A Comprehensive Estimation of Kinetic Parameters in Lumped Catalytic Cracking Reaction Models

7/27/2019 A Comprehensive Estimation of Kinetic Parameters in Lumped Catalytic Cracking Reaction Models

1/10

A comprehensive estimation of kinetic parameters in lumped catalyticcracking reaction models

Jos Roberto Hernndez-Barajas a, Richart Vzquez-Romn b,*, Ma.G. Flix-Flores c

a Universidad Jurez Autnoma de Tabasco, Divisin Acadmica de Ciencias Biolgicas, Carretera Villahermosa-Crdenas Km 0.5, 68039 Villahermosa, Mexicob Instituto Tecnolgico de Celaya, Departamento de Ingeniera Qumica, Av. Tecnolgico y G, Cubas s/n, 38010 Celaya, Mexicoc Universidad Autnoma de Zacatecas, Unidad Acadmica de Ciencias Qumicas, Carretera a Cd. Cuauhtmoc Km 0.5, Guadalupe, Zacatecas 98600, Mexico

a r t i c l e i n f o

Article history:

Received 12 November 2007Received in revised form 16 July 2008Accepted 17 July 2008Available online 19 August 2008

Keywords:

Catalytic crackingLumpingKinetic modelingDistribution function

a b s t r a c t

This work presents a comprehensive approach to estimate kinetic parameters when the involved reac-tions contain lumped chemical species. This approach is based on representing rate constants with a con-tinuous probability distribution function. In particular, the beta function is used to estimate kineticparameters in catalytic cracking reactions. Thus, several kinetic models for the catalytic process contain-ing different number of lumps are selected and a discretization procedure is carried out to estimate thecorresponding kinetic parameters. The kinetic representation based on the probability distribution sub-stantially reduces the computational and experimental effort involved in the numerical evaluation ofkinetic parameters.

Published by Elsevier Ltd.

1. Introduction

The catalytic cracking process converts heavy oil cuts into prod-ucts of better quality such as olefins and high octane gasoline usinga zeolite-type catalyst. The fluid catalytic cracking process (FCC) isin fact the key step of conversion in petroleum refineries. The FCCunit employed as a reference in this work is capable of processing30,000 barrels per day as given in [1]. Catalytic reactions take placein the riser consisting of a vertical pipe with a diameter between0.5 and 1.5 m and a height between 30 and 50 m. The heavy feed-stock is instantaneously vaporized when it mixes with the hot andregenerated catalyst (catalyst residence time in the riser is around5 s) and then the reaction proceeds in rather little time because ofthe high catalyst activity. During the reaction, some FCC productsand a hydrogen-deficient compound named coke is formed anddeposited on catalyst surface. As a result, the coke deposition tem-porarily deactivates the catalyst. FCC products are then disengagedvia cyclones while spent catalyst is passed through a stripper toseparate the FCC products adsorbed on catalyst surface. Finally,coke is burnt in the regenerator and converted into CO, CO2, H2O,sulfur compounds and nitro compounds. This action restores thecatalyst activity though fresh catalyst must be added periodically

to keep the desired activity (catalyst residence time in the densebed is around 9 min).Several studies have been focused on modeling of cracking

reactions kinetics. Some of them proposed kinetic models basedon empirical correlations with a limited range of applicability[27]. Most of kinetic studies consider the lumping technique,which establishes that various chemical species can be lumpedaccording to similar characteristics (e.g. the boiling point). Thefirst model based on this technique considered two lumps [8]: ga-soil as the reactant, and a product containing gasoline, gases andcoke. A three-lump model consisting in gasoil, gasoline, and lightgases and coke was developed [9]. The gasoil cracking is repre-sented with second-order kinetics although coupled to first-orderactivity decay, whereas gasoline conversion is represented withfirst-order kinetics. Using different gasoil streams, this model de-tected a significant effect of the feedstock quality on reaction rateconstants. Others have [10,11] separated the third lump in Nacesmodel to produce a four-lump model to ratify that rate constantsare strongly dependent on feedstock quality. Several kinetic mod-els considering five lumps have been published: Larocca et al.[12] split oil feed into paraffin, naphtha and aromatic (PNA) frac-tions; Corella et al. [13] separate oil feed in two gasoil fractions. Asix-lump model that was also applied to residual oil cracking[14]. Then, the lumping approach has been extended to includemore lumps: eight lumps [15], 11 lumps [16], 13 lumps [17],and 19 lumps [18]. One of the most widely used lumping modelsis the 10-lump model proposed by Jacob et al. [19]. This modeltakes into account PNA fractions for two feed fractions as well

0016-2361/$ - see front matter Published by Elsevier Ltd.doi:10.1016/j.fuel.2008.07.023

* Corresponding author. Tel.: +52 461 61 17575x153; fax: +52 461 61 17744.E-mail addresses: [email protected] (J.R. Hernndez-Barajas),

[email protected] (R. Vzquez-Romn), [email protected] (Ma.G.Flix-Flores).

Fuel 88 (2009) 169178

Contents lists available at ScienceDirect

Fuel

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / f u e l
mailto:[email protected]:[email protected]:[email protected]://www.sciencedirect.com/science/journal/00162361http://www.elsevier.com/locate/fuelhttp://www.elsevier.com/locate/fuelhttp://www.sciencedirect.com/science/journal/00162361mailto:[email protected]:[email protected]:[email protected]


2/10

as heavy and light cyclic oils and the authors have indicated thatrate constants are independent of the feedstock quality. The maindisadvantage of all models based on lumping is that a large num-ber of experiments must be carried out to predict their kineticconstants.

In last years, novel contributions have taken into accountadsorption and intra-crystalline diffusion effects in kinetic model-ing [2022]. As a result, non-linear mass balances account for bothdiffusion constraints experienced by hydrocarbon species while

evolving in the zeolite pore network and the effect of the systempressure on the apparent adsorption selectivity.

Another possible approach to model cracking reactions isbased on the kinetic representation at molecular level. Thesemodels use vectors to include the representation of most chem-ical species involved in complex mixtures [23]. In a similar study,kinetic models are based on carbocation chemistry [2426]. Themain advantage of these models is that they provide a detailedknowledge of the performance of catalytic reactions. Unfortu-nately, these techniques require a much larger database of ki-netic information than the database required in the lumping

technique and this information is unavailable in the open litera-ture. Recently, Gupta et al. [27] proposed an elementary reaction

Nomenclature

A riser cross section area, m2

bAj overall pre-exponential factor defined by Eq. (18), [m3

of gas/(kg of catalyst s)][m3 of gas/kg mol]n1

Aji pre-exponential factor for reaction constants, [m3 of

gas/(kg of catalyst s)][m3 of gas/kg mol]n1

aji terms ruled by Eqs. (16)(21)BU butane-butylenes (C4)C concentration, kg mol/m3 of gasC0 gas concentration at z =0, kg mol/m

3 of gasCPg gas feed average heat capacity, kJ/(kg K)CPl liquid feed average heat capacity, kJ/(kg K)CPs catalyst average heat capacity, kJ/(kg K)CPv dispersion steam average heat capacity, kJ/(kg K)CPv coke average heat capacity, kJ/(kg K)CATOIL catalyst/oil ratio, kg of catalyst/kg of oilEji activation energy, kJ/kg molFg feed oil flowrate, kg/sFs catalyst flowrate, kg/sFv steam flowrate, kg/sFv coke flowrate, kg/s

Fj cumulative distribution functionfjTBi probability density function as a function of TBi ,

fjTBi ajiGA gases (butanes C4 + light gases C1C3)HCO heavy cyclic oilHN heavy naphtaDHF heat of formation, kJ/kg molDHv heat of feed vaporization, kJ/kgkij; kji reaction rate constant, [m

3 of gas/(kg of catalyst s)][m3

of gas/kg mol]n1

kv Rate constant of coke formation, kg/kgkvo pre-exponential factor in Arrhenius-type equation for

coke formation, kg/kg^kj overall cracking constant for lump jkHCO,BU kinetic constant for cracking from heavy cyclic oil to bu-

tane-butylenes in a six-lump modelkHCO,GA kinetic constant for cracking from heavy cyclic oil to

gases in a six-lump modelkHCO,HN kinetic constant for cracking from heavy cyclic oil to

heavy naphta in a six-lump modelkHCO,LN kinetic constant for cracking from heavy cyclic oil to

light naphta in a six-lump modelkHN,BU kinetic constant for cracking from heavy naphta to bu-

tane-butylenes in a six-lump modelkHN,GA overall cracking constant from heavy naphta to gases

(light gases + butanes) in a six-lump modelkHN,LG kinetic constant for cracking from heavy naphta to light

gases in a six-lump modelkLCO,BU kinetic constant for cracking from light cyclic oil to bu-

tane-butylenes in a six-lump model

kLCO,GA kinetic constant for cracking from light cyclic oil togases in a six-lump model

kLCO,HN kinetic constant for cracking from light cyclic oil to hea-vy naphta in a six-lump model

kLCO,LN kinetic constant for cracking from light cyclic oil to light

naphta in a six-lump modelkLN,GA overall cracking constant from light naphta to gases

(light gases + butane-butylenes) in a six-lump modelkLN,BU kinetic constant for cracking from light naphta to bu-

tane-butylenes in a six-lump modelkLN,LG kinetic constant for cracking from light naphta to light

gases in a six-lump modelLCO light cyclic oilLG light gasesLN light naphtaM molecular weight, kg/kg moln apparent order of reactionN number of lumps in a kinetic modelNESS normalized error sum of squaresNO number of overall lumps, NO = 4

Npar number of kinetic parameters involved in a crackingmodel

QR heat of reaction, kJ/(m3 of gas s)

R reaction rate, kg mol/(m3 of gas s)R0 reaction rate, kg mol/(kg of catalyst s)Ru universal constant of gasesTB boiling point temperature of oil fraction, KTBf boiling point temperature of FCC feed, KTBi; min ; TBi;max minimum and maximum boiling point tempera-

tures for the lump formed i, KTf preheat feed temperature, KTmix mix temperature in the vaporization zone, KTrs riser temperature, KTs hot catalyst temperature, KTv steam temperature, Kug gas velocity, m/sx experimental or calculated values employed in non-lin-

ear regressionXO overall conversion, kg/kgy mole fraction, kg mol/kg molz axial position, m

Greek symbolsa;b scale parameters of the beta distributionvrs coke on catalyst, kg of coke/kg of catalyste void fraction, m3 of gas/m3 total/ deactivation functionm stoichiometric coefficientqg; qs gas and catalyst densities, kg/m

3

W slip factor, non-dimensional

170 J.R. Hernndez-Barajas et al. / Fuel 88 (2009) 169178


3/10

scheme whereas the kinetic parameters are estimated using asemi-empirical approach based on normal probabilitydistribution.

Reaction rate constants are typically calculated from experi-mental data. Considering that catalytic reactions occurs in irrevers-ible reaction steps [19,28], then the maximum number of reactionpathways and, consequently, of rate constants, is

Number of pathways N2

N!

2!N 2!

NN 1

21

The computational effort to determine the rate constants in-creases when all reaction pathways are considered. For instance,the maximum number of rate constants in the 10-lump model iscalculated as 45. However, the number of kinetic parameters is re-duced because some reaction pathways are considered as improb-able and its contribution in the reaction network is neglected[19,10]. For example, the 10-lump model proposed by Jacob et al.[19] contains no more than 20 reaction pathways. Furthermore,Arbel et al. [29] consider that some kinetic rate constants fromthe Jacobs model are numerically identical and the number of con-stants can thus be reduced to 14.

Even under the above consideration, the number of rate con-stants remains large. Thus, a comprehensive kinetic model is pro-posed in this paper to estimate kinetic constants when crackingreactions representation is based on the lumping technique. Thisapproach characterizes the FCC products in detail, prevents exces-sive reduction of rate constants and reduces computational effortin the numerical evaluation of kinetic parameters.

2. The riser model

A model of the riser is developed in this section since the crack-ing reactions are carried out within it. The riser is fed at the bottomof the unit with an atomized gasoil, the regenerated catalyst, andsteam streams. The gasoil is almost instantaneously vaporized

and mixed with the other streams. In order to model this stage,two basic assumptions are adopted here: instantaneous vaporiza-tion occurs as a result of an intimate gassolid mixing and chemi-cal reactions in the vapor phase due to thermal cracking can beneglected at low temperatures [3033]. The heat carried in the ri-ser via the regenerated catalyst is consumed to vaporize the feed-stock and to sustain the cracking reactions. Both vaporization andcracking processes are endothermic so that the hot catalyst pro-vides energy to make the oil achieve the boiling point, vaporizeand, in the vapor phase, get the mix temperature. Thus, the follow-ing equation can be obtained from an overall energy balance at thefeeding point:

Tmix FsCPsTs FvCPvTs FgCPgTBf FvCPvTv FgCPlTBf Tf FgDHv

FsCPs FvCPv FgCPg FvCPv2

where Fs, Fv, Fg and Fv are the catalyst flowrate, coke flowrate, feedflowrate, and the steam flowrate, respectively; CPs, CPv, CPg, CPl, andCPv represent the average heat capacities for the catalyst, coke, li-quid feed oil, gas feed oil and the dispersion steam, respectively;Ts, TBf, Tv and Tf are the temperatures for catalyst, feed oil at theboiling point, steam and the feed oil leaving the pre-heater; andDHv is the heat of vaporization of gasoil fed to the unit. Heat capac-ities for hydrocarbons were calculated via empirical correlationsbased on thermophysical databases [34,35]. Molecular weightswere calculated by using classical correlations [3638]. Gasoil heatof vaporization was calculated employing the original PengRobin-

son EOS. Heat capacities for steam and coke, were obtained fromsaturated steam and pure carbon (coke is assumed as graphite) ta-

bles, respectively. Catalyst heat capacity depends linearly on alu-mina composition and its function is proprietary, provided bymanufacturer.

A conclusion achieved in several studies on flow-pattern mod-els indicates that the plug flow reactor model for both gas and solidphases provides good approximations in the riser unit [13,3941].As a result of this assumption, steady-state mass balance for allchemical species involved as reactants or products is written as

ugdCjdz

qs1 e/

eR0j; j 1; 2; . . . ; N 3a

with e 1

1 wqgqs

FsFg

3b

ug Fg

Aqge3c

where ug is the gas velocity, Cj is concentration of compoundj, qs isthe catalyst density, qg is the gaseous mixture density e is void frac-tion, w is the ratio between gas and solid velocities in the riser (slipfactor, in this work, no slip between phases is considered: w = 1), Ais the riser cross section area, / is a deactivation function, R0j is the

reaction rate for chemical species j, and zis the axial position. Moredetails related to riser modeling have been provided in a previouswork [1].

The deactivation function is modeled here via the exponentiallaw proposed in [42]. The boundary condition for the above equa-tion is

Cj0 COyj; j 1; 2; . . . ; N 4

where CO represents the gas concentration at the riser inlet andmole fractions yi, which are evaluated employing the ASTM-D1160 distillation curve of the FCC feed. The ASTM-D1160 isconverted into TBP curve according to an algorithm based on proce-dures detailed in [35] and recently reviewed by Ahmed [43].

The reaction rates and the number of lumps involved in cata-lytic cracking reactions depend on the selected kinetic model. Ina generic sense this reaction rate is

R0j Xj1i1

vijkijCn2i

XNij1

kjiCn1j ; j 1; 2; . . . N 5

where

vij MiMj

6

being kij the rate constants, vij the stoichiometric coefficients and Mthe molecular weight. It should be mentioned here, kinetic con-stants defined above are no intrinsic rates because of assumptionstaken in this study make difficult to distinguish between diffusion,adsorption or selective catalyst deactivation phenomena. As a re-

sult, this kinetic approach is useful for calculating observed kineticconstants.

Eq. (5) indicates that lump j is being generated and cracked as afunction of the postulated reaction network with an apparent orderof reaction n, whereas the rate constants depend exclusively onreaction temperature. The temperature effect on kinetic constantsis represented by an Arrhenius-type expression [10,11,14,19].Thus, a reaction rate constant, where a lump j is cracked into alump i, can be written as

kji Ajie

EjiRT 7

whereAji is the pre-exponential Arrhenius factor, Eji is the activationenergy and R is the universal constant of ideal gases.

In particular, coke is a solid with pseudo-graphite nature so thatit cannot be described in terms of the boiling point and a semi-

J.R. Hernndez-Barajas et al. / Fuel 88 (2009) 169178 171


4/10

empirical relationship based on experimental observations is pre-ferred. Thus, coke is related to the overall gasoil conversion by[44]:

vrs kv

CATOIL

XO

1 XO

8

where vrs is the coke in the riser, kv is the rate constant for the cokeformation, CATOIL is the catalyst-oil ratio, and X

Ois the overall

conversion.The rate constant for coke formation can be represented via an

Arrhenius function to take into account the temperature depen-dence [12,45]. This expression assumes catalyst deactivation isno selective for each lump.

Considering the above-described facts the derivative of Eq. (8)with respect to z can be written as

dvrsdz

kvo e

EvRu T

CATOIL

/vrs

1 XO2

9

where Ev is the energy of activation for coke formation. This param-eter depends on feedstock and catalyst type.

The endothermic nature of cracking reactions produces an

appreciable temperature drop along the riser length. To assess thistemperature drop, an energy balance for an adiabatic operation isestablished using similar assumptions adopted for species balanceswith respect to the flow-pattern, e.g. plug flow-pattern:

qgCPgugdTrsdz

QR 10

where QR represents the heat required for catalytic cracking thatcan be calculated via the heat of formation DHF for each reactionpathway according to

QR XNi1

RiDHFi 11

The heat of formation for each lump is calculated with the stan-dard enthalpy of formation and heat capacity of the lumps in-volved in the reaction pathway i. Heat of formation forhydrocarbons were calculated employing empirical correlationsbased on thermophysical databases from [35]. Combining Eqs.(5), (10), and (11), the following equation is obtained:

qgCPgugdTrsdz

XN1i1

Cnii

XNji1

kijDHFjiqs1 e

e/ 12

with,

DHFji mijDHFj DHFi 13

and boundary condition,

Trs0 Tmix 14

It should be observed that the mixing temperature and othervariables evaluated in the vaporization zone such as density, voidfraction and gas velocity also constitute boundary conditions atthe riser inlet.

3. The kinetic model

This novel approach for the kinetic model is supported on theassumption that intrinsic kinetic constants could be representedby a continuous distribution function by selecting an independentstochastic variable. This idea is supported on previous workswhere rate constants for desulphurization of diesel fuel have been

expressed in terms of the C distribution [46] and normal distribu-tion function [27]. Hence frequency factors for Arrhenius-type

equation are expressed here by a probability distribution function.The independent variable is selected here as the boiling point sinceoil feeds are generally defined according to boiling point cuts.

Considering Nlumps where the first lump remains as the heavi-est lump and the Nth-lump is the lightest compound, the first lumphas no generation side for the reaction and the Nth-lump has nodisappearance term. Expanding Eq. (5) and considering the exis-tence generation and disappearance terms, the following tablecan be generated:

Lumpj Generation Disappearance

R1 k1;2 .. . k1;NCn11

R2 m1;2k1;2Cn11 k2;3 .. . k2;NC

n22

.

.

....

.

.

.

RN1 m1;N1k1;N1Cn11 .. . mN2;N1kN2;N1C

nN2N2 kN1;NC

nN1N1

RN m1;Nk1;NCn11 mN1;NkN1;NC

nN1N1

15

The set of rate constants for the disappearance term on theright-hand side is

kj XN

ij1

kji 16

where subscript i refers to the product formed from lump j. Thesummation above is called the overall cracking constant for lumpj. This term is equal to zero for the Nth-lump due to the no-exis-tence of any lump with lower molecular weight. Using the Arrhe-nius-type of equation in Eq. (16) the following equation is obtained:

^kj XN

ij1

Ajie

EjiRu T 17

It should be noted that activation energies remain constant for eachlump and they are in fact known parameters. Thus, the pre-expo-nential factors are represented with a probability distribution func-tion. Defining the overall pre-exponential factor as,

bAj XNij1

Aji bAj XNij1

aji 18

then the summation becomes equal to unity so that each value canbe referred as a proportion, i.e.XNij1

aji 1 19

Aji bAjaji 20The above proportion is defined as a cumulative distribution for

continuous variables:

XNij1

aji FjTBi 21

A cumulative distribution is equivalent to the area under thedistribution function f defined in the positive range TBi; min 6TBi 6 TBi; max:

FjTBi ; TBi; min ; TBi; max

ZTBi; maxTBi; min

fjTBi dTBi 22

Integration is recognized as the summation of the distributionfunctionXNij1

aji XN

ij1

fjTBi 23

aji fjTBi 24



5/10

Combining Eqs. (17), (20) and (23), (24):

kji bAjajie EjiRu T bAjfjTBi e EjiRu T 25

the distribution function would be a function for continuous vari-ables defined in a given positive range TBi; min 6 TB 6 TBi;max. In thispaper, the beta distribution function has been selected because itprovides large flexibility for data fitting and it has been successfullyused in several science fields [47]. The beta distribution is a two-shape parameter continuous function with an interval defined bya minimum and maximum value and a polynomial nature, which

is given by

fjTBi ;aj;bj 1

TBmax TBmin

Cajbj

CajCbj

TBi TBi;minTBi;max TBi;min

!aj 1TBi;max TBi

TBi;max TBi;min

!bj 126

in the range TBmin 6 TB 6 TBmax. The cumulative function will be theresult of using Eq. (26) in the integration according to the selectedrange for the boiling point.

It has mentioned above that Eq. (1) can give an estimation of thenumber of kinetic parameters required to model the cracking reac-tions. Using this approach, the number of parameters required canbe calculated by

Npar N 1 2 27

since there are (N 1) pre-exponential factors and two parametersfor the distribution function. The advantage of using the approachin this paper becomes greater when the number of lumps increases,Table 1.

In cracking, reaction rates are generally considered as pseudo-first-order for light lumps and pseudo-second-order for heavylumps [8,48]. However, pseudo-first-order is adopted here whenmore than 20 lumps are used in the model because the expectedbehavior is like elementary reactions rather than using multiplesteps. The operating conditions used in the evaluation of rate con-stants for the three-lump kinetic model, gasoil lump is crackedinto gasoline, light gases and coke [9], are similar to those usedin [8]. The utilization of an apparent reaction order equal to 2 isfeasible because various elementary steps are represented whenthe overall conversion of FCC feed is considered. Summarizing,the selection of apparent reaction orders may be founded on pre-vious studies but reasonable assumptions may properly justify anyother choice.

4. Case studies definition

Several kinetic models with a marked degree of complexity areused to demonstrate the advantages of this novel approach. Thechoice of a kinetic model depends on particular requirements.

For example, a kinetic model containing a large number of lumpscould permit a detailed characterization and, consequently, a bet-

ter representation of the products quality. It should be recognizedthat a kinetic model with these features implies a greater compu-tational effort. This could be unnecessary if our target is to deter-mine responses in unsteady state of some of the state variables.A more detailed kinetic model is required when it is used foroptimization purposes such maximizing olefin production or theoctane number of gasoline.

In refineries, each lump quality is governed by the operatingconditions and characteristics of the main fractionators. As a con-sequence, the number of lumps established in most kinetic mod-els is commonly related with the number of boiling point cutsconsidered in the fractionators. In this section, a modificationfor the four-lump model published by Yen [10] and a modifica-tion for the six-lump model presented by Takatsuka et al. [14]are studied. In addition, two more complex models are also pro-posed here: a 20-lump model and a 35-lump model. In chemicalkinetics, it has been considered that lumps boiling up to the boil-ing temperature of n-C12 are cracked with an apparent orderequal to 2. On the other hand, lighter lumps will be cracked withfirst-order kinetics.

The modified four-lump model consists of: unconverted gasoilC12, heavy naphtha (approx. C13C14), light naphtha (approx.C5C12), and light gases (C1C4). The modified six-lump model isdefined by: heavy cycle oil C21, light cycle oil (approx. C15C21),heavy naphtha (approx. C13C14), light naphtha (approx. C5C12),butanes-butylenes (C4) and light gases (C1C3). These definitionsare referred to approximate boiling point cuts though the rangeof boiling points depends on each operating case. The 20-lumpmodel is an extension of the modified six-lump model proposedhere. This 20-lump model takes into account four subdivisionsfor each FCC liquid product: heavy cycle oil (HCO), light cycle oil(LCO), heavy naphtha (HN), and light naphtha (LN). This subdivi-sion is based on respective distillation curve cut points. The Iumpcalled light gases (LG) is subdivided into three lumps: methane,ethaneethylene and propanepropylene. The 20th lump is bu-tanes-butylenes (C4). In the 35-lump model it is considered that

a single compound, in this work an n-alkane, represents a singlelump. The result is that the reactive mixture contains 35 lumps,each one represented by a corresponding n-alkane. Lumping for35-lump model was performed via distillation curve splitting asa function of the boiling points of respective n-alkane compound.Finally, coke is not directly considered in the reaction networkand Eq. (9) rules its formation rate.

5. Results and discussion

Numerical experiments were carried out to establish importantissues related to the FCC kinetic models. These experiments in-clude parameters estimation for selected kinetic models and theeffect of particular variables such as changes in the feedstock andoperating conditions.

5.1. Kinetic parameter estimation

Kinetic parameters are firstly estimated to detect the fittingcapability of lumping models. A database containing experimentalvalues based on the real operation of a FCC unit is used in thiswork. Because of the plant database is proprietary, only two oper-ating cases are shown here (Table 4). Typical feedstock character-istics, dimensions and operating conditions of the FCC unit aregiven in Table 2. The general regression package GREG [49] wasemployed for all parameter estimations. In addition, the public do-main FORTRAN code DASSL[50] was used to solve the set of differ-

ential-algebraic equations. More details related to computationalalgorithm have been given in a previous work [1].

Table 1

Kinetic parameters to be estimated with and without a function distribution

Lumps Kineticparametersusing Eq. (1)

Kinetic parameters using thedistribution functionNpar = (N 1 ) + 2

Experimentalvalues

NESS

4 6 5 44 0.246 15 7 66 0.3520 190 21 220 0.23

35 595 36 385 0.22



6/10

Models containing four, six, 20 and 35 lumps were selected inthis first set of numerical experiments. Plant data include elevenoperating cases so that the number of observations, i.e. experimen-tal values, is equivalent to eleven times the number of lumps,Table 1.

In all minimizations, the energies of activation employed in thepre-exponential factors estimation were adapted from Lee et al.

[11], Table 3. To establish a similar basis of comparison, resultsfor the four models were grouped so that four overall lumps wereconfigured as: gasoil (GOL, C12), light naphtha (LN, C5C12), gases(GA, C1C4) and coke. In this form, the minimization procedureyields similar values in the normalized errors of the sumof squaresfor both four-lump and 20-lump models, Table 1 and Fig. 1. Resultsindicate no meaningful difference in the predicted values though itis obvious that using 20 lumps will provide more details of the FCCreactions. A better prediction of gasoline and gasoil production isobserved when the 35-lump model is used whereas prediction ofgases and coke is better with the 6 and 20-lump models.

The distribution function strongly depends on the interval ofboiling temperatures for each type of feedstock. Hence it is ex-pected that values of kinetic constants will also depend on the typeof feedstock (Eq. (26)); however, a, b, and bAj have remained almostunchanged in all cases studied. This apparent invariability is onlyvalid for a specific FCC catalyst. For two types of feedstock consid-ered in this analysis (Table 4) and using a catalyst with selectivityto gasoline, it was observed that the difference in numerical valuesof kinetic constants is negligible since these differences repre-sented 0.10.6%. However, this apparent non-difference in the ki-netic constants is sufficient to generate different axial profiles ofFCC products in different feedstock types.

Average values for kinetic constants at 815 K and 1% of confi-dence are shown in Table 5 where it can be observed that crackingratios for models of four and six-lumps are very similar. Physicalunits depend on the order of reaction. The cracking constantskHN,GA and kLN,GA behave as overall cracking constants sincekHN,GA % kHN,BU + kHN,LG and kLN,GA % kLN,BU + kLN,LG. On the otherhand, in the model containing six lumps, the relationshipskHCO,BU/kHCO,GA = 1.87, kLCO,BU/kLCO,GA = 1.82 and kHN,BU/kHN,GA = 1.77indicate that the rate of the cracking of heavy species to light spe-cies is practically a constant. The relationship kHCO,HN/kLCO,HN = 1.8indicates that HCO strongly contributes in producing HN but therelation kHCO,LN/kLCO,LN = 1.0 means that both cyclic oils contributeto produce LN. A similar analysis shows that LCO contributes in lar-

ger proportion to produce light species.Pre-exponential factors of the kinetic constants were calculated

for the heavy gasoil. Fig. 2a shows the numerical values for 595 ki-netic constants for the model with 35 lumps. Distribution func-tions, denoted with letter C, refer to the frequency factors forlight lumps. It is appreciated in this case that lumps having lessthan 10 carbons tend to be disintegrated to produce lumps withless than five carbons. Letter B in Fig. 2a, stands for the heaviestlumps and it is observed that they are distributed within a largerrange of carbon numbers. Letter A indicates the reactive behaviorof intermediate lumps, which tend to crack into close lumps thatcan also be overcracked to produce light lumps. In Fig. 2b, the pre-diction capability of the novel approach is demonstrated. Predictedyields for lumps with carbon number greater than five agree rea-

sonably well with plant data, especially those lumps constitutingthe light gasoline (C5C12). However, the lumping techniqueemploying a 35-lump kinetic model offers reasonable predictionsfor lumps with carbon number lower than five but it fails signifi-cantly in prediction of C4 yield.

Axial profiles of FCC products were calculated using two kineticmodels: a 20-lump model and a six-lump model. A light gasoil wasused for the simulation and conversion predictions indicate lessthat 0.3 wt% at 10 m high. The conversion at the riser outlet be-comes 69.3 wt% in both cases though the 20-lump model improvesgases prediction. This improvement is because the 20-lump modeldisaggregates the C1C3 lump of six-lump model to have methane,ethaneethylene and propanepropylene. It should be observedthe double functionality of heavy naphtha since it starts as a prod-

uct of the cracking reactions until a maximum yield is achieved sothat heavy naphtha behaves as a reactant.

Table 4

FCC operating cases used in this study

Light gasoil Heavy gasoil

Physical properties

Specific gravity (15/15 C) 0.865 0.911ASTM D 1160, KT10 530 617T30 592 660T50 651 702T70 702 743T90 742 782Molecular weight 296 356Refractive index 1.492 1.510Operating conditions

Riser inlet temperature, K 815 815Preheat feed temperature, K 486 486Catalyst/oil ratio 8.7 8.7Feed flowrate, kg/s 51 51

Table 2

Typical feedstock characteristics, dimensions and operating conditions of main FCC

equipment

Characteristic Value

Min Max

Feedstock (Maya crude oil)

Specific gravity @ 15/15 C 0.880 0.923Molecular weight, kg/kg mol 280 360Mean average boiling point, K 651 690Sulfur content, wt% 1.7 2.3

Item ValueFCC unit dimensions

RiserLength, m 40Diameter, m 1.3

Stripper-reactorHeight, m 3.1Diameter, m 6Catalyst holdup, Tons 42

RegeneratorHeight, m 12Diameter, m 10.2Catalyst holdup, Tons 198

Variable Value

Min Max

Operating conditions

Preheat feed temperature, K 430 490Catalyst/oil ratio, kg/kg 7.5 12.0Riser outlet temperature, K 790 810Dense bed temperature, K 912 973

Table 3

Activation energies employed in this study

Pathway Source Value (kJ/kg mol)

Heavy cyclic oil-light cyclic oil [11] 44,000

Heavy cyclic oil-gases [51] 89,000Gasoil(cyclic oils)-naphtas [51] 68,250Naphtas-light gases [51] 52,700



7/10

5.2. Effects of feedstock and operating conditions

A second set of experiments were carried out to establish theeffect of several important variables on the performance of themodels. One of the most essential goals in simulation of FCC pro-

cess is the knowledge of the effect of feedstock on FCC yields.Hence two feedstock exhibiting considerable physical differences

have been studied and their impact on the FCC process is summa-rized in Table 6 where both the 20-lump and the 35-lump modelswere considered. The most relevant difference found in this simu-lation is that the overall conversion achieved with the heavy gasoilis greater than that with light gasoil. In contrast, gases and coke

yields are greater for light gasoil. As a consequence, the degree ofcracking severity should be diminished when light gasoil is pro-

a) 4 lumps

Calculated Yields [% wt]

0 10 20 30 40 50

PlantYields[%w

t]

0

10

20

30

40

50

b) 6 lumps


0 10 20 30 40 50

PlantYields[%w

t]

0

10

20

30

40

50Gasoil

Gasoline

Gases

Coke

c) 20 lumps


0 10 20 30 40 50

PlantYields[%

wt]

0

10

20

30

40

50

d) 35 lumps


0 10 20 30 40 50

PlantYields[%

wt]

0

10

20

30

40

50Gasoil

Gasoline

Gases

Coke

Fig. 1. Minimization results for selected kinetic models. Gasoil C12, gasoline or light naphta (C5C12), and gases (C1C4).

Table 5

Averaged kinetic constants of four-lump model (a = 0.2 0.01, b = 1.20 0.02) and six-lump model (a = 4.6 0.04, b = 1.6 0.02)

Four lumps

kGOL,HN = 5.60E2kGOL,LN = 3.01E1 kHN,LN = 6.37E3

kGOL,GA = 8.64E2 kHN,GA = 1.24E1 kLN,GA = 5.26E4

Six lumps

kHCO,LCO = 8.24E1kHCO,HN = 3.01E1 kLCO,HN = 1.67E1kHCO,LN = 3.78E1 kLCO,LN = 3.81E1 kHN,LN = 5.42E1kHCO,BU = 7.22E4 kLCO,BU = 8.67E4 kHN,BU = 1.09E1 kLN,BU = 2.61E4kHCO,LG = 3.87E4 kLCO,LG = 4.76E4 kHN,LG = 6.15E2 kLN,LG = 3.11E4 kBU,LG = 2.51E2



8/10

cessed. The risk of overcracking could then be reduced. At the bot-tom of the riser, most of light feed oil is distributed from 200 to280 kg/kg mol and it is gradually cracked into gasoline and lightgases for the 20-lump model, Fig. 3. Gasoline yield is typically

observed in the range of 80120 kg/kg mol and light gases in therange of 2080 kg/kg mol. The heaviest feed oil is dispersed from

250 to 400 kg/kg mol and, in this case, cracking reactions leadquickly to more valuable products, particularly light gasoline. Onthe other hand, Fig. 4 depicts the weight distribution using a 35-lump model where differences in performance of the 20-lump

and 35-lump models are evident. A significant portion of light feedoil close to 200 kg/kg mol could not be cracked into valuable prod-

a) Pre-exponential factors

Carbon number

5 10 15 20 25 30

Pre-exponential

factor,aji

0.0

0.2

0.4

0.6

0.8

1.0

C

B

A

LN HN LCO HCO

b) Comparison between results of this work andplant data

Carbon number

0 5 10 15 20 25 30 35

Weigthfrac

tion

0.00

0.02

0.04

0.06

0.08

0.10Plant data

This work

Fig. 2. Results of 35-lump model. (a = 5.6 0.04, b = 0.5 0.02).

Table 6

Simulation results using two feedstocks

Results Experimental data Kinetic model

20 Lumps 35 Lumps

Light Heavy Light Heavy Light Heavy

Riser outlet temperature, K 797 794 804 800 804 801

FCC yields, wt%

Coke 6.1 5.0 6.0 5.3 6.3 5.3Gasoil 27.2 29.0 30.7 27.3 33.2 28.4Gasoline 46.4 48.4 45.2 49.2 40.9 48.4Gases 20.3 17.6 18.1 18.2 19.6 17.9

a) Light gasoil

Molecular Weight [kg/kg mole]

50 100 150 200 250 300 350

RiserLength[m]

0

5

10

15

20

25

30

35

40b) Heavy gasoil


50 100 150 200 250 300 350

RiserLength[m]

0

5

10

15

20

25

30

35

40wt / wt

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.070.08

0.09

0.10

Fig. 3. Weight distribution of hydrocarbons for a 20-lump model.



9/10

ucts. This fact is reflected in the FCC yields shown in Table 6. It isworth mentioning that heavy gasoil is adequately converted intogasoline and gases.

In a final set of numerical simulations, the impact of riser oper-ating conditions on FCC yields in steady-state with constant regen-erator operating conditions is studied. A six-lump model is used inorder to illustrate our results for a heavy gasoil. The effects of bothfeed preheat temperature and catalyst/oil ratio on light gasoline

yields is given in Fig. 5. A maximum on gasoline yield appearswhen the feed preheat temperature is 343 K and catalyst/oil ratiois 10 to make gasoline yield going up to almost 50%. The positionof this point depends markedly on the feedstock, type of catalyst,regenerator operating conditions and quality of the availableexperimental information.

Unfortunately, a suitable comparison between kinetic constantsshowed in this work and other constants available in the open lit-erature cannot be carried out since several factors affect the qualityand reproducibility of experimental results. However, some valu-able studies have been published related to the effect of operatingconditions on FCC yields [29,52]. The weight distribution of gasoilcracking obtained in this work reasonably agrees with those resultspublished by Liguras and Allen [53]. Concentration profiles ob-

tained in this work also agree with those presented by severalauthors [24,29,40,41,54].

6. Conclusions

It is always possible to propose a model in accordance to theavailable kinetic information but experimental data is usually lim-ited. The proposed representation has been capable to successfullypredict the performance of cracking reactions for gasoils in a widerange of feedstock and operating conditions. Thus, the novel ap-proach developed in this work shows to be highly flexible to in-clude kinetic models exhibiting different degree of complexity.According to the results, it is possible to obtain a detailed kineticmodel without a large kinetic database of experiments but usingcommonly available information in refineries. In addition, the ki-netic representation based on a probability distribution has per-

mitted to reduce substantially the computational effort involvedin the numerical evaluation of intrinsic kinetic parameters and itprevents excessive reduction of reaction pathways.

Acknowledgments

The authors would thank to the CONACyT and COSNET for theeconomical support for this research.

References

[1] Hernndez-Barajas JR, Vzquez-Romn R, Salazar-Sotelo D. Multiplicity ofsteady states in FCC units: effect of operating conditions. Fuel 2006;85:84959.

[2] Reif HE, Kress RF, Smith JS. How feeds affects cat cracker yields? Petrol Refiner1961;40:237.[3] Kurihara H. Optimal control of fluid catalytic cracking processes, PhD

dissertation, MIT, USA, 1967.[4] Ewell RB, Gadmer G. Design cat crackers by computer. Hydrocarbon Process

1978:12534.[5] Lin TD. FCCU advanced control and optimization. Hydrocarbon Process

1993:10714.[6] McFarlane RC, Reinman RC, Bartee JF, Georgakis C. Dynamic simulation for

model IV fluid catalytic cracking unit. Comput Chem Eng 1993;17:275300.[7] Lappas AA, Iatridis DK, Vasalos I. Production of reformulated gasoline in the

FCC unit. Effect of feedstock type on gasoline composition. Catal Today1999;50:7385.

[8] Blanding FH. Reaction rates in catalytic cracking of petroleum. Ind Eng Chem1953;45:118697.

[9] Nace DM, Voltz SE, Weekman VW. Application of a kinetic model for catalyticcracking. Ind Eng Chem Process Des Develop 1971;10:5307.

[10] Yen LC. Kinetic modelling of fluid catalytic cracking. AIChE Spring Nat Meet,April 26, Houston, Texas, 1987.

[11] Lee LS, Chen YW, Huang TN, Pan WY. Four-lump kinetic model for fluidcatalytic cracking process. Canadian J Chem Eng 1989;67:6159.

a) Light gasoil


50

RiserLength[m]

0

5

10

15

20

25

30

35

40

c) Heavy gasoil

RiserLength[m]

0

5

10

15

20

25

30

35

40wt / wt

0.00

0.01

0.02

0.03

0.040.05

0.06

0.07

0.08

0.09

0.10

400350300250200150100


50 400350300250200150100

Fig. 4. Weight distribution of hydrocarbons for a 35-lump model.

38

40

42

44

46

48

4 6

810 12

14

300

400

500

Lightnaphta[%w

t]

Catalyst/Oil Ra

tio [kg/kg]

PreheatTem

perature

[K]

wt %

38

40

42

44

46

48

Fig. 5. The effect of riser operating conditions on light naphta yields. Heavy gasoilusing a six-lump model.



10/10

[12] Larocca M, Ng S, de Lasa H. Fast catalytic cracking of heavy gas oils: modelingcoke deactivation. Ind Eng Chem Res 1990;29:17180.

[13] Corella J, Francs E. Analysis of the riser reactor of a fluid cracking unit. Fluidcatalytic cracking II, ACS symposium series, vol. 452, 1991. p. 16582.

[14] Takatsuka T, Sato S, Morimoto Y, Hashimoto H. Resid FCC reaction model,AIChE Nat Meet, 1984.

[15] Sugungun MM, Kolesnikov IM, Vinogradov VM, Kolesnikov SI. Kineticmodeling of FCC process. Catal Today 1998;43:31525.

[16] John T, Wojciechowsky BW. On identifying of the primary and secondaryproducts of the catalytic cracking of neutral distillates. J Catal 1975;37:

24050.[17] Gao J, Xu C, Lin S, Yang G, Guo Y. Advanced model for gassolid turbulent flow

and reaction in FCC riser reactors. AIChE J 1999;45:232156.[18] Derouin C, Nevicato D, Forissier M, Wild G, Bernard JR. Hydrodynamics of riser

units and their impact on FCC operation. Ind Eng Chem Res 1997;36:450415.[19] Jacob SM,Gross B, Voltz SE, Weekman VW. A lumping and reaction scheme for

catalytic cracking. AIChE J 1976;22:70113.[20] Al-Khattaf S, de Lasa H. The role of diffusion in alkyl-benzenes catalytic

cracking. Appl Catal A: Gen 2002;226:13953.[21] Avila AM, Bidabehere CM, Sedran U. Diffusion and adsorption selectivities of

hydrocarbons over FCC catalysts. Chem Eng J 2007;132:6775.[22] Al-Sabawi M, Atias JA, de Lasa H. Kinetic modeling of catalytic cracking of gas

oil feedstocks: Reaction and diffusion phenomena. Ind Eng Chem Res2006;45:158393.

[23] Quann RJ, Jaffe SB. Structure-oriented lumping: describing the chemistrycomplex hydrocarbon mixtures. Ind Eng Chem Res 1992;31:248397.

[24] Dewachtere NV, Santaella F, Froment GF. Application of a single-event kineticmodel in the simulation of an industrial riser reactor for the catalytic crackingof vacuum gas oil. Chem Eng Sci 1999;54:365360.

[25] Froment GF. Single event kinetic modeling of complex catalytic processes.Catal Rev 2005;47:83124.

[26] Kumar H, Froment GF. A generalized mechanistic kinetic model for thehydroisomerization and hydrocracking of long-chain paraffins. Ind Eng ChemRes 2007;46:407590.

[27] Gupta RK,Kumar V, Srivastava VK. A newgeneric approach for the modeling offluid catalytic cracking (FCC) riser reactor. Chem Eng Sci 2007;62:451028.

[28] Paraskos JA, Shah YT, McKinney JD, Carr NLA. Kinematic model for catalyticcracking in a transfer line reactor. Ind Eng Chem Process DesDevelop 1976;15:1659.

[29] Arbel A, Huang Z, Rinard IH, Shinnar R, Sapre AV. Dynamic and control offluidized catalytic crackers. 1. Modeling of the current generation of FCCs. IndEng Chem Res 1995;34:122843.

[30] Martin MP. Contribution a ltude des lvateurs de Craquage Catalytique.Effects lies a lInjection de la Charge, PhD dissertation, Institut NationalPolytechnique de Lorraine, France, 1990.

[31] Buchanan JS. Analysis of heating and vaporization of feed droplets in fluidizedcatalytic cracking risers. Ind Eng Chem Res 1994;33:310411.

[32] Ali H, Rohani S. Dynamic modeling and simulation of a riser-type fluidcatalytic cracking unit. Chem Eng Technol 1997;29:11830.

[33] Mirgain C, Briens C, Pozo MD, Loutaty R, Bergougnou M. Modeling of feedvaporization in fluid catalytic cracking. Ind Eng Chem Res 2000;39:43929.

[34] Maxwell JB. Data book on hydrocarbons application to processengineering. Princeton, New Jersey: Van Nostrand; 1950.

[35] American Petroleum Institute (API). Technical data book petroleum refining.New York: EUA; 1997.

[36] Sim WJ, Daubert TE. Prediction of vaporliquid equilibria for undefinedmixtures. Ind Eng Chem Process Des Dev 1980;19:356.

[37] Riazi M, Daubert T. Simplify property predictions. Hydrocarbon Process1980;59:1156.

[38] Riazi M, Daubert T. Prediction of thermophysical properties of petroleumfractions. Ind Eng Chem Res 1987;26:7559.

[39] Froment GF, Bischoff KB. Chemical reactor analysis and design. John Wiley &Sons; 1990.

[40] Theologos KN, Markatos NC. Advanced modeling of fluid catalytic crackingriser-type reactors. AIChE J 1993;39:100717.

[41] Theologos KN, Nikou ID, Lygeros AI, Markatos NC. Simulation and design offluid catalytic cracking riser-type reactors. AIChE J 1997;43:48694.

[42] Froment GF. The modeling of catalyst deactivation by coke formation. In:Bartholomew CH,Butt JB, editors. Catalyst deactivation 1991. Elsevier; 1991. p.5383.

[43] Ahmed T. Equations of state and PVT analysis. Applications for improvedreservoir modeling. Houston, USA: Gulf Publishing; 2007 [Chapter 2].

[44] Krambeck FJ. Continuous mixtures in fluid catalytic cracking and extensions.Mobil workshop on chemical reaction of complex mixtures. New York: VanNostrand; 1991.

[45] Corella J, Bilbao R, Molina JA, Artigas A. Variation with time of the mechanism,observable order and activation energy of the catalyst deactivation by coke inthe FCC process. Ind Eng Chem Process Dev 1985;24:62536.

[46] Inoue S, Takatsuka T, Wada Y, Hirohama S, Ushida T. Distribution functionmodel for deep desulfurization of diesel fuel. Fuel 2000;79:8439.

[47] Gupta PL, Gupta RC. The monotonicity of the reliability measures of the betadistribution. Appl Math Lett 2000;13:59.

[48] Weekman VW. A model of catalytic cracking conversion in fixed, moving andfluid bed reactors. Ind Eng Chem Process Des Develop 1968;7:905.

[49] Stewart WE, Caracotsios M, Srensen JP. Parameter estimation frommultiresponse data. AIChE J 1992;38:64150.

[50] Brenan KE, Campbell SL, Petzold LR. Numerical solution of initial-valueproblems in differential-algebraic equations. New York: North-Holland;1989.

[51] Ancheyta JJ. Estudio cintico de las reacciones de desintegracin cataltica degasleos, PhD thesis, Universidad Autnoma Metropolitana, 1998.

[52] Han IS, Chung CB, Riggs JB. Modeling of a fluidized catalytic cracking process.Comput Chem Eng 2000;24:16817.

[53] Liguras DK, Allen DT. Structural models for catalytic cracking. 2. Reactions ofsimulated oil mixtures. Ind Eng Chem Res 1989;28:67483.

[54] Pitault I, Nevicato D, Forissier M, Bernard J. Kinetic model on a molecular

description for catalytic cracking of vacuum gas oil. Chem Eng Sci 1994;49:424962.


A Comprehensive Estimation of Kinetic Parameters in Lumped Catalytic Cracking Reaction Models

Documents

Transcript of A Comprehensive Estimation of Kinetic Parameters in Lumped Catalytic Cracking Reaction Models