Ind. Eng. Chem. Res. 1993,32, 2997-3005
2997
Single-Event Kinetics of Catalytic Cracking Wu Feng, Erik Vynckier, and Gilbert F. Froment’ Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium
A fundamental kinetic model of catalytic cracking on zeolite catalysts has been developed. The complete network of elementary steps of the carbenium ion reaction intermediates is generated by means of an algorithm based on Boolean relation matrices. Elementary steps on Lewis and Brransted sites are taken into consideration. Single-event rate parameters are estimated for the cracking of paraffins, accounting for the thermodynamic constraints. Because of their fundamental chemical nature, these rate parameters are independent of the feedstock. It is shown how the model can be adapted to the availability of a lumped analysis of the feedstock. Lumped Hougen-Watson rate equations, incorporating a maximum of information about the complex reaction networks, are derived. The lumped rate parameters are reconstructed from the fundamental kinetics by means of multiplication with lumping coefficients.
Introduction Fluid catalytic cracking of gas oil is a major refining process, producing high-quality gasolines. Design and operation of catalytic crackers require accurate process models. An important challenge in the process modeling effort is the development of reliable kinetic equations for processes with complex feedstocks. Current day practice resorts to lumping reactants and products into a small number of pseudocomponents (Nace et al., 1971;Jacob et al., 1976). These lumped models do not reflect the underlying chemistry, however, and require extensive experimental programs for each feedstock, since the rate parameters depend on the feedstock composition. The approach discussed in this paper takes into account the detailed carbenium ion chemistry occurring on the active sites of the zeolite catalyst. The rate is expressed for each of the elementary steps involved in the transformation of the intermediates. This approach leads to rate coefficients which are independent of the feedstock, due to their fundamental chemical nature. They can be determined from experiments with typical key components and simple mixtures of these. The approach was developed first for hydrocracking on Pt-loaded Y-zeolites (Baltanas et al., 1989; Froment, 1991a,b; Vynckier and Froment, 1991). It is now extended to catalytic cracking on Y-zeolites. Today, the rigorous application to complexhydrocarbon fractions is limited by the analytical techniques used for the characterization of petroleum mixtures. A lumping scheme has been developed that allows the calculation of the rate coefficients of the reactions between lumps from the knowledge of the fundamental single-event rate parameters.
Carbenium Ion Chemistry of Catalytic Cracking Acid-catalyzed hydrocarbon reactions such as the zeolite-catalyzed processes encountered in petroleum refining proceed via carbenium ion intermediates. A solid body of knowledge on carbenium ion chemistry has been accumulated through the study of liquid superacid solutions (Brouwer, 1980). The main features of carbenium ion chemistry were confirmed in the study of heterogeneous acid catalysis, in model component studies, and more directly by means of infrared spectroscopy. The chemical properties of a carbenium ion are determined mainly by the number of carbon substituents on the charge-bearing carbon atom. Because of the inductive
and the mesomeric effects, tertiary carbenium ions (referred to as “t”) are more stable than secondary carbenium ions (s). Primary (p) and methyl (CH3+)carbenium ions are even less stable. Exceptions occur, such as the primary benzyl cation, which is stable through charge delocalization across the aromatic ring. Catalytic cracking of paraffins proceeds through isomerizations (hydride shifts; methyl and ethyl shifts; and branchings through protonated cyclopropane or -butane intermediates, called PCPs and PCBs) and cracking via p-scissions of carbenium ions producing carbenium ions with a shorter chain and olefins. The olefins can readily protonate on the Bronsted sites and isomerize or crack. The carbenium ion can exchange a hydride ion with a hydrocarbon (hydride transfer). In this way, the reactive center is transmitted to a new feed molecule. A controversy has arisen as to the origin of the initial carbenium ion. It was speculated that olefinic feedstock impurities, or olefins produced from thermal cracking, protonate on Brcansted sites to form the initial carbenium ions. Other authors postulate mechanisms starting with hydride abstraction of paraffins on Lewis acid sites, which subsequently isomerize and crack. Haag and Dessau (1984) gathered evidence for scission of pentacoordinated carbonium ions on Bronsted sites in a-position of the positive charge (protolytic scission), a mechanism which is important at higher temperatures (500-550 “C). In the present paper, reactions on both Bronsted and Lewis sites will be considered.
Automatic Generation of the Network of Elementary Steps Considering the sheer number of reaction pathways in the catalytic cracking process originating from even a simple molecule, a computerized algorithm is needed for the generation of the network of elementary steps. An algorithm has been implemented based on Boolean relation matrices to describe the structure of the hydrocarbon (Clymans and Froment, 1984; Baltanas and Froment, 1985). Figure 1shows such a Boolean relation matrix for (2-methylpropy1idene)cyclohexane. The carbon atoms of the species are numbered in an arbitrary sequence. The matrix element (i,j) is “true” if there is a carbon-carbon bond between atoms i and j . Otherwise, a value “false” is assigned. An array contains the position of double bonds, if any, and the occurrence of a positive charge is also indicated.
OSSS-5885/93/2632-2997$04.00/00 1993 American Chemical Society
2998 Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 9
7
8
1
3
2 1
1
3
4
5
6 1
7 1
9 1 0
1 1
1 1
1
1
1 1
1 1
1 1
8
.1
1
0
0
I
1
10
1
8
0
0
0
0
0
1
0
, no charge.
Figure 1. Boolean relation matrix of (2-methylpropy1idene)cyclohexane. 1 1 1 2 3
4
5
6
7
1
8
9 1 0
1 1
1
1
1
1 1
1
1
The Concept of Single-Event Rate Coefficients
1
1 1
6 7 8
3
1
4 5
2
Eliminating carbon bond 7-8 results in two separate matrices, representing the products of the @-scission,which can be recognized as methylenecyclohexane and 2-propyl. Eliminating bonds 2-3 or 5-6 would result in ring opening, but these possibilities are not allowed in the network, since unstable primary carbenium ions are formed in these steps. For the catalytic cracking of paraffins, the algorithm considers the following elementary steps (Figure 3): hydride abstraction and donation of paraffins on Lewis sites; protonation and deprotonation of olefins on Brernsted sites; hydride, methyl, and ethyl shifts and PCP and PCB branchings on Lewis and Brernsted sites; @-scissionson Lewis and Brernsted sites; protolytic scissions of paraffins on Brernsted sites; and, finally, hydride transfers on Brernsted sites. The algorithm can also deal with naphthenes and aromatics with up to four rings. Additional reaction mechanisms included for naphthenes other than those for paraffins are intraring alkyl shifts, ring contractions and expansions (mechanistically also PCP branchings), exocyclic &scissions,endocyclic @-scissions(amountingto ring opening), and cyclization (Figure 4). Aromatic side chains can isomerize and crack like paraffinic or olefinic molecules. Additional elementary steps included in the network for aromatics, specifically, are alkylation and dealkylation of the aromatic nucleus and aromatic disproportionation on Brernsted sites (Figure 5 ) . Also, condensation of side chains to form polynuclear aromatics occurs through cyclization of the side chain onto the aromatic ring, followed by a number of hydride transfers. This step is also catalyzed by B r ~ n s t e dacidity.
1
1 1
1
1
1 1 1
9 10
1 1
Figure2. A2 = A*- I, indicating 0-positions in (isobutylcyclohexy1)carbenium ion.
The elementary steps are generated by performing operations on the Boolean relation matrix, according to a strict set of rules. Consider the protonations of (2methylpropy1idene)cyclohexane. The position of the double bond is checked (carbon atoms 1 and 7). Elimination of the double bond on 1 and 7 (put 0's into the double-bond array) and positioning a charge on either of the carbon atoms result in two possible products. The character of the products can be seen by summing all positions across a row: carbon atom 1 is tertiary, since row 1contains three 1'9, while carbon atom 7 is secondary. The @-neighborsof each carbon atom can be found by squaring the Boolean relation matrix A (Figure 2). The diagonal elements are irrelevant, since these amount to double counting the a-bond, so I has to be subtracted. A, = A-A - I
(1)
The reaction rates are expressed in terms of the concentrations of the species involved in the elementary steps. An additional refinement has to be included, however, to come to invariant rate parameters. Consider the case of the methyl shift in the cyclic carbenium ion in Figure 6. In the forward reaction, two methyl groups can shift, in the reverse reaction only one. Intuitively, it is expected that the rate coefficient for the forward reaction should be twice that of the reverse reaction. This idea can be formalized with single-event rate coefficients. Accordingto transition-state theory, the rate coefficient can be expressed in terms of the equilibrium constant K S for the formation of the transition state from the reactant: k' = -K* kB
(3) h The entropy effect of the equilibrium constant can be factored into an intrinsic contribution and a global symmetry contribution. The global symmetry contribution contains symmetry numbers of the reactant and transition state as well as factors accounting for optical isomerism in the reactant and transition state. According to Baltanas et al. (19891, the rate coefficient of an elementary step reduces to k' = n,k
(4)
Higher order relations (y-positions, ...I can be found recursively:
with the number of single events ne:
A, = A,,.A - An-2, n = 3, ... (2) The second term of eq 2 effectively eliminates all double counting of bonds. Carbon atom 8 is in the @-positionwith respect to carbon atom 1, as can be seen in row 1 or row 8 of Figure 2.
The symbol u represents the symmetry number, 7 the number of optical isomers, and uglthe ratio of these, called
Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 2999 SRONSTED SmS
LEWIS SITES
L
+
L
===
h
+
L
H
HydrideAbstraction Protonatlon
' + - A c _
A+
Hydride Shift
"--.=+ Methyl Shift
H+--
0 Protolytlor c M o n
Hydride ShlR Ethyl Shiit
+
PCP-Branching
* =+ Ethyl Shnt
&=AH PCP-Branching
&
& + L H =
+
L
Hydrlde Donatlon
vy
h&7&.A=/yw PCB-Branching
Deprotonatlon
Hydride Tranhr
Figure 3. Elementary steps in the catalytic cracking of paraffins.
the global symmetry number. Equation 4 relates the rate coefficient of an elementary step to a parameter which is independent of the steric aspects of the reactant and the transition state of the elementary step, which is, therefore, truly invariant. All steric aspects of the elementary step are factored into ne. For the methyl shift in Figure 6,ne equals 12 for the forward reaction and 6 for the reverse reaction (Vynckier and Froment, 1991).
Reduction of the Number of Single-Event Rate Parameters The number of rate parameters in the network is very large, mainly because of the hydride abstraction and donation on Lewis sites and protonation and deprotonation
steps on Bransted sites, since the nature of the paraffin or olefin enters into the definition of these rate coefficients. The number of rate parameters to be estimated can be significantly reduced by accounting for thermodynamic consistency. Hydride Abstraction and Protonation. The rate coefficient of hydride abstraction on a Lewis site is assumed to be independent of the paraffin. This implies that the transition state lies close to the reactant, so the characteristics of the paraffin are closely reproduced in the transition state. Two parameters are thus introduced to model the rate of hydride abstraction: k u ( s ) and kW(t). The rate parameters for hydride donation are necessarily dependent on the structure of the paraffin. This can be seen from a thermodynamic constraint:
3000 Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 LEWIS AND BRONSTED S m S
4) = 3 . 3
\/+
Intra ring alkyl ahHt
=
n, =
9
.&
= 12
4,’ = 3 / 4
r+
Ring Contraction and Ring Expanslon
9/2 - 6 ”‘= m-
u:,
‘
r
3.3
= 9/2
\
Exocyciicpcission
The symbol
refers t o a c h i r a l carbon atom.
Figure 6. Methyl shift: number of single events.
(7) Cyclization
Figure 4. Elementary steps in the catalytic cracking of naphthenes.
or, generally,
BRON8TEDSITES
with m either s or t and P, a selected reference paraffin of the same carbon number as Pj. Along the same lines, it can be shown that
I
on the assumption that kpr(Oj;m) = kp,(O,;m) = kp,(m), with m either s or t and 0, a reference olefin of the same carbon number of Ob Two rate Coefficients per carbon number are needed for hydride donation and another two per carbon number for deprotonation. Isomerization. A similar thermodynamic analysis can be applied to reduce the number of independent isomerization rate coefficients. For the isomerization rate parameters on Lewis sites
Alkylation and Dealkylation
I,
and on Brernsted sites
Cyclization
Figure 5. Elementary steps in the catalytic cracking of aromatics. kUIA(E1P)
Pl=
km(sP1)
kd90(s;a)
Rl+=
+
R2
knds;~)
=P,
klds;Pd
km(Pz;#)
(6)
By virtue ofkm(P1;s) = km(P2;s) = k m ( s ) ,the equilibrium constant for isomerization of paraffin P1 into P2 can be expressed as
The number of parameters is thus reduced by one for each type of isomerization on both Lewis and Brernsted sites. The ratio of hydride donation parameters in eq 10 is independent of the carbon number, since everything else in eq 10 is. This ratio allows elimination of one hydride donation parameter per carbon number, except for one carbon number, which serves to calculate this constant ratio. Concerning protonation, the same conclusion is reached from eq 11. It is reasonable to assume that the hydride donation (protonation) rate parameters of a homologous series of reference paraffins (olefins) are identical. Finally, only two parameters in total are needed for hydride donation and another two for deprotonation.
Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 3001
Cracking. Four rate parameters are needed for the cracking on the Lewis sites
k:,(s;s), k&(s;t), k&(t;s), k&(t;t)
RPi
= [k’HDO’;pj)cRij+,L
- k’,O’)PpiC~l t
(12)
and another four for the Brernsted sites
kEr(s;s), kEr(s;t), k&),
kEr(t;t)
(13)
The produced olefin is not incorporated in the definition of the cracking rate parameters. Justification for this assumption is found in the fit of the data. No thermodynamic constraints need to be introduced for the cracking rate parameters, since the 0-scissionsare irreversible steps. Hydride Transfer. The rate of hydride transfer is modeled as a first-order process with respect to the carbenium ion concentration. It is assumed that the rate coefficient for hydride transfer only depends on the type of the reacting carbenium ion and not on the number of carbon atoms. This leavestwo rate coefficientsfor hydride transfer, k H T ( s ) and k H T ( t ) , which have to be estimated.
The calculation of the rates of formation of paraffins and olefins on Lewis and Brernsted sites, by means of eqs 20 and 21, is straightforward, once the concentrations of the carbenium ions and of the vacant acid sites are known. These are eliminated through the pseudo-steady-state approximation =0
(22)
RR,+,B = 0
(23)
RRij+,L
and the active site balance for Lewis and for Brernsted sites:
Rate Equations Catalytic cracking consists of a number of steps on two different acid sites. First, paraffins adsorb on Lewis sites through hydride abstraction to form carbenium ions:
Pi + L e Rij+ + LH-
(14)
The carbenium ions undergo hydride shifts, methyl shifts, and PCP branchings: Rj;
F!
Rk;
(15)
&Scission leads to a carbenium ion with a shorter chain and an olefin: R:i
-
+
Rmn+ 0,
(16)
The olefins thus produced can be protonated into a carbenium ion on a Brernsted site:
0,
+ H+ Rag+
(17)
The ion is then involved in hydride and methyl shifts and in PCP branchings, hydride transfers, and 0-scissions. Rate equations for the net formation of carbenium ions can now be written:
Two seta of linear equations are thus obtained one related to the Lewis sites (eqs 22 and 24) and one related to the B r ~ n s t e dsites (eqs 23 and 25). These can be numerically solved for the concentrations of the carbenium ions. For an integral reactor, the numerical solution needs to be repeated in each point of the reactor, since the coefficients of the sets of equations depend on the partial pressures of the paraffins and olefins. The rate equations mentioned above can be easily extended to include naphthenic and aromatic cracking reactions.
Single-Event Parameters for Catalytic Cracking of Paraffins Experiments of n-decane cracking on a commercial RE-Y catalyst in a fixed bed integral reactor have been conducted. n-Decane cracking gives a product spectrum that can be completely identified. Because of the fundamental nature of the rate parameters, their values determined from cracking experiments with a short-chain model component can be used for the modeling of heavier components as well. A total of 20 experiments at temperatures of 450,475, and 500 “C were performed. Yields at zero coke content have been arrived at by extrapolating experimental yields at different process times to time zero. The model predictions require integration of the continuity equations by means of a Runge-Kutta routine. Parameter estimates are determined using a Rosenbrock algorithm to minimize the following objective function: n h u P h P
“=CZ 1-1
Next, the rate of formation of the paraffins and olefins can be derived:
k
P
d k [ z(yij- vij)(yik - v i k ) ]
(26)
$=I
with d k a weight factor. The G,k)element of the inverse of the error covariance matrix and Yij and %‘ij refer to the experimental and predicted yield of product j in experiment i.
3002 Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 Table I. Single-Event Rate Parameters (kmo1/(kgmt.s)) and Activation Energies (kJ/mol) in the Catalytic Cracking of Paraffins on RE-Y-Zeolite Darameter
450 OC 8.459 10.59 3.766 X 106 3.720 X 10-7 1.008 X 104 2.715 X 104 1.767 X 106 1.492 X 10-7 1.292 X 109 9.212 X 106 1.331 X 109 2.887 X 10'0 2.204 X 106 5.107 X 10'2 1.985 X 107 2.902 X 109 1.283 X 1 06 1.093 X 103 3.984 X 103 8.188X 1o-L 1.703 X 10-2 7.163 6.573 X 10' 7.383 X 10' 2.091 X 10' 3.557 x 10'
475 "C 14.25 16.59 4.966 X 106 4.720 X le7 1.528 X lo4 3.915 X lo4 2.449 X 106 2.335 X 1.593 X log 1.111 x 106 2.131 X lo9 3.487 X 1O'O 3.404 X los 5.397 x 10'2 2.185 X lo7 3.712 X log 3.253 X lo6 1.203 X 5.864 X 1.018 X 103 2.700 X 10.16 8.083 X 10' 8.283 X 10' 3.491 X 10' 4.057 X 10'
500 *c 24.25 30.59 5.426 X 106 1.121 x 1o-B 1.617 X 104 4.015 X 104 2.520 X 106 2.712 X 10-7 4.593 x 109 1.241 X 106 2.531 X 109 4.187 X 10'0 3.614 X 106 5.427 X 10'2 2.225 X 10' 3.892 X 109 3.314 X 106 1.413 X 103 6.964 X 103 1.418 X 103 3.403 X 10-2 13.46 8.314 X 10' 8.533 X 10' 3.732 X 10' 4.318 X 10'
EA 97.87 98.57 34.52 102.5 43.92 36.36 32.98 55.68 117.8 27.69 59.72 34.55 45.96 56.48 10.60 27.27 88.18 23.86 51.89 51.03 64.33 56.82 21.83 13.45 60.12 25.57
i
In km~l/(kg,~-s.kPa). Weld (W %) 14
I
0
a,
.?a
40
CQ
! X(0) %
Figure 7. Simulated and experimental yields of paraffins versus total conversion of n-decane (7' = 475 "C). Single-event model. Veld (W %)
io
I
4 -
4
A
A
,
I
0
20
30
40
e4
X(0) %
Figure 8. Simulated and experimental yields of olefins versus total conversion of n-decane (2' = 475 O C ) . Single-event model.
The optimal parameter values for the catalytic cracking of paraffins are given in Table I. Figures 7 and 8compare predicted yields of paraffins and olefins with the experimental yields. The fit is excellent. It was found that the same values could be used for the isomerizationrate parameters on Lewis and Bransted sites. The parameter values consistently increase with temperature, in agreement with the Arrhenius relation. Proto-
Lumped Kinetic Models
For heavy feedstock components, a gas chromatographic analysis that quantifies all the individual isomers is not available. An ASTM method which combines information from high-pressure liquid chromatography and gas chromatography/mass spectrometry provides the weight fraction per carbon number of n-paraffin; isoparaffins; mono-, di-, tri-, and quaternaphthenes; and mono-, di-, and triaromatics (Froment, 1991b). It will now be discussed how the single-event model may be adapted to the availability of a lumped analysis of the feedstock. Figure 9 shows the network of lumped reactions for the case of n-decane catalytic cracking. The isoparaffins of each carbon number have been lumped, since a separation of the different isomers is not possible for a heavy feedstock. The normal and isoolefins of a given carbon number are also lumped. The isomerization reactions of these components proceed I order of magnitude faster than their cracking reactions. Therefore, the composition of the olefin lump approaches equilibrium. Rate coefficients of the lumped model can be reconstructed from the single-eventrate coefficients,accounting for the full network of elementary steps. The reaction rate of an arbitrary lump LI to lump La is simply taken to be the sum of the reaction rates of all elementary steps that convert carbenium ions of L1 into carbenium ions of Lp. The calculation of the reaction rate of an elementary step requires the single-event rate coefficient and the concentration of the carbenium ion. The concentration
Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 3003 of the carbenium ion can be calculated assuming quasiequilibrium in the adsorption step (hydride abstraction or protonation) and equilibrium composition for the lump. For isomerization of the paraffin lump L1 into Lz on Lewis sites, the following kinetic equation is obtained:
4so =
kkso(PLI - PL2/KL1;,) (27) 1+ C K L ~ P L , 1
For cracking of paraffin lump L1 on Lewis sites, the equation is (28)
For the isomerization of the lump of olefins Lt into Lq on Br~rnstedsites
Figure 10. Lumping coefficientfor isomerizationof n-paraffineinto isoparaffins.
kko(PL3 - pL,/KLS;L> 4 0
=
(29) 1+ CKBjPLj I
and for the cracking of olefin lump L3
The isomerization coefficient of L1 into L2 on Lewis sites can be calculated from
o / 8
e
10
11
11
1s
1.
cubonnmbr
16
I
Figure 11. Productionof isobutenethrough (t;t)@-scissionson Lewis sites. Lumping coefficient.
(31) The rate coefficient of the elementary step s amounts to (n,),kpcpL(m;n). The ratio in the middle of eq 31represents the equilibrium constant for hydride abstraction of the paraffin Pi into the carbenium ion Rim+undergoing the step s. Its denominator takes into account the thermodynamic constraint for hydride donation (eq 81, where P, is the reference paraffin of the same carbon number of Pi. The mole fraction of paraffin Pi in lump L1, yiA1, relates the partial pressure of Pi to the partial pressure of L1. Equation 31 can be rearranged into
kkso = (Lc);,p(s;s) K,(s) kb,p(s;s) + (LC)kcp(s;t)K,(s)
kbcp(s;t) +
(LC)bcp(t;s)K,(t)
kbcp(t;s) +
(LC)bcp(t;t) K,(t)
&p(t;t)
(32)
where (33)
(34) The sums in eqs 31 and 33 are taken over all relevant elementary steps s; the symbol m in eq 34 is either s or t.
The constant K b for adsorption on the Lewis sites needed for the denominator of the kinetic equations (27) and (28) can also be expressed in terms of more fundamental coefficients:
KLi = (Lc)ii(s)KHA(s) + (LC)kiA)K,(t)
(35)
Analogous equations can be written which relate the cracking rate parameters and the rate parameters of the reactions on Br~rnstedsites to the single-event coefficients. The lumping coefficients (LC) depend on the choice of the lumps and the elementary step network, not on the fundamental rate parameters. The lumps are chosen according to the analytical capabilities. Equations 32 and 35 also allow a determination of a subset of the singleevent rate coefficients from lumped rate data directly. Figure 10 shows the lumping coefficient for PCP isomerization of normal paraffin into isoparaffin for various carbon numbers. The stepwise increase of the lumping coefficient with the carbon number can be explained in terms of the stepwise increase of the number of PCPs with the chain length. The lumping coefficient for @-scissionof an isoparaffin into isobutene and another isoparaffin through (et)steps is given in Figure 11. This coefficient decreases from CS onward. For each carbon number, only one of the (t;t) &scissions produces isobutene (Figure 14). The number of molecules in the lump increases very rapidly with carbon number, however, so the mole fraction y i , of ~ the specific molecule (2,4,4-trimethylalkane) undergoing this cracking
3004 Ind. Eng. Chem. Res., Vol. 32,No. 12, 1993 (LC);Q)
Aqk - A + A (t;t)fl-Scission of iroparamnto inobutene and another isoparafin.
4
6
8
I
8
0
10
11
12
13
16
14
k-h
18
cvaonnmbr
Adsorption of isoparafllnwith formatlon of a tertiary ion on Lewlo sttea.
Figure 12. Adsorption of isoparaffins with formation of tertiary carbenium ions on Lewis sites. Lumping coefficient.
(q (t)
'Oj
\
1s 4
6
I)
7
8
0
10
11
12
13
CYDoInmbr
Figure 13. Adsorptionof olefiiwithformation oftertiarycarbenium ions on Br~nstedsites. Lumping coefficient.
10
S
step decreases very rapidly. The lumping coefficient should therefore also decrease (eq 33). The initial increase from C8to Cgcan be explained as well. For CS,the molecule (2,2,4-trimethylpentane) undergoing this step contains a tert-butyl group (Figure 141,with a threefold rotational symmetry axis. This lowers the entropy of the 2,2,4trimethylpentane and thus its stability, and therefore its mole fraction in the isoparaffin lump is unusually low. The lumping coefficient for adsorption of isoparaffins with formation of tertiary carbenium ions is shown in Figure 12. For high carbonnumbers, the lump increasingly consists of dibranched and tribranched paraffins, which yield more than one tertiary carbenium ion (Figure 14). On the other hand, monobranched paraffins, which are an important fraction of the short chain lumps, produce only one tertiary carbenium ion. A monotonically increasing lumping coefficient is therefore obtained. The lumping coefficient for adsorption of isoolefins on Brornsted sites with formation of tertiary carbenium ions decreases rapidly with carbon number (Figure 13). Only isoolefins with the double bond on a tertiary carbon atom contribute to this lumping coefficient (Figure 14). The fraction of these decreases with the chain length. The lumped rate coefficient for cracking of isoparaffins into isobutene and isoparaffins can be written as k& = (LC)&(t;s) K,(t) k&s) + (LC)&(t;t)K,,(t) (36) The (t;t)&scissions dominate for small carbon numbers,
0
8
0
10
11
12
IS
14
16
18
Carbon number
Figure 16. Lumped rate coefficient for cracking of isoparaffins into isobutene and isoparaffim. Contributions from (t;t)and (6s)&scissions and total coefficient at 475 "C.
but for larger carbon numbers the (t;s) @-scissionsplay an important role as well (Figure 15). The lumping coefficient of the (t;t) mechanism diminishes markedly after Cg (Figure ll), while the lumping coefficient of the (t;s) mechanism reaches a maximal value at C11 after which it declines slowly.
Conclusion and Outlook The present paper introduces a new approach to the kinetic modeling of the catalytic cracking of gas oil components. A fundamental model was developed, accounting in detail for the carbenium ion mechanism. The fundamental approach leads to single-event rate parameters which are invariant, i.e., independent of the feedstock, and to a detailed prediction of the product distribution. A lumped model, whose rate parameters can be derived from the fundamental kinetics, is also introduced. The lumped rate parameter is calculated from the fundamental rate parameters by multiplication with a coefficientderived from the elementary step network. The lumps have to be selected in accordance with the analytical characterization of gas oil feeds. The approach presented here can be
Ind. Eng. Chem. Res., Vol. 32, No. 12, 1993 3005 readily extended to the catalytic cracking of mono- and multiring naphthenes and aromatics and to other acidcatalyzed complex processes in petroleum refining. The rates dealt with here are initial rates, Le., in the absence of coke on the catalyst. In this respect, the present work would have to be extended to include the effect of coke on the catalyst activity. The coke content would have to be predicted by kinetic equations for coke formation. This would require a selection of precursor molecules and the generation of networks leading to coke. Nomenclature A,, = nth-order Boolean relation matrix Ct,B = total number of Brcansted sites Ct,L = total number of Lewis sites h = Planck constant H+= vacant Brcansted site k~ = Boltzmann constant k = single-event rate coefficient k’ = elementary step rate coefficient kHA(m) = rate coefficient for hydride abstraction with formation of carbenium ion of type m kHD(m;P1) = rate coefficient for hydride donation of carbenium ion of type m into paraffin PI kp,(m) = rate coefficient for protonation with formation of carbenium ion of type m kD,(m;Ol) = rate coefficient for deprotonation of carbenium ion of type m into olefin 01 kFso(m;n) = rate coefficient for isomerization (hydride shift, methyl shift, or PCP branching) of carbenium ion of type m into carbenium ion of type n; B = Brcansted sites k&(m;n) = rate coefficient for cracking of carbenium ion of type m into carbenium ion of type n; B = Brcansted sites k:?(m) = rate coefficient for hydride transfer to carbenium ion of type m KB,= adsorption constant of lump of olefins Li on Brcansted sites K b = adsorption constant of lump of paraffins Li on Lewis sites KISO= isomerization equilibrium constant K L ~= ;equilibrium ~ constant of the isomerization reaction between lumps L1 and LZ L = vacant Lewis site (LC)Iso(m;n) = lumping coefficient for isomerization of carbenium ions of type m to carbenium ions of .type n (LC)b(m) = lumping coefficient for adsorption of paraffins on Lewis sites forming carbenium ions of type m m, n = general notation for type of carbenium ion: s or t rnresp= number of responses nelp = number of experiments ne, (ne)8= number of single events (of elementary step s) yi,= ~ ~mole fraction of component i in lump L1 Greek Letters = number of optical isomers of molecule A UA = symmetry number of molecule A
qA
aglA=
dk
global symmetry number of molecule A
0 , k ) element of inverse of error covariance matrix
Superscripts B = Brcansted site L = Lewis site = carbenium ion
+
Literature Cited Baltanas, M. A.; Froment, G. F. Computer Generation of Reaction Networks and Calculation of Product Distributions in the Hydroisomerizationand Hydrocracking of Paraffiis on Pt-containing Bifunctional Catalysts. Comput. Chem. Eng. 1985,9,71-81. Baltanas, M. A.; Van Raemdonck, K. K.; Froment, G. F.; Mohedas, S. R. Fundamental Kinetic Modeling of Hydroisomerization and Hydrocracking on Noble-Metal-Loaded Faujasites. 1. Rate Parameters for Hydroisomerization. Znd. Eng. Chem. Res. 1989,28, 899-910. Brouwer, D. M. Reactions of Alkylcarbenium Ions in Relation to Isomerization and Cracking of Hydrocarbons. In Chemistry and Chemical Engineering of Catalytic Processes; Prins, R., Schuit, G. C. A,, Eds.; Sijthoff & Noordhoff: Alphen a m den Rijn, 1980; pp 137-160. Clymans, P. J.; Froment, G. F. Computer Generation of Reaction Paths and Rate Equations in the Thermal Cracking of Normal and Branched Paraffins. Comput. Chem. Eng. 1984,4137-142. Froment, G. F. Fundamental Kinetic Modeling of Complex Processes. In Chemical Reactions in Complex Mixtures-The Mobil Workshop; Sapre, A.V., Krambeck, F. J., Eds.; Van Nostrand Reinhold New York, 1991a,pp 77-100. Froment, G. F. Kinetic Modeling of Complex Catalytic Reactions. Rev. L’Znst. Fr. P6t. 1991b,46,491-500. Haag, W. 0.; Dessau, R. M. Duality of mechanism for acid catalyzed paraffin cracking. In Proceedings 8th International Congress on Catalysis; Dechema: Frankfurt-am-Main, 1984; pp 308-314. Jacob, S. M.; Gross, B.; Voltz, S. E.; Weekman, V. W. ALumping and Reaction Scheme for Catalytic Cracking. AIChE J. 1976,22,701713. Liguras, D. K.;Allen, D. T. Structural Models for Catalytic Cracking. 1. Model Compound Reactions. Znd. Eng. Chem. Res. 1989a,28, 665-673. Liguras, D. K.;Allen,D. T. Structural Models for Catalytic Cracking. 2. Reactions of Simulated Oil Mixtures. Znd. Eng. Chem. Res. 1989b,28,674-683. Nace, D. M.; Voltz, S. E.; Weekman, V. W. Application of a Kinetic Model for Catalytic Cracking-Effects of Charge Stocks.Znd. Eng. Chem. Process Des. Dev. 1971,I O , 530-538. Quann, R. J.; Jaffe, S. B. Structure-Oriented Lumping: Describing the Chemistry of Complex Hydrocarbon Mixtures.Znd.Eng. Chem. Res. 1992,31,2483-2497. Vynckier, E.; Froment, G. F. Kinetic Modeling of Complex Catalytic Processes based upon Elementary Steps. In Kinetic and Thermodynamic Lumping of Multicomponent Mixtures; Astarita, G., Sandler, S. I., Eds.; Elsevier SciencePublishers B. V.: Amsterdam, 1991,pp 131-161.
Received for review January 15, 1993 Revised manuscript received August 6 , 1993 Accepted August 12, 1993.
Abstract published in Advance ACS Abstracts, October 15, 1993.
