Yong Li,Jizheng Chu*,Jiarui Zhang

College of Information Science and Technology,Beijing University of Chemical Technology,Beijing 100029,China

1.Introduction

Fluid catalytic cracking(FCC)is a critical process of petroleum refineries where heavy distillates such as vacuum gas oils or even residues are cracked to produce liquefied petroleum gas,gasoline,diesel and propylene.Design and operation optimizations of industrial FCC units are of great significance because the throughputs of such units are huge.Therefore,modeling and simulation of FCC processes have been an important topic of research ever since about 1940’s.Notable early pioneers on this topic include[1,2],and more recent contributors include[3-11].Pinheiroet al.[12]presented a comprehensive review on the subject of fluid catalytic cracking process modeling,simulation and control.

In modeling a fluid catalytic cracking unit,one challenging problem is to describe the chemical reactions of the feed and product oils which are complicated mixtures of numerous hydrocarbons and nonhydrocarbons.The kinetic models proposed in the past can be primarily classified by the entities used to express the oils.In the kinetic model of Weekman and Nace[13],the entities are three lumps,stock oil,gasoline(C5-410°F),and C3+C4+dry gas+coke.Jacobet al.[14]presented a kinetic of 10 lumps which are the gasoline(C5-430°F),coke,and other eight light and heavy fractions of paraffins,naphthenes,aromatic rings and aromatic substituent groups.The single-event kinetics gives a way to estimate the kinetic parameters of lumps(or other entities)from the weight fractions per carbon number ofn-paraffin;isoparaffins;mono-,di-,tri-,and quaternaphthenes;and mono-,di-,and triaromatics[15,16].In the carbon center approach of Liguras and Allen[17,18],stock oils are expressed with pseudo-components which have different but definite molecular structures and different number and types of carbon centers accordingly,and the cracking behavior of such a pseudocomponent is described by the reactions of the carbon centers.Since reaction schemes using a few lumps suffer from the disadvantage that a change in product specifications or in the number of products requires reformulating the model and refitting the data,Stangeland[19],Guptaet al.[6],Hernández-Barajaset al.[20]and Sildiret al.[11]used pseudo-components or narrow cuts derived from true boiling point(TBP)distillation of feedstock oils.

Narrow cuts are a practical choice of the above mentioned entities,since they give a description of stock and product oils with proper details suitable for production use without over burden of computation,and since they have been widely and successfully applied in correlating various thermodynamic properties of crude and product oils[10].Though pseudo-components have made success of different degrees as the cracking reaction entities[6,10,11,19,20],problems still exist for generic reaction PCi→ PCm+PCn+λi,m,ncoke suggested by Guptaet al.[6]:(1)The number of possible reactions satis fied with λi,m,n=MWi-MWm-MWn≥0,is big,up to tens of thousands,which forms a serious burden of computation.(2)Over 1/3 of the possible reactions are exothermic,which is physically unreasonable.Simple exclusion of such exothermic reactions will disable the original kinetic model as well as the riser model.On the other side,generic reaction PCi→Σpi,jPCj+λcoke proposed by Sildiretal.[11]is hard fortheoretical analysis and needs empirical correlation for yield(pi,j)of product pseudo-components,though it reduces the number of reactions involved as compared with the scheme of Guptaet al.[6].

Characterization of the stock and productoils is a key step in the way toward a predictive kinetic model[14].However,the characterization procedures of Jacobet al.[14],Froment[15]and Fenget al.[16],and Liguras and Allen[17,18]demand detailed analytical data unusual in daily production.Hernández-Barajaset al.[20]and Sildiret al.[11]correlated the kinetic parameters to the normal boiling temperatures of pseudo-components,whereas Zhang,J.et al.[10]employed special pseudo-components to correlate the kinetic parameters to the normal boiling temperatures and densities of pseudo-components.In addition,forms of the correlations for the frequency factor and activity energy of the generic reactions with pseudo-components are open for deliberation,as indicated by the practice of Guptaet al.[6],Hernández-Barajaset al.[20],Zhang,J.et al.[10]and Sildiret al.[11],though consensus exists for the cracking rate expression where the rate is proportionalto the concentration of the reactant pseudo-component in question and to a catalyst activity coefficient related to the coke concentration on the catalyst and for an Arrhenius type expression for the rate constant.

In the approach with pseudo-components,the generic reaction is fundamental.As a new attempt in modeling FCC risers,a variation to the generic reactions of Guptaet al.[6]and Sildiret al.[11]is proposed in this study and is coupled with special pseudo-components(Zhang,J.etal.[10])to describe the complex cracking reactions involved in a riser.The rest of this paper is organized in five sections.Section 2 is dedicated to the development of the proposed generic reaction for describing the cracking behavior of pseudo-components or narrow cuts of true boiling point distillation.The characterization procedure for stock and product oils based on specialpseudo-components and the steady state model for a prototype riser are brie fly introduced respectively in Section 3.A strategy for identifying the model parameter is presented in Section 4.Section 5 shows the results of tests where the proposed model is applied to fit and predict the production data in different operational scenarios of four commercial risers,and the conclusion is made in Section 6.

2.The Generic Reaction and the Cracking Reaction Network

According to the transition state theory[21,22],the cracking path for pseudo-componenti(PCi)can be postulated in Fig.1 or by the following generic reaction

where[PCi]*is the activated state of PCi,PCmis the product pseudocomponent,[i,m]is the intermediate substance,CK is the coke,λi,mis the amount of the coke in kg·kmol-1-PCi,and ΔHi,mis the heat consumed in kJ·kmol-1-PCi.In the above reaction,the first step is assumed to be the controlling one where PCiand[PCi]*are in equilibrium.The heat consumed by the reaction can be calculated as

Fig.1.Cracking path for a pseudo-component.

where=32950 kJ·kg-1is the combustion heat of coke suggested by Guptaet al.[6]

The surplusage in the above reaction is not given a name such as PCmin the generic reaction of Guptaet al.[6],since it will not enter the cracking reaction network for stock and product oils.For a system of pseudocomponents expressing stock and product oils,a cracking reaction network can be constructed by collecting all the possible reactions in the form of(1),or PCi→ PCm+ λi,mcoke+ ΔHi,mfor short,with the following criteria:

where Eq.(5)ensures an endothermic reaction.It is noted that based on the generic reaction in Eq.(1),the resulted cracking reaction network or scheme includes much less reactions than that of Guptaet al.[6].

To estimate the coke amount λi,m,we assume that the coke be produced through cracking of intermediate substance[i,m],or the left part of molecule PCiminus molecule PCm.This left part has an amount of MWi-MWmand a carbon-to-hydrogen mass ratio(CH)of

It is intuitively reasonable to suppose that λi,mbe affected positively by CH[i,m]and by amount MWi-MWm.At the same time, fluctuation should exist in the effect of CH[i,m]on λi,msince CH[i,m]can be seen as some index reflecting the molecular type(e.g.,relative contents of paraffins,naphthenes,aromatics,etc.)of the left part and molecules of different types have different coking tendencies.Therefore,the following correlation is formulated empirically

where α,β and ω are parameters to be determined from production or experiment data.

The rate of generic Reaction(1)can be expressed as

with φ andki,mbeing the activity coefficient of the catalyst and the rate constant.In this study,the correlation for φ of Pitaultet al.[23]is used

whereA=4.29,B=10.4.The rate constant is correlated to temperature with an Arrhenius type expression of

wherek0andvare the parameters to be identified from production data,ηiis the distribution factor which indicates the fraction of cracked PCiamong all the PCs cracked already,and δi,mis the tendency factor signifying the ease with which PCmis produced from cracking PCi,relative to other PCs as products also produced from cracking PCi.In addition,E0=1500 is taken to be constant with some arbitrariness to reduce the number of regression parameters of the model,since it would vary in a range of 1400-1550 if it were treated as a regression parameter[6,10].

At this point,it is noted that deactivation of catalysts for petroleum cracking is an important and complex phenomenon.Catalysts commonly used in fluid catalytic cracking will lose their activity due to poisoning of Ni,Fe,Na,V and other metals,leaching/vaporizing of active components,and adversely changing of surface and/or porous inner texture of the particle body.Deactivation caused by these factors is permanent and cumulative,though it usually develops slowly.In commercial production,this kind of deactivation is balanced through substitution of fresh catalystfor that in use at a certain rate,and the catalyst has a stable and equilibrium activity.In normal operation of commercial risers,coke formation and deposition on the surface of catalysts is the main cause of deactivation.This kind of deactivation is reversible since the activity can is recovered through coke burning in a regenerator.Pinheiroetal.[12]presented a concise review on issues in modeling this kind of deactivation,such as the acting mechanism of coke,selectivity for different reactions or reactant molecules,and model simplification with practical considerations for availability of data inputs,computational intensity,etc.Recently,Xionget al.[24]decomposed the deactivation effect of coke into two parts:one part caused by aromatics,resin and asphaltene,and the other by the basic nitrogen.Eq.(9)is a so-called coke-on-catalyst correlation(as contrast to the time-on-stream ones)and is adopted also by Guptaet al.[6].The problem of selective deactivation is partially considered in ηiand δi,m.

As indicated in Eq.(1),we may find a root for Eq.(10)from the transition state theory[21,22].As exemplified by Zhang,X.et al.[25]who used this theory to correlate the frequency factor of the cracking reactions of monocyclic cycloparaffins,the frequency or pre-exponential factor in Eq.(10)includes three multipliers related to temperature,entropy increment and molecule number increment,respectively.Since the reaction in Eq.(1)is assumed to be generic and is followed in cracking of all the components(including PCs and all the light definite components),ηi,the distribution factorfor PCi,can be roughly estimated from the multiplier of entropy increment,exp(ΔSi/R)

wherencis the number of all components and ΔSiis the entropy increment of the reaction for cracking of PCi.Following Zhang,X.et al.[25],the entropy increment of the controlling step in Reaction(1)is approximated by the translational entropy of PCi,

since the entropy of the activated state is assumed to be zero.Substituting ΔSi/Rin the above equation into Eq.(11),we have

To estimate the tendency factor δi,m,we consider the entropy increment of the reaction producing PCm.By an analogy to Eq.(12),this entropy increment can be approximated as

Using ΔSi,mas a measure for the ease with which PCiis cracked to produce PCm,the tendency factor is quantified as

wherekin the summation is for all the PCs produced through cracking of PCi,and μ a parameter to be determined from production data,though it may be interpreted in a broad sense as an indicator for the position at which the chain of PCiis likely to break off:positions close to the center or the ends of the chain are preferred if|μ|＞ 0 and all the positions in the chain are equally probable if μ=0.

In comparison with the correlation of Guptaet al.[6]for the rate constant

of their generic reaction PCi→ PCm+PCn+ λi,m,ncoke,the blocking factor in the above equation is replaced in Eq.(10)by two multipliers,the distribution factor(ηi)and the tendency factor(δi,m),in order to get a better differentiation for different PCs both as the reactant and the product of the cracking reaction in Reaction(1).

3.Characterization of the Oils and Steady State Model for a Prototype Riser

3.1.Characterization based on special pseudo-components

Narrow cuts of true boiling point(TBP)distillation offeed-stock oils,which were characterized with their boiling point temperatures and densities,were used as conventional pseudo-components(CPCs)by Guptaet al.[6].In this paper,however,special pseudo-components(SPCs)as proposed by the authors[10]are used as the entities of the proposed cracking reactions.SPCs are defined in pairs of narrow cuts of TBP distillation on the basis of CPCs.The two SPCs in each pair have the same normal boiling temperature or normal boiling temperature range,but different Watson characterization factors.With the normal boiling temperature and Watson characterization factor known,the properties of a SPC such as density,molecular weight,combustion heat,carbon-to-hydrogen weight ratio and liquid and vapor heat capacities can be fully determined by well established correlations.The correlations used in this work are detailed in Appendix A together with basic properties for SPCs acquired by the cutting temperatures set to be 30°C.

SPCs are distributed by their normal boiling temperatures in a range covering the true boiling point(TBP)distillation temperature ranges of all possible stock oils,and the normal boiling temperature interval between neighboring pairs of SPCs is suggested to be 20-30°C.

With the boiling temperature ranges of the defined SPCs,the TBP distillation recovery curves of all the stock oils are cut.Distillate narrow cut or pseudo-componentiof stock oiljcontributes to the contents of thei-th pair of SPCs of the same boiling temperature range in the following way

wherewis the concentration of a PC or SPC among all the PCs or SPCs in weight fraction,Δwis the increment of concentration,and ρ is the density in kg·m-3,respectively.The concentrations of SPCs in the feed oil as a whole are calculated as

The above characterization procedure also includes light definite components hydrogen,methane,ethylene,ethane,propylene,propane,butene,butane and pentane as cracking products.Detailed steps of this procedure is referred to[10]with a modification to the Watson characterization factors for light(L)and heavy(H)SPCs,Kw,L=12.9147 andKw,H=9.6393 which were determined by one time backward optimization after other model parameters were primarily regressed withKw,L=12.6 andKw,H=10.0,as indicated in Section 4.

3.2.Steady state model for a prototype riser

The steady state model used in this paper is built under the following assumptions:(1)the gas is ideal;(2)vaporization of stock oils is instantaneous;(3)Conradson carbon is included explicitly;(4)the catalyst particles exist as loose clusters;(5)the coke exists in solid and deposits on the catalyst particles;(6)both the gas and solid move upwards in plug flow,but with different velocities;and(7)perfect mixing and heat equilibrium exist among the gas and the solid particles in each cross section area of the riser.These assumptions are partially used by Guptaet al.[5,6],Fernandeset al.[7,8],Han and Chung[3,4]and Ali and Rohani[26].While complicated and computationally intensive 2-or 3-dimensional computational flow dynamics models are necessarily valuable for structural analysis and design of risers and their feed injection area in particular[12],one-dimension models resulted from the above assumptions are suitable for the purpose of process control and optimization,since for commercial risers,the big lengths make the back-mixing effect negligible and the big diameters together with the turbulent flow eliminate the wall effect.At this point,it is noted that the big errors with the plug flow model of Duet al.[27]may be explained from their 3×0.016 m riser where the wall effect is significant.

The prototype for fluid catalytic risers is shown in Fig.2 where a side feed oil is included.Its steady state model together with the solution method was developed in a previous work of our laboratory(Zhang,J.et al.[10])and is detailed in Appendix B with an exception for the heatbalance of Eq.(B.3)where ΔHlossin kJ per kg of coke is a parameter to be determined from production data.ΔHlosscould be interpreted roughly as the heat loss from the riser to the environment or as the correction for systematic deviations caused by factors affecting the heat balance in the above equation.It is found in our practice that ΔHlossis important in modeling the outlet temperature of risers,though its magnitude is usually small.

Fig.2.Schematic diagram of the prototype riser:1,regenerated catalyst;2,dispersion steam;3,stock oil;4,side feed oil;5,gas and solid to the stripper and separator.

4.Parameter Identification

The above riser model includes nine parameters K={Kw,L,Kw,H}and X={k0,μ,υ,α,β,ω,ΔHloss}which can be obtained through the following minimization

s.t.

wherejstands for the production case or scenario(one or more sets of production data can be used),YpandandtROandare the yields(wt%)of productpand the temperature(ROT,in°C)at the outlet of the riser respectively predicted by the model and taken from the plant data,withp=GS for dry gas(H2+C1+C2),LPG for lique fied petroleum gas(C3+C4),GSL for gasoline with normal boiling points(b.p.)of 38.5-221 °C,LCO for light cycle oil with b.p.221-410 °C,RO for recycle oil with b.p.410-531 °C,RES for residue with b.p.＞531 °C and CK for coke.The predicted yields of GS,LPG,GSL,LCO,RO and RES are determined by summing up the flowrates of the constituting discrete components or pseudo-components with b.p.temperatures in the corresponding b.p.ranges of the products,at the outlet of the riser.The weight factors(ψ)in Eq.(21)are set with some arbitrariness to be ψp=1 forp=GSL,LCO and RO,ψp=15 forp=LPG and GS,ψCK=15 and ψt=1.Besides,the residue(RES)with b.p.＞531 °C is not be included in Eq.(21)in the actual calculation,since its flowrate can be expressed by those of other products.

The minimization in Eq.(21)is solved with the strategy shown in Fig.3 where the model parameters are divided by experience into groups which can be initialized and bounded separately according to the regression errors of part of the target variables.On this strategy,the following four points are worth noting:

(1)This strategy is necessary since the feasible reactions are involved with the model parameters.

(2)The effect of Watson factors for light and heavy special pseudocomponents,K={Kw,L,Kw,H},on the model performance is significant and fundamental,and K and X are asynchronously identified.K is determined by keeping all the parameters of X to be constant values identified withKw,L=12.6 andKw,H=10.0.In this way,the values ofKw,L=12.9147 andKw,H=9.6393 used in this study were determined with the production data of case 1 for riser I as introduced in Section 5.

(3)The global optimization procedure,a simulated annealing algorithm followed by a trust-region-reflective Newton method,as suggested in previous work of our laboratory(Zhang,J.et al.[10])is employed with the two searching hyper-cubic spaces for X and K defined by the numbers in Table 1.

(4)The normal boiling temperature intervals for cutting conventional pseudo-components(PCs or CPCs)and special pseudocomponents(SPCs)have effects on the performance of the riser model,but in the range of 15 to 30°C,the effects are limited as demonstrated in Section 5.1.

5.Tests with Production Data

Production data from four commercial risers are used to test the model proposed in this study.These data were reported by Zhang,J.et al.[10]for Riser I,Hernández-Barajaset al.[20,28]for Riser II,Araujo-Monroy and López-Isunza[29]for riser III,and Dasilaet al.[30]for riser IV.

Table 2 lists the geometric sizes of the risers and the properties of the involved catalysts.The properties of stock oils and operational conditions for different production cases of Risers I,II and III were detailed in Zhang,J.et al.[10],and those for the four production cases of Riser IV are listed in Table 3.The Conradson carbon contents of stock oils used in this study are 0.42 wt.%(Case 1)and 3.1 wt%(Case 2)for Riser I,1.0 wt%for the two cases of Riser II,and 0.43 wt%for the only case of Riser III.Note that some revisions as listed in Table 4 have been made to the data for Riser I reported by Zhang,J.et al.[10],after a careful survey of the original production records.

Fig.3.Strategy for identifying the model parameters.

In addition,we assume in all the calculation of this section that coke have the same density and heat capacity as those of the catalystin question,the catalyst clusters have an average diameter of 6 mm,and the volume fraction of clusters at the riser's inlet be 0.5.

Table 1Lower and upper bounds(LB and UB)for the model parameters

Table 2Geometrics of the risers and properties of the catalysts

Table 3Properties of stock oils and operational conditions for Riser IV

Table 4Revision to the operational conditions of Riser I

In the same way as that of Zhang,J.et al.[10],the regression and prediction capabilities of the riser model are characterized by the following two errors

where RMSE is the root mean square relative error,Emaxthe maximum absolute relative error,andNpthe number of products.

5.1.Test results with Riser I

For Riser I,there are two production cases where the stock oils and operational conditions are different and recycle oil exists as side feed in Case 2.In this test,the production data of Case 1 were used to determine the parameters of the proposed model using the method in Section 4,and those of Case 2 were used to verify the model's prediction capability.Table 5 lists three sets of parameters for the model with the normal boiling temperature interval(ΔTB)set to be 15,20 and 30 °C,respectively,for cutting the special pseudo-components(SPCs)and common pseudo-components(PCs or CPCs).On this test,the following three observations can be made:

(1)The number of feasible cracking reactions in the form of(1)is 2568,1666 and 806 for ΔTB=15,20 and 30 °C,respectively,a sharp decrease compared with that in the work of Zhang,J.et al.[10]where the generic reaction of Guptaet al.[6]was used and the corresponding number of reactions is respectively 69,052,33,932 and 13,244,which means a great reduction in computational intensity.

Table 5Model parameters identified for riser I

(2)As indicated by the root mean square relative error(RMSE)and the maximum absolute relative error(Emax)in Table 6,the production data of riser I in both cases can be well fit and predicted by the model proposed in this study.From a comparison with Zhang,J.et al.[10],it is clear that the model of this paper has a regression and prediction performance comparable to or better than that of the model of Zhang,J.et al.

(3)The normal boiling temperature interval(ΔTB)for cutting SPCs and PCs,as mentioned previously and shown in Table 6,has a limited effect on the performance of the model,and is taken to be 30°C in the tests with risers II,III and IV stated later.

Table 6Fitting and prediction errors of the model for riser I

In addition,the proposed model is sensitive to its nine parameters X={k0,μ,υ,α,β,ω,ΔHloss}and K={Kw,L,Kw,H},which is demonstrated in Table 7 where listed are the relative increments of gasoline(GSL)and coke(CK)production rates in wt%and temperature in°C at the outlet of Riser I in Case 1 with respect to the relative increment of model parameters in Table 5 for ΔTB=30 °C.Note that in calculating the relative sensitivities in Table 7,parameters other than the one in question are kept unchanged.With the same set of model parameters,the coking amount defined in Eq.(7)for the generic Reaction in Eq.(1)is calculated and shown in Fig.4 for Riser I in Case 1,as a function of the intermediate substance's amount and carbon-to-hydrogen mass ratio.Figs.5,6 and 7 depict the distributions of temperature and product yields along Riser I in both Cases 1 and 2,calculated with the proposed model using the same parameters,where the jumps in temperature and recycle oil yield happen in Case 2 because of the middle feed.

At the end of this subsection,an additional test with riser I is provided to show the fact that parameters of the proposed model change withthe objective function in regression.In this test,the above calculation was repeated for ΔTB=30 °C using a different objective function of

Table 7Relative increments of two product rates in wt.%and temperature in°C at the outlet of Riser I in Case 1 with respect to the relative increment of model parameters for ΔTB=30 °C

Fig.4.Coking amount of the generic reaction in Eq.(1)as a function of the intermediate's amount and carbon-to-hydrogen weight ratio,defined in Eq.(7)with the model parameters for riser I and ΔTB=30 °C.

whereψt=2,ψE=100,andψps are the same as those stated previously.The seven parameters were regressed to bek0=421.7359,μ=-0.8046,υ =0.0540,α =0.0027,β =-0.0019,ω =0.1095 andΔHloss=18,103.59,and the corresponding fitting and prediction errors are listed in Table 8.From the viewpoint of RMSE andEmax,results in both Tables 6 and 8 are comparable,but for the temperature at the outlet of the riser(ROT),both fitting and prediction errors in Table 8 are reduced from 2.56 and 5.37 °C in Table 6 to 1.12 and 2.64 °C in Table 8,respectively.In addition,it is noted from tests previously conducted by the authors[10],that problems exist with the identifiablility of the parameters in the above riser model as a whole,and multiple sets of solutions exist for the problem of Eqs.(21)and(24).

5.2.Test results with Risers II,III and IV

In the tests with Risers II,III and IV,ΔTB=30 °C,Kw,L=12.9147 andKw,H=9.6393 as already mentioned previously.Table 9 lists three sets of the seven parameters X of the proposed model for these three risers,identified with the method in Section 4 and using the production data in one case of each of the risers,respectively.Using these parameters,the product yields and temperatures at the outlet of Riser II and IV in other case(s)are predicted.The regression and prediction errors of the model,as defined in Table 6,are tabulated in Tables 10-12 for different production cases of Riser II,III and IV,respectively.Note that for riser III,data are available only for one production case.From the errors listed in the last three tables,it is clear that the proposed model is powerful in correlating and predicting the production performance of different risers,and is preferably compared with the model of Zhang,J.et al.[10]where test results are reported for Risers II and III,not to mention the dramatic decrease in computational intensity due to more than one order of magnitude reduction in the number of the involved reactions.

Fig.5.Calculated distribution of temperature along Riser I in Cases 1 and 2.

Fig.6.Calculated distribution of product yields along Riser I in Case 1.

6.Conclusions

A new generic reaction is proposed for describing the cracking behavior of petroleum narrow cuts or pseudo-components(PCs),together with a novel coking amount correlation built by analysis and a rate constantformula derived from the transition state theory.With this generic reaction and special pseudo-components(SPCs),a predictive onedimensional steady state model is constructed for fluid catalytic cracking risers in the sense that for a given riser and given catalyst,the model parameters are independent of stock oils,product schemes and other operational conditions.This riser model is theoretically more reasonable and easy for analysis,and has great correlating and predicting capability and low computation intensity.

There are ten parameters in total for the riser model.Among them,the normal boiling temperature interval(ΔTB)for cutting PCs and SPCs can be taken to be 30°C,the Watson factors for light and heavy SPCs can be set asKw,L=12.9147 andKw,H=9.6393,and the left seven parameters X={k0,μ,υ,α,β,ω,ΔHloss}are sufficient for the model to fit and predict a riser's performance adequately.

Fig.7.Calculated distribution of product yields along Riser I in Case 2.

Table 8Fitting and prediction errors for riser I with ΔTB=30 °C and different model parameters regressed again

Table 9Model parameters identified for Risers II,III and IV

Table 10Fitting and prediction errors of the model for Riser II

Table 11Fitting errors of the model for Riser III

Table 12Fitting and prediction errors of the model for Riser IV

Nomenclature

Adeactivation parameter

Bdeactivation parameter

Cconcentration,kg·m-3

CH carbon-to-hydrogen mass ratio

Cpheat capacities,kJ·kg-1·K-1

DRSdiameter of riser,m

E0activation energy,kJ·kmol-1

Emaxmaximum absolute relative error

Fflowrates,kg·s-1

ΔHreaction or combustion heat,kJ·kg-1

ΔHlossheat loss,kJ·kg-1

ΔHi,mheat consumed by the cracking reaction,kJ·kmol-1

Kw,LWatson characterization factor for light SPCs

Kw,HWatson characterization factor for heavy SPCs

k0frequency factor,m3·(Cat kg)-1·s-1

krate constant of cracking reaction,m3·(Cat kg)-1·s-1

MW molecular weight,kJ·kmol-1

Npnumber of products

ncnumber of all components

Preaction pressure,kPa

Rgas constant,8.3145 kPa·m3·kmol-1·K-1

RMSE root mean square relative error

ri,mcracking reaction rate,kg·m3·s-1

ΔSentropy increment

Ttemperature,K

Tbmean boiling temperature,K

tROtemperature at the riser's outlet,°C

wmass fraction

Δwincrement of mass fraction

Yyields of product,wt%

Zlength of riser,m

ZRlocation of side feed oil,m

zposition along the riser,m

α coking parameter

β coking parameter

δi,mtendency factor

η distribution factor

λ coke produced in cracking reaction,kg·kmol-1

μ kinetic parameter

ρ density,kg·m3

τ kinetic parameter

υ kinetic parameter

φ catalyst activity coefficient

χ mass fraction of coke on the catalyst

ψ mass factor

ω coking parameter

Ω cross section area of the riser,m2

Subscripts

CAT catalyst

CK coke

H heavy end SPC

i,mcomponent or pseudo-componenti,m

L light end SPC

pproduct

RO riser's outlet

RS riser

STM steam

Superscripts

comb combustion

lliquid

v vapor/gas

Appendix A

According to the definition[10],the two SPCs in thei-th pair have the same mean boiling temperature,or boiling temperature in short

where subscriptB=L or H denotes the light and heavy special pseudocomponents,or SPCLand SPCH,respectively.

Fig.A.1.TBP distillation curve and narrow cuts(ΔTB=30 °C)of the feedstock oil in Case 1 of Riser I.

Table A.1SPCs for the feedstock oil in Case 1 of Riser I with ΔTB=30 °C,K w,L=12.6 and K w,H=10.

With the boiling temperature and density known,other physicochemical properties of a SPC(SPCLor SPCH)can be easily determined from the following correlations

where ΔHcombis calculated with API=141.5/ρ -131.5,and working temperatureTw=523.15 K(250 °C)for Cl p and 823.15 K(550 °C)for Cv p.

Fig.A1 shows the TBP distillation curve and narrow cuts(ΔTB=30°C)of the feedstock oil in Case 1 of Riser I,and Table A1 a benchmark of SPCs.

Appendix B

The flowrates of pseudo-component PCiand coke deposited on the catalyst along the height(z)of the riser can be derived from material balance

From heat balance,the temperature distribution is determined as

where ΔHlossis the heat loss in kJ per kg of coke as a tuning parameter,andCp,CK,Cp,CATandCp,STMare taken to be 1.15,1.15 and 1.97 kJ·kg-1·K-1.

In evaluating reaction rateri,mwith Eq.(8),concentrations ofPCiand catalyst particles in the riser are calculated by definition

and the mass fraction of coke on the catalyst is

wherevgandvcare respectively the gas and cluster phase velocities in m·s-1,δgis the volume fraction of the gas phase,andFc=FCAT+FCKthe cluster phase flowrate in kg·s-1.

The volume fraction of the gas phase is

being the volume fraction of the cluster phase.In the above equation,ρcis the cluster density calculated by

where ρpis the density of solid particles of catalyst+coke and εcthe voidage of the clusters taken to be 0.5.

The gas phase velocity is calculated by definition

whereFg=FSTM+Fiand ρgthe gas phase density in kg·m-3calculated as an ideal gas

whereg=9.8 m·s-2is the gravity constant,dc=6.0× 10-3m the cluster diameter,and μgthe gas phase viscosity in kg·m-1·s-1calculated by

with

In the above equations,the gas phase viscosity of thei-th definite component or pseudo-component is calculated by the following correlation

wheretis the temperature in°C.And the viscosity of steam is determined by the correlation

the distribution of pressure along the riser is calculated by the following equation

wherefgis the Blasius friction factor calculated by

[1]A.Voorhies Jr.,Carbon formation in catalytic cracking,Ind.Eng.Chem.37(1945)318-322.

[2]F.H.Blanding,Reaction rates in catalytic cracking of petroleum,Ind.Eng.Chem.45(1953)1186-1192.

[3]I.S.Han,C.-B.Chung,Dynamic modeling and simulation of a fluidized catalytic cracking process.Part I:Process modeling,Chem.Eng.Sci.56(2001)1951-1971.

[4]I.S.Han,C.-B.Chung,Dynamic modeling and simulation of a fluidized catalytic cracking process.Part II:Property estimation and simulation,Chem.Eng.Sci.56(2001)1973-1990.

[5]R.K.Gupta,V.Kumar,V.K.Srivastava,Modeling and simulation of fluid catalytic cracking unit,Rev.Chem.Eng.21(2005)95-131.

[6]R.K.Gupta,V.Kumar,V.K.Srivastava,A new generic approach for the modeling of fluid catalytic cracking(FCC)riser reactor,Chem.Eng.Sci.62(2007)4510-4528.

[7]J.L.Fernandes,J.J.Verstraete,C.I.C.Pinheiro,N.M.C.Oliveira,F.R.Ribeiro,Dynamic modelling of an industrial R2R FCC unit,Chem.Eng.Sci.62(2007)1184-1198.

[8]J.L.Fernandes,C.I.C.Pinheiro,N.M.C.Oliveira,J.Inverno,F.R.Ribeiro,Model development and validation of an industrial UOP fluid catalytic cracking unit with a high-efficiency regenerator,Ind.Eng.Chem.Res.47(2008)850-866.

[9]V.K.Koratiya,S.Kumar,S.Sinha,Modeling,simulation and optimization of FCC dower reactor,Pet.Coal52(2010)183-192.

[10]J.Zhang,Z.Wang,H.Jiang,J.Chu,J.Zhou,S.Shao,Modeling fluid catalytic cracking risers with special pseudo-components,Chem.Eng.Sci.102(2013)87-98.

[11]H.Sildir,Y.Arkun,U.Canan,S.Celebi,U.Karani,I.Er,Dynamic modeling and optimization of an industrial fluid catalytic cracker,J.Process Control31(2015)30-44.

[12]C.I.C.Pinheiro,J.L.Fernandes,L.Domingues,A.J.S.Chambel,I.Gra?a,N.M.C.Oliveira,H.S.Cerqueira,F.R.Ribeiro,Fluid catalytic cracking(FCC)process modeling,simulation,and control,Ind.Eng.Chem.Res.51(2012)1-29.

[13]V.W.Weekman Jr.,D.M.Nace,Kinetics of catalytic cracking selectivity in fixed,moving,and fluid bed reactors,AIChE J.16(1970)397-404.

[14]S.M.Jacob,B.Gross,S.E.Voltz,V.M.Weekman Jr.,A lumping and reaction scheme for catalytic cracking,AIChE J.22(1976)701-713.

[15]G.F.Froment,Kinetic modeling of complex catalytic reactions,Rev.Inst.Fr.Pét.46(1991)491-500.

[16]W.Feng,E.Vynckier,G.F.Froment,Single event kinetics of catalytic cracking,Ind.Eng.Chem.Res.32(1993)2997-3005.

[17]D.K.Liguras,D.T.Allen,Structural models for catalytic cracking.1.Model compound reactions,Ind.Eng.Chem.Res.28(1989)665-673.

[18]D.K.Liguras,D.T.Allen,Structural models for catalytic cracking.2.Reactions of simulated oil mixtures,Ind.Eng.Chem.Res.28(1989)674-683.

[19]B.E.Stangeland,A kinetic model for the prediction of hydrocracker yields,Ind.Eng.Chem.Process.Des.Dev.13(1974)71-76.

[20]J.R.Hernández-Barajas,R.Vázquez-Román,M.G.Félix-Flores,A comprehensive estimation of kinetic parameters in lumped catalytic cracking reaction models,Fuel88(2009)169-178.

[21]H.Eyring,The activated complex in chemical reactions,J.Chem.Phys.3(1934)107-115.

[22]H.Eyring,The activated complex and the absolute rate of chemical reactions,Chem.Rev.1(1935)65-77.

[23]I.Pitault,M.Forissier,J.R.Bernard,Détermination de constantes cinétiques du craquage catalytique par la modélisation du test de microactivité (MAT),Can.J.Chem.Eng.73(1995)498-503.

[24]K.Xiong,C.Lu,Z.Wang,X.Gao,Quantitative correlations of cracking performance with physiochemical properties of FCC catalysts by a novel lump kinetic modelling method,Fuel161(2015)113-119.

[25]X.Zhang,J.Guo,X.Zhou,X.Wang,B.Yu,C.Ge,Kinetic modeling of catalytic cracking of monocyclic cycloparaffins—Calculation of pre-exponential factors,Acta Petrolei Sin.Pet.Process.Sect.29(2013)283-288.

[26]H.Ali,S.Rohani,Dynamic modeling and simulation of a riser-type fluid catalytic cracking unit,Chem.Eng.Technol.20(1997)118-130.

[27]Y.Du,H.Zhao,A.Ma,C.Yang,Equivalent reactor network model for the modeling of fluid catalytic cracking riser reactor,Ind.Eng.Chem.Res.54(2015)8732-8742.

[28]J.R.Hernández-Barajas,R.Vázquez-Román,D.Salazar-Sotelob,Multiplicity of steady states in FCC units:Effect of operating conditions,Fuel85(2006)849-859.

[29]C.Araujo-Monroy,F.López-Isunza,Modeling and simulation of an industrial fluid catalytic cracking riser reactor using a lump-kinetic model for a distinct feedstock,Ind.Eng.Chem.Res.45(2006)120-128.

[30]P.K.Dasila,I.R.Choudhury,S.Singh,S.Rajagopal,S.J.Chopra,D.N.Saraf,Simulation of an industrial fluid catalytic cracking riser reactor using a novel 10-lump kinetic model and some parametric,Ind.Eng.Chem.Res.53(2014)19660-19670.