o! the increased cokein the dense bed nor to sustain after-burning reactions inthe freeboard, CO concentration in the stack gas steadilyrises (Fig. 8e). The oxygen de"ciency in the regeneratoralso leads to no more rise in the freeboard temperatureabove the dense bed temperature at the new steady state(Fig. 8a).

When the gas oil feed rate is decreased to its previousvalue at time equal to 150 min, the system completelyrecovers its original steady state. The transient responsesover the second time interval in Fig. 8 show in what anorderly and coordinated fashion the process variables arereturning to the old steady state.

A 5% step decrease in the gas oil feed rate at 300 mincauses the system to move in the opposite direction to thecase of the 5% step increase but the detailed responsesshow quite di!erent aspects due to process nonlinearity.The gas oil conversion increases by about 3.9 wt% due toincreased catalyst-to-oil ratio in the riser as well as betterregeneration of catalyst in the regenerator (Figs. 8d}f ).The reactor bottom pressure and the spent catalyst #owrate again show inverse responses which, on this occa-sion, are characterized by initial drop followed by event-ual rise (Figs. 8c and d). Accordingly, catalyst holdupshows a steady increase in the reactor whereas asteady decrease in the regenerator (Fig. 8b). Contraryto the oxygen de"ciency encountered before, oxygensurplus prevails throughout the regenerator because of


Fig. 8. Dynamic responses to step changes in gas oil feed rate (case 1).

the decreased spent catalyst in#ow from the reactor. Thiscauses a rise in the dense bed temperature, a much higherrise in the freeboard temperature due to after-burn ofCO, and a consequent drop in the CO concentration ofstack gas (Figs. 8a and 8e).

It was found in the simulations described above thatthe step changes in gas oil feed rate immediately alter thereactor pressure which subsequently triggers a series ofchanges upon the process dynamics. Since the stem posi-tions of the slide valves on catalyst transport lines areheld "xed in our open-loop simulation, catalyst circula-tion rates are solely determined by pressure di!erencesacross the valves. Accordingly, the pressure variationleads to serious unbalance between the #ow rates of spentand regenerated catalyst and consequently to signi"cantchanges in the catalyst holdups in two vessels. In oursimulations, the process was found to keep on stableoperation in the face of step changes in feed rate of magni-

tude of about $7%. However, a large change exceedingthis range caused the process to drift to a quenched statewhere normal operation of the unit is impossible.

3.4.2. Changes in air yow rateFig. 9 shows the predicted dynamic responses to the

changes in the air #ow rate to the regenerator. A 5% stepincrease in air #ow causes a sharp increase in the regener-ator pressure as well as in the regenerated catalyst #owrate to the riser bottom (Figs. 9c and d). On the otherhand, the spent catalyst #ow rate shows an inverse re-sponse behavior of initial decrease followed by ultimateincrease (Fig. 9d). This behavior can be explained bya steady increase in the reactor bottom pressure (Fig. 9c)due to increasing static pressure exerted by the risingcatalyst holdup in the reactor (Fig. 9b). The increased air#ow rate also accelerates coke burning and thus raisestemperature in every part of the unit (Fig. 9a) and reduces


Fig. 9. Dynamic responses to step changes in air #ow rate (case 2).

the CO concentration in the stack gas (Fig. 9e). It alsocauses the coke concentrations on both spent and regen-erated catalyst to steadily drop to their respective steadystate values (Fig. 9f). The conversion of gas oil is pro-moted by about 3.2 wt% by the elevated riser temper-ature and cleaner regenerated catalyst (Fig. 9e). When theair #ow rate is decreased to its previous value, however,all the process variables are completely brought back totheir original steady state.

A 5% step decrease in the air #ow rate at time equal to300 min brings about the state of oxygen de"ciency in theregenerator. A large amount of coke cannot be burnt o!,resulting in gradual accumulation on catalyst surfaces inboth vessels over a long time (Fig. 9f, where the responsesare partially shown). Such a long response time is charac-teristics of the composition dynamics in the regeneratorthat has large mass and thermal holdups and stronginteractions with the reactor. CO concentration alsoshows a considerable increase because of poor after-

burning reactions in both the dense bed and freeboard(Fig. 9e). This oxygen de"ciency lowers the temperaturesof both vessels by about 23}39 K (Fig. 9a) as well as theconversion of gas oil by 6.3 wt% (Fig. 9e). It was alsofound in our simulations that the process reaches a newstable state in the face of step changes in air #ow rate ofmagnitude up to about $8%.

3.4.3. Changes in the stem positions of slide valvesFig. 10 shows responses due to the changes in both the

spent and regenerated catalyst #ow rates as e!ected byslide valve manipulation. The stem positions of the slidevalves on both the transport lines are adjusted upward by5% at time equal to 10 min which corresponds to 8.5%increase in the catalyst circulation rate. Since both thespent and regenerated catalyst #ow rates are raised bythe approximately same amount, the catalyst holdup ineach vessel is maintained constant (Fig. 10b). There is


Fig. 10. Dynamic responses to step changes in stem positions of the slide valves (case 3).

also little variation in the pressures of the reactor andregenerator (Fig. 10c). However, the regenerator temper-atures steadily drop both in the dense bed and freeboardbecause the increased #ow of spent catalyst implies en-hanced heat removal in energy balance for the regener-ator. On the other hand, the reactor temperature initiallyrises due to increased catalyst #ow from the regeneratorbut drops in a while as the dense bed temperature islowered (Fig. 10a). The CO concentration slightly risesbecause after-burning reactions are suppressed bylowered freeboard temperature (Fig. 10e). Consequently,the cokes on both the regenerated and spent catalystincrease to new steady-state values (Fig. 10f ). Thegas oil conversion slightly increases by about1.2 wt% due to an increased catalyst-to-oil ratio andelevated reactor temperature (Fig. 10e). If the stempositions of the slide valves are shifted back to theiroriginal positions, the process variables converge againto their previous values.

On the other hand, a 5% decrease in the stempositions at 300 min reduces the catalyst circulation rateby 9.6%. This reduction in the catalyst circulation ratedecreases the gas oil conversion by 1.1% (Fig. 10e). Theregenerator temperatures increase because the reducedspent catalyst #ow provides not only a lowered heatremoval rate but also a new oxygen-rich environmentfavorable to coke-burning reactions (Figs. 10a and e).Accordingly, there is a slight decrease in both the coke onregenerated catalyst and the CO concentration in thestack gas (Figs. 10e and f ).

4. Conclusions

A dynamic simulator for #uid catalytic crackerscalled DSim-FCC was developed which implements thedetailed dynamic model for an FCC process and the


model solver presented in Part I of this paper. Thecorrelation equations were prepared for the thermodyn-amic properties and transport parameters contained inour model either by literature survey or by nonlinearregression of literature data.

The steady-state behavior was investigated as func-tions of the catalyst circulation rate and the air #ow rateand the results showed good matches with those in theliterature. For an industrial scale FCC unit of 30,000BPD capacity, the base case steady-state pro"leswere obtained for velocity, pressure, temperatureand composition in the reactor riser and the regenerator.Some steady-state predictions showed satisfactoryagreement with the literature data. Then the issue ofmultiple steady states in FCC operations was addressedand con"rmed by investigating the sensitivity ofour model to initial conditions. Depending on initialconditions, the process was found to drift either towardan upper (ignited) steady state or toward a lower(quenched) steady state where normal operation of theunit is impossible. It was also found that the regeneratorwith exothermic reactions and back-mixed thermal dy-namics is responsible for multiple steady states in FCCoperation.

The dynamic step responses were obtained in anopen-loop mode for gas oil feed rate, air #ow rate, andstem positions of the slide valves on catalyst transportlines. The presented responses show typical inverse re-sponses and nonlinear behavior which stem from com-plicated interaction between the reactor and regeneratordynamics.

Notation

A, B, C coe$cients of the Antoine equationAPI API gravityC mole concentration, kg mol/m�

C��

coke on catalyst, kg-coke/kg-catalystC

��minimum coke content attainable by strip-ping, kg-coke/kg-catalyst

C�

heat capacity, kJ/(kg K)CM��

mean heat capacity, kJ/(kg K)d average diameter, mD diameter, mD�

e!ective di!usion coe$cient, m�/sE activation energy, kJ/kg molE��

exponent in the stripping function, s/kgf mole fractionF mass #ow rate, kg/sg acceleration due to gravity, 9.8 m/s�h�

interface heat transfer coe$cient betweencatalyst and gas phases, kJ/(m� s K)

k heat conductivity, kJ/(s m K)k

valve #ow rating factor, kg/(s kPa��),

k��

, k��

#ow rating factors of the cyclone dip-legs,kg/(s m��)

K�

Watson characterization factor, K��

K�

interchange coe$cients between bubbleand emulsion phase, 1/s

M�

molecular weightN

��, N

��numbers of cyclones in the reactor andregenerator, respectively

P pressure, kPaP��

pseudo-critical pressure, kPaP��

pseudo-reduced pressure, kPaR�

aromatics to naphthenes ratio in a liquidfeedstock

S�

speci"c gravity¹ Temperature, K¹��,¹

��,¹

��,

¹��

, ¹��

ASTM D86 distillation temperatures atdistilled vol% equal to 10,30,50,70, and 90,respectively, K

¹��

ASTM D86 distillation temperature, K¹��

initial dense bed temperature, K¹�

ambient temperature, K¹

��molal average boiling temperature, K

¹��

mean average boiling temperature, K¹��

pseudo-critical temperature, K¹��

pseudo-reduced temperature¹

��reference temperature, 298.15 K

¹��

TBP distillation temperature, K¹

normal boiling point, K¹

��volume average boiling temperature, K

u super"cial velocity, m/s; overall heat transfer coe$cient between

a process unit and the surroundings,kJ/(m� s K)

v interstitial velocity, m/sv��

super"cial gas velocity at a minimum#uidizing condition, m/s

w holdup, kgx

valve stem position, [0}1]y weight fraction>��

weight fraction of Conradson carbon resi-due in feedstock

Greek letters

��

catalyst deactivation coe$cient�

(valve head di!erential at maximum#ow)/(valve head di!erential at zero #ow),[0}1]

��

catalyst decay constant, 1/s�H

�heat of formation, kJ/kg mol

�H��

heat of stripping, kJ/kg�H

heat of vaporization, kJ/kg

� volume fraction, [0}1]��

void fraction at a minimum #uidizing con-dition

��

, ��

collection e$ciencies of cyclones, [0}1]


Table 6Coe$cients in Eqs. (A.1) and (A.2)

Vol% distilled a b

0 0.9167 1.001910 0.5277 1.090030 0.7429 1.042550 0.8920 1.017670 0.8705 1.022690 0.9490 1.011095 0.8008 1.0355

� viscosity, kg/(m s)��

pseudo-critical viscosity, kg/(m s)��

pseudo-reduced viscosity� density, kg/m�

� intrinsic CO�/CO molar ratio in coke

Subscripts

a airb bubble or catalyst bulkB bubble phasec catalystck cokeC¸1 regenerated catalyst transport line (to

reactor)C¸2 spent catalyst transport line (to regener-

ator)CO carbon monoxideCO

�carbon dioxide

CY1 reactor cycloneCY2 regenerator cycloneds dispersion steamD dense bedE emulsion phaseF freeboardg gasgl gasolinego gas oilgs C

�}C

�(lighter) gases

H�O water

lg liquid feedstock (gas oil)m mixtureMF main-fractionatorN

�nitrogen

O�

oxygenRG regeneratorR¹ reactorSG stack gas valvess stripping steamST stripping sectionS<1 regenerated catalyst slide valveS<2 spent catalyst slide valve

Acknowledgements

The study was "nancially supported by Korea Scienceand Engineering Foundation under Grant No. 981-1104-013-2.

Appendix A. Correlation of physical properties and trans-port parameters

ASTM D86 and TBP distillation curves can be con-verted into each other by the following expressions

(Riazi, 1988):

¹��

"a(¹��

)� (A.1)

¹��

"a��(¹��

)��, (A.2)

where the coe$cients a and b vary with the percent ofdistilled volume as shown in Table 6. Then the ASTMD86 distillation curve can be used to estimate the vol-ume, molal, and mean average boiling points, respective-ly (Technical Data Committee, 1988)

¹��

"0.2(¹��

#¹��

#¹��

#¹��

#¹��

), (A.3)

¹��

"¹��

!0.5556 exp[!0.5638

!0.0080(1.8¹��

!491.67)��

#3.0473(Sl)��], (A.4)

¹��

"¹��

!0.5556 exp[!0.9440

!0.0087(1.8¹��

!491.67)��

#2.9972(Sl)��], (A.5)

where

(Sl)"0.0225(¹��

!¹��

). (A.6)

The Watson characterization factor is calculated usingspeci"c gravity and mean average boiling point as fol-lows:

S�"

141.5

(API)#131.5, (A.7)

K�"

(1.8¹��

)��

S�

. (A.8)

The molecular weights of gas oil and gasoline lumpcan be estimated by Eq. (A.9) (Riazi, 1988), and the


average molecular weight of n component gas mixture iscalculated by Eq. (A.10):

M��

"42.965[exp(2.097�10��¹��

!7.787S�#2.085�10�¹

��S�)]

�¹��

S��

, (A.9)

M��

"1��

y�

M��. (A.10)

The liquid- and gas-phase heat capacities of gas oil andgasoline lump are estimated using a modi"ed Lee}Keslercorrelation (Lee and Kesler, 1988) which neglects thepressure e!ect since typical FCC processes are operatedunder relatively low pressures ranging between 200 and300 kPa:

C��

"��#�

�¹#�

�¹�, (A.11)

C��

"��#�

�¹#�

�¹�, (A.12)

where

��"!4.90383#(0.099319#0.104281S

�)K

�

#

(4.814066!0.194833K�)

S�

, (A.13)

��"(7.53624�10��)(1.0#0.82463K

�)

��1.12172!

0.27634

S��, (A.14)

��"(!1.356523�10��)(1.0#0.82463K

�)

��2.9027!

0.70958

S��, (A.15)

��"!1.492343#0.124432K

�#�

�

��1.23519!

1.04025

S��, (A.16)

��"(!7.53624�10��)[2.9247!(1.5524

!0.05543K�)K

�#�

��(6.0283!5.0694

S�

)��,(A.17)

��"(1.356523�10��)(1.6946#0.0884�

�), (A.18)

��"��

12.8

K�

!1.0��1.0!

10.0

K��

�(S�!0.885)(S

�!0.70)(10�)]�

for 10.0(K�(12.8,

��"0 for all other cases. (A.19)

The heat capacity of the light gas lump is calculatedby Eq. (A.20) assuming the composition (H2"0.2%,C1"5.7%, C2"7.8%, C3"29.7%, and C4"56.6%)found in typical "eld operations (Mcketta and Cunning-ham, 1976):

C��

"0.2457#5.3�10��¹!2.1527�10��¹�. (A.20)

The heat capacities of carbon monoxide, carbon dioxide,nitrogen, oxygen, and steam are calculated by the follow-ing:

C��

"1.081#0.000034¹, (A.21)

C��

"0.986#0.00018¹, (A.22)

C��

"0.983#0.00026¹, (A.23)

C� ��

"1.91#0.000035¹, (A.24)

C� �

"0.971#0.00015¹. (A.25)

Then the mean heat capacity of n componentmixture canbe calculated by

CM��

"

��

��

y�C��(¹) d¹

¹!¹��

. (A.26)

The gas phase viscosities of hydrocarbon lumps areestimated by Eq. (A.27) which factorizes the viscosity intopseudo-reduced viscosity and pseudo-critical viscosity(Nelson, 1958)

��"�

��

"3.515�10��

�M��

P��

¹��

. (A.27)

The correlation equation (A.28) for pseudo-reduced vis-cosity was obtained by nonlinear regression of literaturedata (Nelson, 1958) over the range of ¹

��andP

��given in

Eq. (A.29)

��

"0.435 exp[(1.3316!¹��

)P��]¹

��

#0.0155, (A.28)

0.75(¹��

"

¹

¹��

(3.0, and 0.01(P��

"

P

P��

(0.2,

(A.29)


where the critical properties of hydrocarbons are esti-mated by the following equations:

¹��

"17.1419[exp(!9.3145�10��¹��

!0.5444S�#6.4791�10��¹

��S�)]

�¹��

S��

, (A.30)

P��

"4.6352�10�[exp(!8.505�10��¹��

!4.8014S�#5.749�10��¹

��S�)]

�¹��

S��

. (A.31)

On the other hand, the viscosities of the components inthe coke burning reaction mixture are expressed as func-tions of temperature only as follows

��

"6.476�10��#4.818�10��¹, (A.32)

��

"5.38�10��#4.04�10��¹, (A.33)

��

"1.34�10��#4.5�10��¹, (A.34)

� ��

"!1.90�10��#3.85�10��¹, (A.35)

��

"1.101�10��#3.074�10��¹, (A.36)

Finally, the mean viscosity of gaseous mixture is cal-culated by

��"

��

��1#

��

[1#(��/��)��(M

��/M

��)��]�

�8[1#M��/M

��]��

f�f��

��.

(A.37)

The correlation equation for heat of vaporization ofgas oil was obtained as Eq. (A.38) by nonlinear regressionof literature data (Nelson, 1958). This equation is applic-able when the molecular weight of gas oil ranges from200 to 400.

�H��

"0.3843¹��

#1.0878�10�exp�!M

��100 �!98.153. (A.38)

The vapor pressure of gas oil is calculated by solvingfor a trial-and-error solution of the following set of cor-relation equations adopted from literature (TechnicalData Committee, 1988):

P�"0.133322�10��

for '0.0022,

P�"0.133322�10��

for 0.0013))0.0022,

P�"0.133322�10��

for (0.0013, (A.39)

where

"

¹H��

/¹!0.00051606¹H

��748.1!0.3861¹H

��

, (A.40)

¹H��

"¹��

!1.3889�

�(K�!12)log(0.0098684P

�), (A.41)

�"1 for ¹��

'477.8 K,

�"0 for ¹��

(333.3 K,

�"(1.8¹��

!659.7)/200, for 366.7K

)¹��

)477.8 K. (A.42)

To calculate the three coe$cients in the Antoine equa-tion for gas oil, vapor pressures are evaluated at threetemperatures (¹

��, ¹

��!15, and ¹

��#15)

using Eqs. (A.39)}(A.42) and are substituted into thefollowing equations:

F�(A

��,B

��,C

��)"(¹

�#C

��)[A

��!log(P

��)]

!B��

"0, i"1,2,3. (A.43)

The resulting set of equations are solved using the New-ton's method to get A

��, B

��, and C

��.

The thermal conductivity of hydrocarbons is needed tocalculate thermal di!usivity and heat transfer coe$cient.The following equation was obtained by nonlinear re-gression of the data in API technical data book (TechnicalData Committee, 1988):

k�"1�10��(1.9469!0.374M

��

#1.4815�10��M��

#0.1028¹). (A.44)

Then the interface heat transfer coe$cient between solidsand hydrocarbon gases can be estimated from the cor-relation between the Nusselt and Reynolds numbers(Kunii & Levenspiel, 1991):

h�"0.03

k�

d��v�!v

��

��

��

. (A.45)

Then the overall interchange coe$cient K�

for masstransfer between the emulsion and the bubble phases canbe computed using the interchange coe$cient K

�be-

tween bubble and cloud and K�

between cloud andemulsion (Kunii & Levenspiel, 1991)

K�"

��

1/K�#1/K

�

, (A.46)


K�"4.5

v��d�

#5.85�D��

g��

d��

�, (A.47)

K�"6.77�

D��v�

d��

��, (A.48)

where the e!ective di!usion coe$cient of gaseousmixture in the reactor and regenerator is calculated usingthe correlation equation proposed by Baird and Rice(1975):

D�"0.35(gu

�)��D��. (A.49)

Appendix B. Additional simulation data

The following is a list of additional data used inour simulation. These data together with those givenin Tables 1}4 correspond to the base case simulationcondition.

1. Initial conditions:C��

"0.009, w��

"485.0 kg,w��

"38 000.0 kg, y��

"0.27,y��

"0.51, y��

"0.14, ¹��

"787.0 K,w��

"990 kg, w��

"182 000 kg,C��

"0.001, ¹�

"991.0 K,C

��"0.0005 kg mol/m�, C

��"0.0003 kg mol/m�,

C��

"0.004 kg mol/m�, C ��

"0.003 kg mol/m�,C

��"0.02 kg mol/m�, C

�� "0.0005 kg mol/m�,

C��

"0.0003 kg mol/m�, C��

"0.004 kg mol/m�,C

�� "0.003 kg mol/m�, C

�� "0.02 kg mol/m�,

C��

"0.0001 kg mol/m�, C��

"0.0002 kg mol/m�,C

��"0.004 kg mol/m�, C

��"0.003 kg mol/m�,

C��

"0.02 kg mol/m�, ¹�"1010.0 K,

C��

"0.0008.

2. Valve parameters:k��

"4.35 kg/(s kPa��), k��

"120.0 kg/(s m��),k��

"140.0 kg/(s m��), k�

"4.25 kg/(s kPa��),k��

"69.0 kg/(s kPa��), k��

"69.0 kg/(s kPa��),��

"1.0, ��

"1.0, ��

"1.0, ��

"0.8,��

"0.9, ��

"0.9.

3. Heat transfer coezcients:;��

"0.035 kJ/(m� s K), ;�

"0.05 kJ/(m� s K),;�"0.05 kJ/(m� s K).

4. Miscellaneous parameters:C

��"0.0004, k

��"0.0054, E

��"0.3311 s/kg,

�H��

"0 kJ/kg, ��

"350 kg/s,��

"350 kg/s, ��!"�

"560 kg/s,��!"�

"560 kg/s, c�

"0K, ��

"0.6,��"1.5 s��, �

��"1,

��

"1, N#��

"10, N#��

"10.

References

Ali, H., & Rohani, S. (1997). Dynamic modeling and simulation ofa riser-type #uid catalytic cracking unit. Chemical Engineering Tech-nology, 20, 118.

Ancheyta-Juarez, J., Lopez-Isunza, F., Aguila-Rodriguez, E.,& Moreno-Mayorga, J. C. (1997). A strategy for kinetic parameterestimation in the #uid catalytic cracking process. Industrial andEngineering Chemistry Research, 36, 5170.

Arandes, J. M., & de Lasa, H. I. (1992). Simulation and multiplicity ofsteady states in #uidized FCCUs. Chemical Engineering Science, 47,2535.

Arbel, A., Huang, Z., Rinard, I. R., Shinnar, R., & Sapre, A. V. (1995a).Dynamic and control of #uidized catalytic crackers-1. Modeling ofthe current generation of FCC's. Industrial and Engineering Chem-istry Research, 34, 1228.

Arbel, A., Rinard, I. R., Shinnar, R., & Sapre, A. V. (1995b). Dynamicand control of #uidized catalytic crackers-2. Multiple steady statesand instabilities. Industrial and Engineering Chemistry Research, 34,3014.

ASTM (1991). Standard test method for distillation of petroleumproduct. In A. S. Roberta et al. (Eds.), 1991 annual book of ASTMstandards: Petroleum products, lubricants, and fossil fuels. Easton:ASTM.

Baird, H. M., & Rice, R. G. (1975). Axial dispersion in large unba%edcolumns. Chemical Engineering Journal, 9, 171.

Callahan, K. P., & Ushiba, K. K. (1988). Advances in yuid catalyticcracking part 2. Mountain View: Catalytica.

Edwards, W. E., & Kim, H. N. (1988). Multiple stead states in FCC unitoperations. Chemical Engineering Science, 43, 1825.

Elnashaie, S. S. E. H., & Elshishini, S. S. (1993). Digital simulation ofindustrial #uid catalytic cracking units-IV. Dynamic behavior.Chemical Engineering Science, 48, 567.

Elshishini, S. S., & Elnashaie, S. S. E. H. (1990). Digital simulation ofindustrial #uid catalytic cracking units-I. Bifurcation and itsimplications. Chemical Engineering Science, 45, 553.

Errazu, A. F., de Lasa, H. I., & Sarti, F. (1979). A #uidized bed catalyticcracking regenerator model: Grid e!ects. Canadian Journal of Chem-ical Engineering, 57, 191.

Faltsi-Saravelou, O., Vasalos, I. A., & Dimogiorgas, G. (1991). FBSim:A model for #uidized bed simulation-II. Simulation of an industrial#uidized catalytic cracking regenerator. Computers & Chemical En-gineering, 15, 647.

Howard, J. B., Williams, G. C., & Fine, D. H. (1973). Kinetics of carbonmonoxide oxidation in post#ame gases. Fourteenth symposium oninternational combustion (p. 975).

Iscol, L. (1970). The dynamics and stability of a yuid catalyticcracker. Presented at 1970 JACC meeting, Atlanta, Ga, Paper 23-B(p. 602).

Kumar, S., Chadha, A., Gupta, R., & Sharma, R. (1995). CATCRACK:A process simulator for an integrated FCC-regeneratorsystem. Industrial and Engineering Chemistry Research, 34,3737.

Kunii, D., & Levenspiel, O. (1991). Fluidization engineering. Boston:Butterworth-Heinemann.

Lee, B. I., & Kesler, M. G. (1988). Isobaric heat capacity of petroleumfraction liquids/vapors. Technical data book-Petroleum rexning.Tulsa, OK: American Petroleum Institute.

Lee, W., & Kugelman, A. M. (1973). Number of steady-state operatingpoints and local stability of open-loop #uid catalytic cracker. Indus-trial and Engineering Chemistry, Process, Design and Development,12, 197.

Maya-Yescas, R., & Lopez-Isunza, F. (1997). Comparison of two dy-namic models for FCC units. Catalysis Today, 38, 137.

Mcketta, J. J., & Cunningham, W. A. (1976). Encyclopedia of chemicalprocessing and design. New York: Marcel Dekker.

Meissner, L. P. (1995). Fortran 90. Boston: PWS Publishing Co.


Morley, K., & de Lasa, H. I. (1987). On the determination of kineticparameters for the regeneration of cracking catalyst. Canadian Jour-nal of Chemistry and Engineering, 65, 773.

Nelson, W. L. (1958). Petroleum rexnery engineering. Tokyo: McGraw-Hill.

Riazi, M. R. (1988). Interconversion of ASTM D86-TBP distillationcurves at atmospheric pressure. Technical data book-Petroleum rexn-ing. Tulsa, OK: American Petroleum Institute.

Technical Data Committee, X. (1988). Technical data book-Petroleumrexning. Tulsa, OK: American Petroleum Institute.

Theologos, K. N., Nikou, I. D., Lygeros, A. I., & Markatos, N. C. (1997).Simulation and design of #uid catalytic-cracking riser-type reactors.A.I.Ch.E. Journal, 43, 486.

Zheng, Y. Y. (1994). Dynamic modeling and simulation of a catalyticcracking unit. Computers & Chemical Engineering, 18, 39.


561228

Documents

Transcript of 561228