A comprehensive estimation of kinetic parameters in lumped catalytic cracking reaction models

Fuel 88 (2009) 169–178

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A comprehensive estimation of kinetic parameters in lumped catalytic cracking reaction models José Roberto Hernández-Barajas a, Richart Vázquez-Román b,*, Ma.G. Félix-Flores c a

Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Biológicas, Carretera Villahermosa-Cárdenas Km 0.5, 68039 Villahermosa, Mexico Instituto Tecnológico de Celaya, Departamento de Ingeniería Química, Av. Tecnológico y G, Cubas s/n, 38010 Celaya, Mexico c Universidad Autónoma de Zacatecas, Unidad Académica de Ciencias Químicas, Carretera a Cd. Cuauhtémoc Km 0.5, Guadalupe, Zacatecas 98600, Mexico b

a r t i c l e

i n f o

Article history: Received 12 November 2007 Received in revised form 16 July 2008 Accepted 17 July 2008 Available online 19 August 2008 Keywords: Catalytic cracking Lumping Kinetic modeling Distribution function

a b s t r a c t This work presents a comprehensive approach to estimate kinetic parameters when the involved reactions contain lumped chemical species. This approach is based on representing rate constants with a continuous probability distribution function. In particular, the beta function is used to estimate kinetic parameters in catalytic cracking reactions. Thus, several kinetic models for the catalytic process containing different number of lumps are selected and a discretization procedure is carried out to estimate the corresponding kinetic parameters. The kinetic representation based on the probability distribution substantially reduces the computational and experimental effort involved in the numerical evaluation of kinetic parameters. Published by Elsevier Ltd.

1. Introduction The catalytic cracking process converts heavy oil cuts into products of better quality such as olefins and high octane gasoline using a zeolite-type catalyst. The fluid catalytic cracking process (FCC) is in fact the key step of conversion in petroleum refineries. The FCC unit employed as a reference in this work is capable of processing 30,000 barrels per day as given in [1]. Catalytic reactions take place in the riser consisting of a vertical pipe with a diameter between 0.5 and 1.5 m and a height between 30 and 50 m. The heavy feedstock is instantaneously vaporized when it mixes with the hot and regenerated catalyst (catalyst residence time in the riser is around 5 s) and then the reaction proceeds in rather little time because of the high catalyst activity. During the reaction, some FCC products and a hydrogen-deficient compound named coke is formed and deposited on catalyst surface. As a result, the coke deposition temporarily deactivates the catalyst. FCC products are then disengaged via cyclones while spent catalyst is passed through a stripper to separate 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 the catalyst activity though fresh catalyst must be added periodically

* Corresponding author. Tel.: +52 461 61 17575x153; fax: +52 461 61 17744. E-mail addresses: [email protected] (J.R. Hernández-Barajas), [email protected] (R. Vázquez-Román), g_felixfl[email protected] (Ma.G. Félix-Flores). 0016-2361/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.fuel.2008.07.023

to keep the desired activity (catalyst residence time in the dense bed is around 9 min). Several studies have been focused on modeling of cracking reactions kinetics. Some of them proposed kinetic models based on empirical correlations with a limited range of applicability [2–7]. Most of kinetic studies consider the lumping technique, which establishes that various chemical species can be lumped according to similar characteristics (e.g. the boiling point). The first model based on this technique considered two lumps [8]: gasoil as the reactant, and a product containing gasoline, gases and coke. A three-lump model consisting in gasoil, gasoline, and light gases and coke was developed [9]. The gasoil cracking is represented with second-order kinetics although coupled to first-order activity decay, whereas gasoline conversion is represented with first-order kinetics. Using different gasoil streams, this model detected a significant effect of the feedstock quality on reaction rate constants. Others have [10,11] separated the third lump in Nace’s model to produce a four-lump model to ratify that rate constants are strongly dependent on feedstock quality. Several kinetic models considering five lumps have been published: Larocca et al. [12] split oil feed into paraffin, naphtha and aromatic (PNA) fractions; Corella et al. [13] separate oil feed in two gasoil fractions. A six-lump model that was also applied to residual oil cracking [14]. Then, the lumping approach has been extended to include more lumps: eight lumps [15], 11 lumps [16], 13 lumps [17], and 19 lumps [18]. One of the most widely used lumping models is the 10-lump model proposed by Jacob et al. [19]. This model takes into account PNA fractions for two feed fractions as well

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Nomenclature A b A j Aji aji BU C C0 C Pg C Pl C Ps C Pv C Pv CATOIL Eji Fg Fs Fv Fv Fj fj ðT Bi Þ GA HCO HN DHF DHv kij ; kji kv kvo ^ k j kHCO,BU kHCO,GA kHCO,HN kHCO,LN kHN,BU kHN,GA kHN,LG kLCO,BU

riser cross section area, m2 overall pre-exponential factor defined by Eq. (18), [m3 of gas/(kg of catalyst s)][m3 of gas/kg mol]n1 pre-exponential factor for reaction constants, [m3 of gas/(kg of catalyst s)][m3 of gas/kg mol]n1 terms ruled by Eqs. (16)–(21) butane-butylenes (C4) concentration, kg mol/m3 of gas gas concentration at z =0, kg mol/m3 of gas gas feed average heat capacity, kJ/(kg K) liquid feed average heat capacity, kJ/(kg K) catalyst average heat capacity, kJ/(kg K) dispersion steam average heat capacity, kJ/(kg K) coke average heat capacity, kJ/(kg K) catalyst/oil ratio, kg of catalyst/kg of oil activation energy, kJ/kg mol feed oil flowrate, kg/s catalyst flowrate, kg/s steam flowrate, kg/s coke flowrate, kg/s cumulative distribution function probability density function as a function of T Bi , fj ðT Bi Þ  aji gases (butanes C4 + light gases C1–C3) heavy cyclic oil heavy naphta heat of formation, kJ/kg mol heat of feed vaporization, kJ/kg reaction rate constant, [m3 of gas/(kg of catalyst s)][m3 of gas/kg mol]n1 Rate constant of coke formation, kg/kg pre-exponential factor in Arrhenius-type equation for coke formation, kg/kg overall cracking constant for lump j kinetic constant for cracking from heavy cyclic oil to butane-butylenes in a six-lump model kinetic constant for cracking from heavy cyclic oil to gases in a six-lump model kinetic constant for cracking from heavy cyclic oil to heavy naphta in a six-lump model kinetic constant for cracking from heavy cyclic oil to light naphta in a six-lump model kinetic constant for cracking from heavy naphta to butane-butylenes in a six-lump model overall cracking constant from heavy naphta to gases (light gases + butanes) in a six-lump model kinetic constant for cracking from heavy naphta to light gases in a six-lump model kinetic constant for cracking from light cyclic oil to butane-butylenes in a six-lump model

as heavy and light cyclic oils and the authors have indicated that rate constants are independent of the feedstock quality. The main disadvantage of all models based on lumping is that a large number of experiments must be carried out to predict their kinetic constants. In last years, novel contributions have taken into account adsorption and intra-crystalline diffusion effects in kinetic modeling [20–22]. As a result, non-linear mass balances account for both diffusion constraints experienced by hydrocarbon species while evolving in the zeolite pore network and the effect of the system pressure on the apparent adsorption selectivity.

kinetic constant for cracking from light cyclic oil to gases in a six-lump model kLCO,HN kinetic constant for cracking from light cyclic oil to heavy naphta in a six-lump model kinetic constant for cracking from light cyclic oil to light kLCO,LN naphta in a six-lump model overall cracking constant from light naphta to gases kLN,GA (light gases + butane-butylenes) in a six-lump model kinetic constant for cracking from light naphta to bukLN,BU tane-butylenes in a six-lump model kinetic constant for cracking from light naphta to light kLN,LG gases in a six-lump model LCO light cyclic oil LG light gases LN light naphta M molecular weight, kg/kg mol n apparent order of reaction N number of lumps in a kinetic model NESS normalized error sum of squares number of overall lumps, NO = 4 NO number of kinetic parameters involved in a cracking Npar model heat of reaction, kJ/(m3 of gas s) QR R reaction rate, kg mol/(m3 of gas s) reaction rate, kg mol/(kg of catalyst s) R0 universal constant of gases Ru boiling point temperature of oil fraction, K TB boiling point temperature of FCC feed, K T Bf T Bi; min ; T Bi;max minimum and maximum boiling point temperatures for the lump formed i, K preheat feed temperature, K Tf mix temperature in the vaporization zone, K T mix riser temperature, K T rs hot catalyst temperature, K Ts steam temperature, K Tv gas velocity, m/s ug x experimental or calculated values employed in non-linear regression overall conversion, kg/kg XO y mole fraction, kg mol/kg mol z axial position, m kLCO,GA

Greek symbols scale parameters of the beta distribution coke on catalyst, kg of coke/kg of catalyst e void fraction, m3 of gas/m3 total / deactivation function m stoichiometric coefficient qg ; qs gas and catalyst densities, kg/m3 W slip factor, non-dimensional

a; b vrs

Another possible approach to model cracking reactions is based on the kinetic representation at molecular level. These models use vectors to include the representation of most chemical species involved in complex mixtures [23]. In a similar study, kinetic models are based on carbocation chemistry [24–26]. The main advantage of these models is that they provide a detailed knowledge of the performance of catalytic reactions. Unfortunately, these techniques require a much larger database of kinetic information than the database required in the lumping technique and this information is unavailable in the open literature. Recently, Gupta et al. [27] proposed an elementary reaction

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scheme whereas the kinetic parameters are estimated using a semi-empirical approach based on normal probability distribution. Reaction rate constants are typically calculated from experimental data. Considering that catalytic reactions occurs in irreversible reaction steps [19,28], then the maximum number of reaction pathways and, consequently, of rate constants, is

Number of pathways ¼

N  2

¼

N! NðN  1Þ ¼ 2!ðN  2Þ! 2

ð1Þ

dC j qs ð1  eÞ/ 0 Rj ; ¼ e dz 1 with e ¼ q 1 þ w qg FFgs

ug

The computational effort to determine the rate constants increases when all reaction pathways are considered. For instance, the maximum number of rate constants in the 10-lump model is calculated as 45. However, the number of kinetic parameters is reduced because some reaction pathways are considered as improbable 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 from the Jacob’s model are numerically identical and the number of constants can thus be reduced to 14. Even under the above consideration, the number of rate constants remains large. Thus, a comprehensive kinetic model is proposed in this paper to estimate kinetic constants when cracking reactions representation is based on the lumping technique. This approach characterizes the FCC products in detail, prevents excessive reduction of rate constants and reduces computational effort in the numerical evaluation of kinetic parameters. 2. The riser model A model of the riser is developed in this section since the cracking reactions are carried out within it. The riser is fed at the bottom of the unit with an atomized gasoil, the regenerated catalyst, and steam 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 vaporization occurs as a result of an intimate gas–solid mixing and chemical reactions in the vapor phase due to thermal cracking can be neglected at low temperatures [30–33]. The heat carried in the riser via the regenerated catalyst is consumed to vaporize the feedstock and to sustain the cracking reactions. Both vaporization and cracking processes are endothermic so that the hot catalyst provides energy to make the oil achieve the boiling point, vaporize and, in the vapor phase, get the mix temperature. Thus, the following equation can be obtained from an overall energy balance at the feeding point:

T mix ¼

bles, respectively. Catalyst heat capacity depends linearly on alumina composition and its function is proprietary, provided by manufacturer. A conclusion achieved in several studies on flow-pattern models indicates that the plug flow reactor model for both gas and solid phases provides good approximations in the riser unit [13,39–41]. As a result of this assumption, steady-state mass balance for all chemical species involved as reactants or products is written as

F s C Ps T s þ F v C Pv T s þ F g C Pg T Bf þ F v C Pv T v  F g C Pl ðT Bf  T f Þ  F g DHv F s C Ps þ F v C Pv þ F g C Pg þ F v C Pv ð2Þ

where F s , F v , F g and F v are the catalyst flowrate, coke flowrate, feed flowrate, and the steam flowrate, respectively; C Ps , C Pv , C Pg , C Pl , and C Pv represent the average heat capacities for the catalyst, coke, liquid feed oil, gas feed oil and the dispersion steam, respectively; T s , T Bf , T v and T f are the temperatures for catalyst, feed oil at the boiling point, steam and the feed oil leaving the pre-heater; and DHv is the heat of vaporization of gasoil fed to the unit. Heat capacities for hydrocarbons were calculated via empirical correlations based on thermophysical databases [34,35]. Molecular weights were calculated by using classical correlations [36–38]. Gasoil heat of vaporization was calculated employing the original Peng–Robinson EOS. Heat capacities for steam and coke, were obtained from saturated steam and pure carbon (coke is assumed as graphite) ta-

j ¼ 1; 2; . . . ; N

ð3aÞ ð3bÞ

s

ug ¼

Fg Aq g e

ð3cÞ

where ug is the gas velocity, C j is concentration of compound j, qs is the catalyst density, qg is the gaseous mixture density e is void fraction, w is the ratio between gas and solid velocities in the riser (slip factor, in this work, no slip between phases is considered: w = 1), A is the riser cross section area, / is a deactivation function, R0j is the reaction rate for chemical species j, and z is the axial position. More details related to riser modeling have been provided in a previous work [1]. The deactivation function is modeled here via the exponential law proposed in [42]. The boundary condition for the above equation is

C j ð0Þ ¼ C O yj ;

j ¼ 1; 2; . . . ; N

ð4Þ

where CO represents the gas concentration at the riser inlet and mole fractions yi, which are evaluated employing the ASTMD1160 distillation curve of the FCC feed. The ASTM-D1160 is converted into TBP curve according to an algorithm based on procedures detailed in [35] and recently reviewed by Ahmed [43]. The reaction rates and the number of lumps involved in catalytic cracking reactions depend on the selected kinetic model. In a generic sense this reaction rate is

R0j ¼

j1 X

vij kij C ni 2 

i1

N X

kji C nj 1 ;

j ¼ 1; 2; . . . N

ð5Þ

i¼jþ1

where

vij ¼

Mi Mj

ð6Þ

being kij the rate constants, vij the stoichiometric coefficients and M the molecular weight. It should be mentioned here, kinetic constants defined above are no intrinsic rates because of assumptions taken in this study make difficult to distinguish between diffusion, adsorption or selective catalyst deactivation phenomena. As a result, this kinetic approach is useful for calculating observed kinetic constants. Eq. (5) indicates that lump j is being generated and cracked as a function of the postulated reaction network with an apparent order of reaction n, whereas the rate constants depend exclusively on reaction temperature. The temperature effect on kinetic constants is represented by an Arrhenius-type expression [10,11,14,19]. Thus, a reaction rate constant, where a lump j is cracked into a lump i, can be written as Eji

kji ¼ Aji e RT

ð7Þ

where Aji is the pre-exponential Arrhenius factor, Eji is the activation energy and R is the universal constant of ideal gases. In particular, coke is a solid with pseudo-graphite nature so that it cannot be described in terms of the boiling point and a semi-

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

vrs ¼



  kv XO CATOIL 1  X O

ð8Þ

where vrs is the coke in the riser, kv is the rate constant for the coke formation, CATOIL is the catalyst-oil ratio, and X O is the overall conversion. The rate constant for coke formation can be represented via an Arrhenius function to take into account the temperature dependence [12,45]. This expression assumes catalyst deactivation is no selective for each lump. Considering the above-described facts the derivative of Eq. (8) with respect to z can be written as Ev

kv eRu T dvrs /ðvrs Þ ¼ o  dz CATOIL ð1  X O Þ2

dT rs ¼ Q R dz

ð10Þ

where QR represents the heat required for catalytic cracking that can be calculated via the heat of formation DHF for each reaction pathway according to

QR ¼

N X

R i ð DH F Þ i

ð11Þ

i¼1

The heat of formation for each lump is calculated with the standard enthalpy of formation and heat capacity of the lumps involved in the reaction pathway i. Heat of formation for hydrocarbons were calculated employing empirical correlations based on thermophysical databases from [35]. Combining Eqs. (5), (10), and (11), the following equation is obtained:

qg C Pg ug

N1 N X X dT rs ð1  eÞ n ½C i i kij ðDHF Þji qs / ¼ e dz i¼1 j¼iþ1

ð12Þ

ð15Þ

The set of rate constants for the disappearance term on the right-hand side is N X

^  k j

kji

ð16Þ

i¼jþ1

where subscript i refers to the product formed from lump j. The summation above is called ‘‘the overall cracking constant” for lump j. This term is equal to zero for the Nth-lump due to the no-existence of any lump with lower molecular weight. Using the Arrhenius-type of equation in Eq. (16) the following equation is obtained: N X

^ ¼ k j

Aji e



Eji Ru T

ð17Þ

i¼jþ1

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

bj  A

N X

bj Aji  A

i¼jþ1

N X

aji

ð18Þ

i¼jþ1

then the summation becomes equal to unity so that each value can be referred as a proportion, i.e. N X

aji ¼ 1

ð19Þ

b j aji Aji  A ð13Þ

and boundary condition,

T rs ð0Þ ¼ T mix

Disappearance ðk1;2 þ...þk1;N ÞC n11 ðk2;3 þ...þk2;N ÞC n22 .. . N1 ðkN1;N ÞC nN1

i¼jþ1

with,

ðDHF Þji ¼ mij ðDHF Þj  ðDHF Þi

Lump j Generation R1 ¼ R2 ¼ m1;2 k1;2 C n11 .. .. . . N2 RN1 ¼ m1;N1 k1;N1 C n11 þ...þ mN2;N1 kN2;N1 C nN2 n1 nN1 RN ¼ m1;N k1;N C 1 þþ mN1;N kN1;N C N1

ð9Þ

where Ev is the energy of activation for coke formation. This parameter depends on feedstock and catalyst type. The endothermic nature of cracking reactions produces an appreciable temperature drop along the riser length. To assess this temperature drop, an energy balance for an adiabatic operation is established using similar assumptions adopted for species balances with respect to the flow-pattern, e.g. plug flow-pattern:

qg C Pg ug

equation are expressed here by a probability distribution function. The independent variable is selected here as the boiling point since oil feeds are generally defined according to boiling point cuts. Considering N lumps where the first lump remains as the heaviest lump and the Nth-lump is the lightest compound, the first lump has no generation side for the reaction and the Nth-lump has no disappearance term. Expanding Eq. (5) and considering the existence generation and disappearance terms, the following table can be generated:

The above proportion is defined as a cumulative distribution for continuous variables: N X

ð14Þ

It should be observed that the mixing temperature and other variables evaluated in the vaporization zone such as density, void fraction and gas velocity also constitute boundary conditions at the riser inlet. 3. The kinetic model This novel approach for the kinetic model is supported on the assumption that intrinsic kinetic constants could be represented by a continuous distribution function by selecting an independent stochastic variable. This idea is supported on previous works where rate constants for desulphurization of diesel fuel have been expressed in terms of the C distribution [46] and normal distribution function [27]. Hence frequency factors for Arrhenius-type

ð20Þ

aji ¼ F j ðT Bi Þ

ð21Þ

i¼jþ1

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

F j ðT Bi ; T Bi; min ; T Bi; max Þ ¼

Z

TB

i; max

TB

fj ðT Bi ÞdT Bi

ð22Þ

i; min

Integration is recognized as the summation of the distribution function N X i¼jþ1

aji ¼

N X

fj ðT Bi Þ

ð23Þ

i¼jþ1

aji ¼ fj ðT Bi Þ

ð24Þ

J.R. Hernández-Barajas et al. / Fuel 88 (2009) 169–178 Table 1 Kinetic parameters to be estimated with and without a function distribution Lumps

Kinetic parameters using Eq. (1)

Kinetic parameters using the distribution function Npar = (N  1) + 2

Experimental values

NESS

4 6 20 35

6 15 190 595

5 7 21 36

44 66 220 385

0.24 0.35 0.23 0.22

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

Eji

b j aji e Ru T ¼ A b j fj ðT B Þe Ru T kji ¼ A i

ð25Þ

the distribution function would be a function for continuous variables defined in a given positive range T Bi; min 6 T B 6 T Bi;max . In this paper, the beta distribution function has been selected because it provides large flexibility for data fitting and it has been successfully used in several science fields [47]. The beta distribution is a twoshape parameter continuous function with an interval defined by a minimum and maximum value and a polynomial nature, which is given by

fj ðT Bi ; aj ; bj Þ ¼

1 T Bmax  T Bmin T Bi  T Bi;min Cðaj bj Þ  Cðaj ÞCðbj Þ T Bi;max  T Bi;min

!aj 1

T Bi;max  T Bi T Bi;max  T Bi;min

!bj 1

ð26Þ in the range T Bmin 6 T B 6 T Bmax . The cumulative function will be the result of using Eq. (26) in the integration according to the selected range for the boiling point. It has mentioned above that Eq. (1) can give an estimation of the number of kinetic parameters required to model the cracking reactions. Using this approach, the number of parameters required can be calculated by

Npar ¼ ðN  1Þ þ 2

ð27Þ

since there are (N  1) pre-exponential factors and two parameters for the distribution function. The advantage of using the approach in this paper becomes greater when the number of lumps increases, Table 1. In cracking, reaction rates are generally considered as pseudofirst-order for light lumps and pseudo-second-order for heavy lumps [8,48]. However, pseudo-first-order is adopted here when more than 20 lumps are used in the model because the expected behavior is like elementary reactions rather than using multiple steps. The operating conditions used in the evaluation of rate constants for the three-lump kinetic model, gasoil lump is cracked into gasoline, light gases and coke [9], are similar to those used in [8]. The utilization of an apparent reaction order equal to 2 is feasible because various elementary steps are represented when the overall conversion of FCC feed is considered. Summarizing, the selection of apparent reaction orders may be founded on previous studies but reasonable assumptions may properly justify any other choice. 4. Case studies definition Several kinetic models with a marked degree of complexity are used to demonstrate the advantages of this novel approach. The choice of a kinetic model depends on particular requirements. For example, a kinetic model containing a large number of lumps could permit a detailed characterization and, consequently, a bet-

173

ter representation of the products quality. It should be recognized that a kinetic model with these features implies a greater computational effort. This could be unnecessary if our target is to determine responses in unsteady state of some of the state variables. A more detailed kinetic model is required when it is used for optimization purposes such maximizing olefin production or the octane number of gasoline. In refineries, each lump quality is governed by the operating conditions and characteristics of the main fractionators. As a consequence, the number of lumps established in most kinetic models is commonly related with the number of boiling point cuts considered in the fractionators. In this section, a modification for the four-lump model published by Yen [10] and a modification for the six-lump model presented by Takatsuka et al. [14] are studied. In addition, two more complex models are also proposed here: a 20-lump model and a 35-lump model. In chemical kinetics, it has been considered that lumps boiling up to the boiling temperature of n-C12 are cracked with an apparent order equal to 2. On the other hand, lighter lumps will be cracked with first-order kinetics. The modified four-lump model consists of: unconverted gasoil ðC þ 12 Þ, heavy naphtha (approx. C13–C14), light naphtha (approx. C5–C12), and light gases (C1–C4). The modified six-lump model is defined by: heavy cycle oil ðC þ 21 Þ, light cycle oil (approx. C15–C21), heavy naphtha (approx. C13–C14), light naphtha (approx. C5–C12), butanes-butylenes (C4) and light gases (C1–C3). These definitions are referred to approximate boiling point cuts though the range of boiling points depends on each operating case. The 20-lump model is an extension of the modified six-lump model proposed here. This 20-lump model takes into account four subdivisions for each FCC liquid product: heavy cycle oil (HCO), light cycle oil (LCO), heavy naphtha (HN), and light naphtha (LN). This subdivision is based on respective distillation curve cut points. The Iump called ‘‘light gases” (LG) is subdivided into three lumps: methane, ethane–ethylene and propane–propylene. The 20th lump is butanes-butylenes (C4). In the 35-lump model it is considered that a single compound, in this work an n-alkane, represents a single lump. The result is that the reactive mixture contains 35 lumps, each one represented by a corresponding n-alkane. Lumping for 35-lump model was performed via distillation curve splitting as a function of the boiling points of respective n-alkane compound. Finally, coke is not directly considered in the reaction network and Eq. (9) rules its formation rate. 5. Results and discussion Numerical experiments were carried out to establish important issues related to the FCC kinetic models. These experiments include parameters estimation for selected kinetic models and the effect of particular variables such as changes in the feedstock and operating conditions. 5.1. Kinetic parameter estimation Kinetic parameters are firstly estimated to detect the fitting capability of lumping models. A database containing experimental values based on the real operation of a FCC unit is used in this work. Because of the plant database is proprietary, only two operating cases are shown here (Table 4). Typical feedstock characteristics, dimensions and operating conditions of the FCC unit are given in Table 2. The general regression package GREG [49] was employed for all parameter estimations. In addition, the public domain FORTRAN code DASSL [50] was used to solve the set of differential-algebraic equations. More details related to computational algorithm have been given in a previous work [1].

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Table 2 Typical feedstock characteristics, dimensions and operating conditions of main FCC equipment Characteristic

Value

Feedstock (Maya crude oil) Specific gravity @ 15/15 °C Molecular weight, kg/kg mol Mean average boiling point, K Sulfur content, wt% Item FCC unit dimensions Riser Length, m Diameter, m

Min

Max

0.880 280 651 1.7

0.923 360 690 2.3

Value

40 1.3

Stripper-reactor Height, m Diameter, m Catalyst holdup, Tons Regenerator Height, m Diameter, m Catalyst holdup, Tons

3.1 6 42 12 10.2 198

Variable

Value

Operating conditions Preheat feed temperature, K Catalyst/oil ratio, kg/kg Riser outlet temperature, K Dense bed temperature, K

Min

Max

430 7.5 790 912

490 12.0 810 973

Table 3 Activation energies employed in this study Pathway

Source

Value (kJ/kg mol)

Heavy cyclic oil-light cyclic oil Heavy cyclic oil-gases Gasoil(cyclic oils)-naphtas Naphtas-light gases

[11] [51] [51] [51]

44,000 89,000 68,250 52,700

Table 4 FCC operating cases used in this study

Physical properties Specific gravity (15/15 °C) ASTM D 1160, K T10 T30 T50 T70 T90 Molecular weight Refractive index Operating conditions Riser inlet temperature, K Preheat feed temperature, K Catalyst/oil ratio Feed flowrate, kg/s

Light gasoil

Heavy gasoil

0.865

0.911

530 592 651 702 742 296 1.492

617 660 702 743 782 356 1.510

815 486 8.7 51

815 486 8.7 51

Models containing four, six, 20 and 35 lumps were selected in this first set of numerical experiments. Plant data include eleven operating cases so that the number of observations, i.e. experimental values, is equivalent to eleven times the number of lumps, Table 1. In all minimizations, the energies of activation employed in the pre-exponential factors estimation were adapted from Lee et al.

[11], Table 3. To establish a similar basis of comparison, results for the four models were grouped so that four overall lumps were configured as: gasoil (GOL, C þ 12 ), light naphtha (LN, C5–C12), gases (GA, C1–C4) and coke. In this form, the minimization procedure yields similar values in the normalized errors of the sum of squares for both four-lump and 20-lump models, Table 1 and Fig. 1. Results indicate no meaningful difference in the predicted values though it is obvious that using 20 lumps will provide more details of the FCC reactions. A better prediction of gasoline and gasoil production is observed when the 35-lump model is used whereas prediction of gases and coke is better with the 6 and 20-lump models. The distribution function strongly depends on the interval of boiling temperatures for each type of feedstock. Hence it is expected that values of kinetic constants will also depend on the type b j have remained almost of feedstock (Eq. (26)); however, a, b, and A unchanged in all cases studied. This apparent invariability is only valid for a specific FCC catalyst. For two types of feedstock considered in this analysis (Table 4) and using a catalyst with selectivity to gasoline, it was observed that the difference in numerical values of kinetic constants is negligible since these differences represented 0.1–0.6%. However, this apparent non-difference in the kinetic constants is sufficient to generate different axial profiles of FCC products in different feedstock types. Average values for kinetic constants at 815 K and ±1% of confidence are shown in Table 5 where it can be observed that cracking ratios for models of four and six-lumps are very similar. Physical units depend on the order of reaction. The cracking constants kHN,GA and kLN,GA behave as overall cracking constants since kHN,GA  kHN,BU + kHN,LG and kLN,GA  kLN,BU + kLN,LG. On the other hand, in the model containing six lumps, the relationships kHCO,BU/kHCO,GA = 1.87, kLCO,BU/kLCO,GA = 1.82 and kHN,BU/kHN,GA = 1.77 indicate that the rate of the cracking of heavy species to light species is practically a constant. The relationship kHCO,HN/kLCO,HN = 1.8 indicates that HCO strongly contributes in producing HN but the relation kHCO,LN/kLCO,LN = 1.0 means that both cyclic oils contribute to produce LN. A similar analysis shows that LCO contributes in larger 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 kinetic constants for the model with 35 lumps. Distribution functions, denoted with letter ‘‘C”, refer to the frequency factors for light lumps. It is appreciated in this case that lumps having less than 10 carbons tend to be disintegrated to produce lumps with less than five carbons. Letter ‘‘B” in Fig. 2a, stands for the heaviest lumps and it is observed that they are distributed within a larger range of carbon numbers. Letter ‘‘A” indicates the reactive behavior of intermediate lumps, which tend to crack into close lumps that can also be overcracked to produce light lumps. In Fig. 2b, the prediction capability of the novel approach is demonstrated. Predicted yields for lumps with carbon number greater than five agree reasonably well with plant data, especially those lumps constituting the light gasoline (C5–C12). However, the lumping technique employing a 35-lump kinetic model offers reasonable predictions for lumps with carbon number lower than five but it fails significantly in prediction of C4 yield. Axial profiles of FCC products were calculated using two kinetic models: a 20-lump model and a six-lump model. A light gasoil was used for the simulation and conversion predictions indicate less that 0.3 wt% at 10 m high. The conversion at the riser outlet becomes 69.3 wt% in both cases though the 20-lump model improves gases prediction. This improvement is because the 20-lump model disaggregates the C1–C3 lump of six-lump model to have methane, ethane–ethylene and propane–propylene. It should be observed the double functionality of heavy naphtha since it starts as a product of the cracking reactions until a maximum yield is achieved so that heavy naphtha behaves as a reactant.

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b) 6 lumps

50

50

40

40 Plant Yields [% wt]

Plant Yields [% wt]

a) 4 lumps

30

20

10

Gasoil Gasoline Gases Coke

30

20

10

0

0 0

10

20

30

40

50

0

10

Calculated Yields [% wt]

c) 20 lumps

30

40

50

d) 35 lumps

50

50

Gasoil Gasoline Gases Coke

40 Plant Yields [% wt]

40 Plant Yields [% wt]

20

Calculated Yields [% wt]

30

20

10

30

20

10

0

0 0

10

20

30

40

50

0

10

Calculated Yields [% wt]

20

30

40

50

Calculated Yields [% wt]

Fig. 1. Minimization results for selected kinetic models. Gasoil

ðC þ 12 Þ,

gasoline or light naphta (C5–C12), and gases (C1–C4).

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 = 5.60E2 kGOL,LN = 3.01E1 kGOL,GA = 8.64E2

kHN,LN = 6.37E3 kHN,GA = 1.24E1

kLN,GA = 5.26E4

Six lumps kHCO,LCO = 8.24E1 kHCO,HN = 3.01E1 kHCO,LN = 3.78E1 kHCO,BU = 7.22E4 kHCO,LG = 3.87E4

kLCO,HN = 1.67E1 kLCO,LN = 3.81E1 kLCO,BU = 8.67E4 kLCO,LG = 4.76E4

kHN,LN = 5.42E1 kHN,BU = 1.09E1 kHN,LG = 6.15E2

5.2. Effects of feedstock and operating conditions A second set of experiments were carried out to establish the effect of several important variables on the performance of the models. One of the most essential goals in simulation of FCC process is the knowledge of the effect of feedstock on FCC yields. Hence two feedstock exhibiting considerable physical differences

kLN,BU = 2.61E4 kLN,LG = 3.11E4

kBU,LG = 2.51E2

have been studied and their impact on the FCC process is summarized in Table 6 where both the 20-lump and the 35-lump models were considered. The most relevant difference found in this simulation is that the overall conversion achieved with the heavy gasoil is greater than that with light gasoil. In contrast, gases and coke yields are greater for light gasoil. As a consequence, the degree of cracking severity should be diminished when light gasoil is pro-

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b) Comparison between results of this work and plant data

a) Pre-exponential factors LN

HN

LCO

HCO 0.10

0.8

C

Plant data This work

0.08

0.6

Weigth fraction

Pre-exponential factor, aji

1.0

A

0.4 B

0.2

0.06 0.04 0.02 0.00

0.0 5

10 15 20 Carbon number

25

0

30

5

10

15 20 25 Carbon number

30

35

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 Gasoil Gasoline Gases

6.1 27.2 46.4 20.3

5.0 29.0 48.4 17.6

6.0 30.7 45.2 18.1

5.3 27.3 49.2 18.2

6.3 33.2 40.9 19.6

5.3 28.4 48.4 17.9

b) Heavy gasoil

40

40

35

35

30

30 Riser Length [m]

Riser Length [m]

a) Light gasoil

25 20 15

wt / wt 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

25 20 15

10

10

5

5 0

0 50

100

150

200

250

300

350

Molecular Weight [kg/kg mole]

50

100

150

200

250

300

350

Molecular Weight [kg/kg mole]

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

cessed. The risk of overcracking could then be reduced. At the bottom of the riser, most of light feed oil is distributed from 200 to 280 kg/kg mol and it is gradually cracked into gasoline and light gases for the 20-lump model, Fig. 3. Gasoline yield is typically observed in the range of 80–120 kg/kg mol and light gases in the range of 20–80 kg/kg mol. The heaviest feed oil is dispersed from

250 to 400 kg/kg mol and, in this case, cracking reactions lead quickly to more valuable products, particularly light gasoline. On the other hand, Fig. 4 depicts the weight distribution using a 35lump model where differences in performance of the 20-lump and 35-lump models are evident. A significant portion of light feed oil close to 200 kg/kg mol could not be cracked into valuable prod-

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a) Light gasoil

c) Heavy gasoil

40

40 35

30

30

Riser Length [m]

Riser Length [m]

wt / wt 35

25 20 15

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

25 20 15

10

10

5

5 0

0 50

100 150 200 250 300 350 400

50

Molecular Weight [kg/kg mole]

100 150 200 250 300 350 400

Molecular Weight [kg/kg mole]

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

Light naphta [% wt]

6. Conclusions

Pr

48 46 44 42 40 38

wt %

38 40 42 44 46 48

eh ea 500 tT em 400 14 pe 10 12 ra 300 8 6 tu 4 re g] tio [kg/k [K t/Oil Ra ] Catalys

It is always possible to propose a model in accordance to the available kinetic information but experimental data is usually limited. The proposed representation has been capable to successfully predict the performance of cracking reactions for gasoils in a wide range of feedstock and operating conditions. Thus, the novel approach developed in this work shows to be highly flexible to include kinetic models exhibiting different degree of complexity. According to the results, it is possible to obtain a detailed kinetic model without a large kinetic database of experiments but using commonly available information in refineries. In addition, the kinetic representation based on a probability distribution has permitted to reduce substantially the computational effort involved in the numerical evaluation of intrinsic kinetic parameters and it prevents excessive reduction of reaction pathways.

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

Acknowledgments ucts. This fact is reflected in the FCC yields shown in Table 6. It is worth mentioning that heavy gasoil is adequately converted into gasoline and gases. In a final set of numerical simulations, the impact of riser operating conditions on FCC yields in steady-state with constant regenerator operating conditions is studied. A six-lump model is used in order to illustrate our results for a heavy gasoil. The effects of both feed preheat temperature and catalyst/oil ratio on light gasoline yields is given in Fig. 5. A maximum on gasoline yield appears when the feed preheat temperature is 343 K and catalyst/oil ratio is 10 to make gasoline yield going up to almost 50%. The position of this point depends markedly on the feedstock, type of catalyst, regenerator operating conditions and quality of the available experimental information. Unfortunately, a suitable comparison between kinetic constants showed in this work and other constants available in the open literature cannot be carried out since several factors affect the quality and reproducibility of experimental results. However, some valuable studies have been published related to the effect of operating conditions on FCC yields [29,52]. The weight distribution of gasoil cracking obtained in this work reasonably agrees with those results published by Liguras and Allen [53]. Concentration profiles obtained in this work also agree with those presented by several authors [24,29,40,41,54].

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