3284
Ind. Eng. Chem. Res. 2009, 48, 3284–3292
Single-Event Microkinetic Model for Long-Chain Paraffin Hydrocracking and Hydroisomerization on an Amorphous Pt/SiO2 · Al2O3 Catalyst Marios Mitsios,† Denis Guillaume,*,† Pierre Galtier,† and Daniel Schweich‡ Institut Franc¸ais du Pe´trole, BP3 69390, Vernaison, France, and CNRS ESCPE Lyon, BP 2077, Villeurbanne, France
Hydrocracking of a long-chain paraffin, n-hexadecane, was carried out on an amorphous Pt/SiO2 · Al2O3 bifunctional catalyst. Through an isomerization selectivity analysis, it was found that the behavior of the system approaches the ideal hydrocracking conditions. The kinetic modeling of paraffin hydrocracking and hydroisomerization was realized by using the principles of the single-event microkinetic concept. The singleevent microkinetic concept has been demonstrated to be efficient in the modeling of acid-catalyzed reactions. A lumped single-event microkinetic model was developed for heavy paraffin hydrocracking in the liquid phase, which considers a group of only nine rate constants for the reactions on the acid phase of the catalyst. The model’s lumping coefficients were calculated by the lateral-chain method, a computer-based approach that does not imply the generation of the whole reaction network. The rate constants were estimated at 340 °C from n-hexadecane hydroisomerization experiments in a plug-flow pilot reactor. The kinetic model was validated (upon extrapolation) by the simulation of two heavier paraffin feeds: a C20-C30 wax mixture and pure squalane. The agreement between the calculated and experimental data was satisfactory. 1. Introduction The hydroconversion of n-alkanes plays an important role in the petroleum industry. High-molecular-weight linear paraffins present high viscosities and pour points, making their application as diesel or aviation fuels difficult. The branching of normal paraffins is needed to improve the octane number of gasoline and to enhance the low-temperature performance of diesel or lubricating oils.1,2 The hydrocracking and hydroisomerization of long-chain paraffins are important refinery processes for upgrading petrol heavy paraffins or Fischer-Tropsch waxes into more valuable lighter fractions such as diesel, aviation fuel, and gasoline. Removal of long-chain normal paraffins (dewaxing) is essential for the acceptability of lubricating oils. The hydrocracking and hydroisomerization of paraffins occur on bifunctional catalysts having a metal (noble metal Pt or Pd or transition metals Ni, Mo, or Co) and an acid phase (zeolite or amorphous silica-alumina). If gasoline is the required product, the acidic component of the catalyst is preferably a zeolite, the strong acidity of which favors successive cracking reactions of the feed molecules, with the formation of the desired light products. On the other hand, for an optimal gasoil yield, the catalyst should have a moderate acidity, lower than that of zeolites (low selectivity) and greater than that of aluminas (low activity). Amorphous supports such as silica-aluminas could present such an acid strength.3,4 The paraffin reaction scheme follows a bifunctional mechanism.5 The first step in the paraffin hydroisomerization process is the dehydrogenation of paraffins to produce olefin intermediates. These olefin intermediates can be adsorbed (protonated) on acid sites and form carbenium ions. The carbenium ions can undergo acid-catalyzed reactions such as type A and type B isomerization and cracking reactions in the β position with respect to the carbon atom bearing the positive charge (βscission).6 The isomerized and cracked carbenium ions can be * To whom correspondence should be addressed. E-mail:
[email protected]. † Institut Franc¸ais du Pe´trole. ‡ CNRS ESCPE Lyon.
desorbed from the acid sites (deprotonation) and hydrogenated on the metal sites to form the corresponding paraffins. Catalysts with high hydrogenation abilities and low acidities are desirable for the hydroisomerization of long-chain hydrocarbons.7,8 When the acid-catalyzed reaction steps are rate-determining and the metal-catalyzed hydrogenation and hydrogenation reactions are in quasi-equilibrium, the hydrocracking process is characterized as “ideal”.6 Under these conditions, the product distribution is a unique function of conversion. Ideal hydrocracking conditions are enhanced when both hydrogenating and acid functions are in close proximity, which can be achieved through good metal dispersion on the catalyst’s surface.6 The kinetic modeling of the ideal hydrocracking and hydroisomerization of long-chain paraffins entails a great number of kinetic parameters to describe each reaction step of the mechanism on the acid sites of the catalyst. The kinetic model would have to take into account the different reactions and mechanisms relevant to all components of the reaction mixture. Every elementary reaction step between two carbenium ions requires one kinetic constant that depends only on the type of reaction and the reactant ions. Given the number of the acid reaction steps and the complexity of the hydrocracking reaction systems (e.g., 383 acid reactions steps for n-octane hydrocracking), modeling of such processes has been particularly difficult, and it has been necessary to apply a drastic lumping of the feed, intermediate, and end-product species. Lumped models are based on an appropriate number of pseudocomponents (lumps) whose simplified reaction scheme is studied. Several types of lumped models for the prediction of the hydrocracking of complex feeds have been proposed in the literature, each of them presenting a different strategy of lumping.
Figure 1. One elementary reaction step: secondary-secondary methyl-shift isomerization.
10.1021/ie800974q CCC: $40.75 2009 American Chemical Society Published on Web 03/03/2009
Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3285
Figure 2. Decomposition of the activated complex into one activated zone and two lateral chains.
A well-known family of lumped models is based on a discrete lumping strategy.9,10 The pseudocomponents generated are identified by means of a property such as the true boiling point (TBP) or molecular weight. Another family of lumped models is based on the continuous lumping approach11 in which the reacting mixture is considered as a continuous mixture with respect to a specific physical property such as the true boiling point (TBP) or molecular weight. Most lumped models proposed in the literature can provide satisfactory predictions of the reactivities between their lumps, but in most cases, the rate parameters depend strongly on the feed composition and the hydrodynamic conditions (process configuration and operating conditions), reducing their extrapolation ability. A recent attempt to model, in a more accurate way, the hydroisomerization and hydrocracking process has been made by the Ghent research group. Baltanas et al.12 developed the now well-known single-event methodology that is based on carbenium ion chemistry. This methodology takes into account the knowledge of the elementary reactions on the acid sites of the catalyst, maintaining the complete details of the reaction scheme. According to the single-event kinetic concept, the total number of rate constants describing the acid-phase reactions can be drastically reduced, and the remaining kinetic parameters present an intrinsic character, as they do not depend on the feed composition or the process configuration. The number of types of elementary reaction steps that are possible for hydrocarbons reacting on a given catalyst is much smaller than the number of molecules in the mixture. By assigning a unique kinetic constant to a certain type of elementary step and by taking into account the contribution of several configurational aspects (branching degree and number of CsC bonds of the positively charged carbon atom), a group of intrinsic kinetic parameters can be obtained. These intrinsic kinetic parameters depend only on the type of elementary reaction step and on the carbenium ions involved.12 After a brief review of the single-event concept, the present work presents the development of single-event rate equations and the computation of lumped reactivities using the “lateralchain method”20 without the generation of the whole reaction network. Until now, the single-event microkinetic concept has been applied to the hydrocracking of paraffins using as model compounds linear and branched paraffins of up to 18 carbon atoms.12-20 This work aims to apply the single-event microkinetic concept to the hydroisomerization and hydrocracking of
heavier paraffin feeds such as a C20-C30 Fischer-Tropsch wax fraction and a highly branched heavy paraffin (squalane). All kinetic data were obtained from the hydrocracking of n-hexadecane on an amorphous Pt/SiO2 · Al2O3 catalyst. 2. Kinetic Modeling 2.1. Single-Event Microkinetic Concept. The first kinetic model using the single-event kinetic concept was introduced by Baltanas and Froment12 for acid-catalyzed reactions (carbocation chemistry). The development of this fundamental microkinetic model is realized first by the generation of all possible elementary reaction steps of the paraffins on the acid sites. In this work, only paraffins (alkanes) are considered as reactive compounds. One elementary step is a single reaction on the acid sites starting from a carbenium ion to give another carbenium ion (in the case of isomerization). An example of a methyl-shift isomerization elementary step is given in Figure 1. Every elementary reaction step requires one invariant kinetic constant that does not depend on the feed molecules or the process configuration. The reaction network of elementary steps is large and complex even for short-chain normal paraffins (e.g., 383 steps for n-octane hydrocracking). However, this apparent complexity is reduced by applying the assumptions of the singleevent microkinetic concept that dramatically reduce the number of kinetic parameters describing the overall reaction system. The two main assumptions introduced by the single-event concept are the following:12,13 (1) The reactivity of the carbenium ions is treated locally. The single-event concept considers that the kinetic constant of the reaction of each carbenium ion on the acid sites of the catalyst depends only on the nature of the reaction (isomerization, β-scission) and the number of the CsC bonds of the positively charged carbon atom (primary, secondary, or tertiary character). (2) The number of single events for each elementary step is introduced to take into account the contribution of the structure of the carbenium ions to the kinetic constants. The fundamental, general character of an elementary rate constant is ensured only if it refers to a single event. Every elementary-step reaction could consist of several identical single events. To explain how one elementary step is decomposed into several single events, the example of Figure 1 is used. In the forward direction of the methyl-shift reaction between two secondary ions (Figure 1), two methyl groups are candidates
3286 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009
for the shift. In the reverse direction of the reaction, only one methyl group is a candidate. The numbers of single events are different for the two directions. This can lead to the conclusion that the rate constants of the forward and reverse reactions of the methyl shift are different and that they are different multiples of the single-event rate constants. Moreover, different values of the rate constants of each elementary step would be expected depending on the identity of the two secondary carbenium ions in which methyl shift is occurring. For the example of Figure 1, the number of single events for the forward direction is twice the number of single events for the reverse direction. The rate constant of an elementary step, k, can be written as the product of a single-event rate coefficient, k˜, and the number of single events, ne12,13 k ) nek˜
(1)
The number of single events, ne, involved in an elementary step is related to the symmetry changes corresponding to the formation of the activated complex from the reactant carbenium ion. That number can be calculated from the symmetry numbers of the reactants, σr, and the activated complex, σq ne )
σr σq
(2)
The parameter k˜ is assumed to be identical for the same reaction type, involving reactants and products with the same ion nature (secondary and tertiary). Moreover, this parameter does not depend on the number of carbon atoms in the ions. 2.2. Further Reduction of the Number of Rate ParameterssThermodynamic Coherence. A number of assumptions considering the nature of the reaction steps occurring during paraffin hydrocracking can reduce the number of acidphase intrinsic kinetic parameters.13 These assumption are as follows: 1. Only secondary and tertiary carbenium ions are considered in the reaction scheme. Primary carbenium ions are neglected because of their instability. 2. The single-event kinetic parameters for β-scission cracking depend only on the types of initial and final carbenium ions and not on the olefins formed. 3. Group-shift isomerizations (hydride, methyl, and ethyl shifts) are considered to be very fast in comparison to protonated-cyclopropane- (pcp-) type isomerizations, and they are assumed to be at equilibrium. Only the pcp-type isomerizations are considered. 4. Protonation and deprotonation steps on the acid sites are considered to be at equilibrium. 5. The single-event kinetic parameter of protonation (adsorption) depends only on the type of carbenium ion produced and not on the olefin. Thermodynamic considerations allow for a reduction of the numbers of parameters for adsorptions and for reactions.12-14 As for the single-event kinetic parameter for deprotonation (desorption), it depends on the type of the carbenium ion and on the olefin. The adsorption equilibrium constant can be expressed with reference to an olefin chosen in the homologous series (Oref) k˜pr(m) k˜dep(m, Oij)
)
k˜pr(m)
1 eq k˜dep(m, Oref) K˜isom [Oref(nc) S Oij]
(3)
By assuming that the single-event kinetic parameter of deprotonation of the reference olefin is carbon-number-
independent, the corresponding equilibrium constant for adsorption does not depend on the chain length of the reference olefin.13 In the same way, the equilibrium constants of the elementary steps can be expressed for the case of pcp isomerization reactions, thus further reducing the number of kinetic parameters k˜isom(s, t) k˜dep[s, Oref(nc)] k˜pr(t) ) k˜isom(t, s) k˜dep[t, Oref(nc)] k˜pr(s)
(4)
From the above reductions, only the secondary-secondary, secondary-tertiary, and tertiary-tertiary kinetic constant have to be estimated. The tertiary-secondary parameter is calculated by a later equation from the secondary-tertiary parameter. 2.3. Rate Equations. The kinetic pathways between paraffins involve hydrogenation/dehydrogenation on the metal phase, protonation/deprotonation on the acid sites and then the reactions of isomerization and cracking on the acid phase. According to the assumptions concerning the ideal hydrocracking of paraffins,6,13 (1) the hydrogenation/dehydrogenation reactions are considered to be at equilibrium, and only the acid reaction steps are ratedetermining, and (2) because the olefins and ion intermediates are unmeasurable and are present in very small quantities compared to the saturated species (paraffins), the quasi-steadystate assumption is reasonable. These assumptions lead to the following equation for the net rate of formation of each paraffin RPi )
∑ ∑ ∑ ne k˜ (m , u )[R ] + ∑ { ∑ ∑ ne k˜ (m , u )[R ] + ∑ ∑ ne k˜ (m , u )[R ] ∑ ∑ ne k˜ (m , u )[R ] ∑ ∑ ne k˜ (m , u )[R +
cr cr
j
q
qr
uV
qr
r
+
k
u
V
isom isom
uV
ik
uV
+
q
cr cr
qr
ik
qr
cr cr
ik
uV
ik
r
+
q
r
u
V
isom isom
ik
uV
+
ik
}
]
(5)
The rate expression in eq 5 contains only the concentration of carbenium ions, which must be estimated. The equilibrium assumption for protonation/deprotonation on the acid sites can directly provide the concentration of carbenium ions on the catalytic surface CRadsik+ )
kpr (m)COL ijCHads+ kdep
(6)
or eq (Oij S Oref(nc)) CRadsik+ ) K˜isom
nepr k˜pr (m)COL ijCHads+ nedep k˜dep
(7)
In the case of a reaction in the liquid phase (three-phase system), where the catalyst pellets are considered to be completely wetted, the concentration of olefins is calculated by the dehydrogenation/hydrogenation equilibrium constant in the liquid phase eq,l KDH ij
)
COL ijCHL 2 CPLi
(8)
Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3287
All experiments were conducted on a macroporous Pt/ SiO2 · Al2O3 amorphous catalyst (i.e., not a zeolitic catalyst), so that no external or internal limitations take place; thus, the paraffin concentration in the pores can be considered to be equal to that of the bulk liquid phase. For the sake of simplicity, the interaction of the reactant with the catalyst surface is modeled only through the protonation/deprotonation reactions, which are then analoguous to the adsorption/desorption steps in LangmuirHinshelwood heterogeneous catalysis modeling. The concentration of free acid sites on the catalyst can be estimated from the total acid site balance Ct ) CHads+ +
∑ ∑C i
k
ads Rik+
(9)
By solving the above system of equations, the concentration of carbenium ions on the catalytic surface can be estimated as CRadsik+ )
[
eq,ads,l (Oij S Oref) CtK˜isom
1+
∑ ikr
nepr k˜pr eq,l (m, Oref)KDH CL ijads Pi nedep k˜dep
]
CPLi k˜ nepr eq,l eq,l ˜Kisom(Oij S Oref) pr (m, Oref)KDH CHL 2 ij L ˜kdep nedep C H2
(10)
The above concentration can be substituted into eq 5 for the net rate formation of a paraffin. If a simple pcp isomerization reaction between two ions of types m and u is considered, the net rate of this elementary step is expressed by the single-event kinetic concept as pcp ) nek˜pcp(m, u)CRadsik+ R(m,u)
(11)
The rate equation can be written as pcp R(m,u) ) eq,l (Oij S Oref) CtK˜isom
[
1+
∑ ikr
nepr k˜pr eq,l ne (m, Oref)KDH k˜ (m, u)CPLi ijads pcp nedep k˜dep
]
CPLi k˜pr nepr eq,l eq,l K˜isom(Oij S Oref) (m, Oref)KDH CHL 2 ij L nedep k˜dep C H2
(12)
This rate expression has the form of Langmuir-type kinetics. All equilibrium constants and concentrations in rate equation 12 are expressed for the liquid phase, for a three-phase system with a completely wetted catalyst. As all equilibrium constants are calculated using the Benson25 contribution method in an ideal-gas phase, it would be convenient to rewrite rate equation 12 by using the gas phase as a reference. For this reason, the liquid concentrations and the equilibrium constants are estimated from partial pressures. By assuming the existence of a continuous thermodynamic equilibrium between the gas and the liquid phase inside the reactor, the Henry partition coefficient can be used to relate liquid concentrations to partial pressures Hi )
Pi Cli
(13)
The substitution of expression 13 into eq 12 provides a rate equation (eq 14) with the gas phase as a reference
pcp R(m,u)
)
eq,g (Oij S Oref) CtK˜isom
[
1+
∑ ne
nepr
nepr k˜pr eq,g ne (m, Oref)KDH k˜ (m, u) ijads pcp nedep k˜dep
eq,g K˜isom (Oij S Oref)
dep
ikr
]
PPi
PPi HOref k˜pr eq,g PH2 (m, Oref)KDH ij PH2HOref k˜dep (14)
2.4. Lumped Reactivities. Up to now, the developed singleevent microkinetic model considers the reactivities of all paraffins at the molecular level. Because the reaction network describes all possible elementary steps, the number of species thus obtained is extremely large (several millions of species for a 30-carbon-atom feed). It is obvious that a lumping approach is inevitable to enable a tractable output to be obtained. For this reason, a late, a posteriori, lumping approach is adopted for the molecules involved. The lumps are chosen in terms of present-day common analytical capabilities: in this work, only gas-phase chromatography (GC) was used for analysis. The full detail of a paraffin mixture is available only up to 8 carbon atoms. From 9 to 33 carbon atoms, the details of the analysis are limited to normal (unbranched) and single- and multibranched paraffins because of peak overlapping among isomers. However, promising techniques as GC-2D (two-dimensional GC, GC × GC) or GC-MS (gas chromatography-mass spectrometry) could be used to improve analysis, especially of multibranched species. A second important aspect of the lumping strategy is the preservation of the detail of the initial, molecular reaction network. Rigorous a posteriori lumping can be done if species are at thermodynamic equilibrium. According to several observations14,15 concerning the hydrocracking of paraffins, all isomers having the same degree of branching are at thermodynamic equilibrium. This equilibrium is established because all group-shift isomerization reactions (hydride, methyl, and ethyl shifts) between carbocations are faster than pcp isomerization and cracking reactions.7,20 As a result, all paraffins having the same number of carbon atoms and the same degree of branching are lumped together. This lumping strategy permits the development of a lumped single-event microkinetic model without the loss of any detail on the initial molecular reaction network. The kinetics between two lumps takes into account the sum of the individual kinetics of all species of each lump. From a molecular-level single-event microkinetic model described by rate equation 14, the new lumped rate equation 15 is given for the pcp isomerization between two lumps Li and Lj ) RLpcp,g ifLj
[
k(LifLj) 1+
∑ ne
nepr
ikr
PLi HOref
- k(LjfLi)
eq,g K˜isom (Oij S Oref)
dep
PLj HOref
]
PPi k˜pr eq,g (m, Oref)KDH PH2 ijads P H ˜kdep H2 Oref (15)
with (LifLj) k(LifLj) ) 98 CtLCisom,(m,u) (m, u ∈ Li f Lj)
k˜pr (m)k˜isom(m, u) k˜dep (16)
where LC is the lumping coefficient for the pcp isomerization between all ions of types m and u for the two lumps Li and Lj
3288 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 Table 1. Parameter Estimation for the Fundamental Rate Constants at 340 °C
(LifLj) eq,g LCisom(m,u) ) 98 K˜isom (Oijads S Li f Lj
eq,g Oref(ads))CtKDH ijads
nepr isom ne y (17) nedep (m,u) I
The molar gas fraction of each paraffin, yi, of the initial lump Li is calculated from the definition of the equilibrium constant
[
]
[ [
∆Gf(Pi) ∆Gf(Pi) exp RT RT yi ) ) ∆Gf(Pj) ∆Gf(Li) exp exp RT RT P ∈{L } exp -
∑
j
i
[
]
] ]
(18)
Each lumping coefficient (eq 17) can be rewritten in a factorized way by substituting the energy definition of all equilibrium constants, to obtain L1fL2 LCisom (m, u) ) ∆G*(Oref) + ∆G(H2) - ∆G(L1) 1 exp 98 isom RT isom(m, u) σq
[
]{
L1 f L2
}
(19) For cracking reactions, we have
[
) 1+ RLcr,g ifLj+L3
k(LifLj+Lk) nepr
∑ ne ikr
PLi
rate constant
value
interval of confidence (95%)
l ˜l (k˜pr /kdepr)(s) l ˜l (k˜pr /kdepr)(t)
2.736 4.205 7.41 E-03 3.452 E-05 8.345 E-06 1.273 E-04 2.466 2.867 1334
(0.193 (0.314 (1.05E-04 (4.5E-07 (1.1E-06 (4.8E-05 (0.712 (0.226 (12
k˜pcp(s,s) k˜pcp(s,t) k˜pcp(t,t) k˜cr(s,s) k˜cr(s,t) k˜cr(t,s) k˜cr(t,t)
The lateral-chain method is based on the group decomposition of Benson.25 Each activated complex corresponding to a cracking reaction of an element of lump L1 into an element of lump L2 and an element of lump L3 is decomposed into three parts: one activated zone (CA) that presents a limited number of carbon atoms that rearrange to give the new bonds and two lateral chains (A and B) that are directly connected to the activated zone. The description of the activated complex decomposition is given in Figure 2. After cracking, lateral chain A will become one element of lump L2, and lateral chain B will become an element of lump L3. The sum of the inverse of the symmetry numbers of the activated complexes is calculated by taking into account the symmetry number of each part (activated zones and lateral chains) and using the relation
HOref
eq,g K˜isom (Oij S Oref)
dep
∑
k˜pr P H2 k˜dep
σq∈R(L1,L2,L3)
PPi PH2HOref ∆G*(Oref) + ∆G(H2) - ∆G(L1) L1fL2+Lk LCcr (m, u) ) exp RT 1 98 (20) σ cr(m, u) q eq,g (m, Oref)KDH ijads
[
]
1 ) σq
∑
(A,ZA,B)∈CAC(R)
1 σAσCAσB
(21)
This can be rewritten as
∑
1 ) σ σ ∈R(L ,L ,L ) q q
1
2
3
∑
1 σ ZA∈CAC(R) CA
(
∑
A(ncA,nbA
∑
1 σ ) A B(nc
B,nbB
1 σ ) B
{L f L + L } i
j
k
The lumping coefficients for the cracking reactions are similar to those for the isomerization reactions. The calculation of the lumping coefficients (eq 19) is realized by lateral-chain method developed at IFP by Vale´ry and co-workers.20,21 In the following, we explain the lateral-chain method for cracking reactions for which the recursive reactions are less complex than for isomerization. For further details on isomerization, refer to Vale´ry.20 The major advantage of this method is that it does not imply the generation of the whole reaction network and it permits the rapid calculation of any lumping coefficient without any limitation in terms of a maximum number of carbon atoms or a maximum degree of branching. We explain here the computation of 98
{L fcr(m,L u)+ L } i
j
1 σq
[
where CA is a pattern of activated complex with ncCA carbon atoms and nbCA branches, A belongs to the class of lateral chains with ncA carbon atoms and nbA branches that gives an element of lump L2, and B belongs to the class of lateral chains with ncB carbon atoms and nbB branches that gives an element of lump L3. They satisfy the constraints ncσq ) ncCA + ncA + ncB nbσq ) nbCA + nbA + nbB
]
∆Gf(Li) RT is also be computed by the lateral-chain decomposition method.
(23)
Let us define U(np, nc, nb) ) SLPC(nc, nb) )
k
The contribution of the Gibbs energy of the lump, namely exp -
)
(22)
∑
1 σ A(np,nc,nb) A
∑ U(np, nc, nb) ) ∑ np
A(nc,nb)
1 σA
(24)
where np is the length of the main chain of lateral chain A. U can be computed recursively through the equation
Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3289
Us(np, nc, nb) ) Us(np - 1, nc - 1, nb)
1 +Us(np σsCH2s
1 +Us(np - 1, nc - 3, nb σsCHMes 1 1 +Us(np - 1, nc - 3, nb - 2) +Us(np 2) σsCHEts σsCMeMes 1 +Us(np - 1, nc - 5, nb 1, nc - 4, nb - 2) σsCEtMes 1 2) (25) σsCEtEts 1, nc - 2, nb - 1)
and then the sum of the inverse of the symmetry numbers (eq 22) can be computed. Other properties of the lateral chains can be computed easily by the group contribution method by replacing the inverse of the symmetry numbers in eq 25 by the group contributions for the property of interest. For the lumping coefficients, this method is strictly equivalent to that developped by Martens and Marin.16 For more details on these calculations, refer to Vale´ry20 and Martens and Marin.16
Figure 3. Experimental isomerization-cracking selectivity toward total n-hexadecane conversion: (- - -) ideal isomerization yield, (9) experimental isomerization yield, (2) and experimental cracking yield.
3. Experimental Section The reaction experiments were performed in a tubular upflow fixed-bed pilot reactor (1.2-m length, 1.6-cm inner diameter) equipped with a series of thermocouples placed in a thermowell on the axis of the reactor’s tube. The catalyst used was an industrial macroporous and amorphous Pt/SiO2 · Al2O3. The catalyst particles had the form of extruded cylinders (0.8-mm diameter and 3-mm length). Three different feedstocks were used: pure n-hexadecane (99% purity, Haltermann Chemicals), a mixture of heavy linear paraffins (Fischer-Tropsch wax fraction presenting a C20-C30 paraffin distribution), and a pure heavy ramified paraffin (squalane, 99% purity, Haltermann Chemicals). All experiments were conducted under the same operating conditions, assuring the presence of a three-phase system for all feedstocks. The tests were performed at the same temperature (340 °C) and pressure (47.5 bar), with a constant ratio of hydrogen to hydrocarbon equal to 200 std L/L (volume). The liquid volume hourly space velocity (LSHV) was varied in the range of 0.25-4.0 h-1. Liquid and gas reaction products were analyzed by gas chromatography. According to the analytical details, there were 35 available analyses for the n-hexadecane effluent (normal, single-, and di-/multiparaffins) for each run. 4. Reactor Model and Simulations The reactor was assumed to be fully isothermal without any pressure drop. For the operating conditions of the tests, no masstransfer limitations were considered between the gas-liquid phase and the liquid-solid interface. The liquid and gas phases inside the reactor were considered to be in thermodynamic equilibrium. The composition of each phase was calculated by means of a thermodynamic model based on the Grayson-Streed method, with pure-compound data covering all possible lumps inside the reaction network (267 lumps). The continuity equations for the liquid-phase hydrocracking for each lump i can be written as dFi ) Ri dW
(26)
The set of ordinary differential equations was solved by the LSODE package.22
Figure 4. Experimental isomerization-cracking selectivity toward total mean conversion of wax C20-C30: (9) experimental isomerization yield and (2) experimental cracking yield.
For parameter estimation, two optimizing routines were used: one single-response Levenberg-Marquardt algorithm23 (DN2FB, available at http://netlib.sandia.gov/port/) and a version of the simulated annealing algorithm.24 5. Results 5.1. Experimental Results. From the experimental results obtained from n-hexadecane and from the C20-C30 mixture (wax), it was concluded that, within the ranges of operating conditions studied, ideal hydrocracking behavior was established. This ideal hydrocracking behavior was verified through an isomerization selectivity analysis and comparison of the experimental curves with data for ideal hydrocracking available in the literature. Figures 3 and 4 show the experimental isomerization-cracking selectivity curves for the hydrocracking of n-hexadecane and C20-C30 wax, respectively. As shown in Figure 3, the actual experimental curve for the isomerization yield of n-hexadecane is very close to the dotted curve corresponding to ideal hydrocracking conditions. The dotted curve was determined using experimental data available in the literature for ideal n-paraffin hydrocracking.15,17,19 According to several experimental isomerization selectivity curves reported in the literature,15-21 when ideal hydrocracking conditions are established, the isomerization yield presents its maximum values, and a unique function between the total conversion and the isomerization-cracking yields exists. The forms of the unique isomerization-cracking curves toward total conversion under ideal conditions are reported to be quite similar for a great number of paraffins with different chain lengths.17 From Figure 4, it can be seen that the isomerization selectivity curve is very similar to that obtained from n-hexadecane (Figure
3290 Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009
Figure 5. Calculated (lines) vs experimental (points) values for (() conversion, (9) isomerization, and (2) cracking. (Left) Selectivity toward total n-hexadecane conversion; (right) parity diagram for total conversion, isomerization, and cracking yield for the liquid-phase hydrocracking of n-hexadecane.
Figure 6. Calculated (lines) vs experimental (points) values for (() conversion, (9) isomerization, and (2) cracking. (Left) Selectivity toward total mean conversion of the waxes; (right) parity diagram for total conversion, isomerization, and cracking yield for the liquid-phase hydrocracking of C20-C30 wax.
Figure 7. Calculated (continuous lines) vs experimental (dashed lines) true-boiling-point distillation curves for different residence times: (top left) 0.25 h, (top right) 0.4 h, (bottom left) 0.5 h, and (bottom right) 1 h. Squalane hydrocracking at 340 °C.
3), especially for conversions below 80%. The high isomerization yields obtained from the hydrocracking of the C20-C30 wax under the same operating conditions provides assurance that, even for a heavier feedstock, the ideal behavior is preserved.
The same trends were found for squalane hydrocracking. Because of the nature of its cracked products (highly ramified isomers), the detailed chromatographic analysis was not very accurate, even for the determination of the squalane content. For this reason, all comparisons of the squalane conversion
Ind. Eng. Chem. Res., Vol. 48, No. 7, 2009 3291
reported herein are based on true boiling point distillation curves of the products. 5.2. SimulationssOptimizations. From the available experimental data on the liquid-phase hydrocracking of nhexadecane, rate constants were estimated at 340 °C. In Table 1 are listed the estimates for the fundamental rate constants (acid phase), in units of moles per gram per hour [mol/(g h)]. The value of the kinetic parameter for cracking seems to be reasonable.7 The low values of k˜pcp(s,t) and k˜pcp(t,t) compared to k˜pcp(s,s) are more surprising. k˜pcp(s,s) is certainly fitted accurately, because protonated-cyclopropane branching is the only way to convert normal paraffins. k˜pcp(s,t) and k˜pcp(t,t) apply mainly to reactions between multibranched species that are lumped together, are present in low quantities, and disappear quickly because of the fast (t,t) cracking. Thus, some improvement must be made in the fitting of these parameters in the future. A comparison between the experimental and calculated yields for n-hexadecane hydrocracking is shown in Figure 5a. The agreement between the calculated and experimental conversion and yields is satisfactory. 5.3. Extrapolation to Heavier FeedssValidation of the Model. The model validation was performed by simulating the hydrocracking of a C20-C30 wax mixture and a feed of pure squalane using the values of the kinetic parameters obtained using n-hexadecane experimental data. The predictions of the model were compared to the available experimental results. Figure 6 shows a comparison between the calculated and experimental conversions and yields for the hydrocracking of a C20-C30 wax mixture. The model seems to be able to predict the reactivity of a heavier linear paraffin feed satisfactorily, presenting differences of less than 10%. For the squalane feed, the analytical detail is not sufficient because of the peak overlapping of multibranched C30 species. Thus, a comparison between the model and experiments was done through macroscopic analysis. The simulation of the hydrocracking of squalane can provide the true-boiling-point distillation curves for the output products. The determination of this distillation curve by the simulation program was achieved by using the lump boiling point data and the calculated output molar flows. A distillation curve can provide direct information about the conversion yield of the feed (squalane) and the distribution of the cracked products. As accurate experimental distillation curves exist for all of the products from squalane hydrocracking, a comparison with those obtained from the simulation was performed. Figure 7 illustrates the experimental and calculated true-boiling-point distillation curves for different residence times. The model seems to be able to predict satisfactorily the reactivity of a heavier highly branched paraffin feed such as squalane. However, the model predictions are less accurate than in the case of C20-C30 wax hydrocracking. From Figure 7, it can be observed that, especially for the smaller residence times, the model overestimates the conversion of squalane and the yield of cracked products (about 15% overestimation). According to these results, it appears that the model can be fitted using a model feed (n-hexadecane, for example) and used for prediction on heavier, more complex feeds (Fischer-Tropsch effluent, for example). 6. Conclusions The single-event microkinetic concept is a powerful tool for modeling acid-catalyzed reactions. The single-event approach allows for the development of a detailed kinetic model for
paraffin hydrocracking and hydroisomerization, leading to invariant rate constants that do not depend on the feedstock composition or the process configuration. Lumps are introduced a posteriori only to account for the limitations of present-day analytical tools. Lumping coefficients can be rapidly and rigorously calculated by the computer-based lateral-chain method without the generation of the whole reaction network. A complete set of only nine rate constants for paraffin hydrocracking and hydroisomerization was obtained from an experimental program involving liquid-phase pure n-hexadecane hydrocracking. This set of parameters leads to a satisfactory fit of the experimental data for the hydrocracking of n-hexadecane. The extrapolation of the model to heavier paraffins such as a C20-C30 wax mixture and pure squalane leads to promising results. Notation Symbols C ) concentration Fi ) molar flow rate of paraffin i Hi ) Henry’s coefficient of paraffin i K ) equilibrium constant K˜ ) intrinsic equilibrium constant k ) elementary-step rate coefficient k˜ ) single-event rate coefficient L ) lump LC ) lumping coefficient m ) identification of ions nc ) number of carbon atoms ne ) number of single events P ) pressure Pi ) paraffin i R ) rate of formation s,t ) type of the reacting ions σ ) symmetry number W ) catalyst weight Subscripts cr ) cracking dep ) deprotonation H+ ) protonated acid site isom ) isomerization Oij ) olefin j issued from olefin i Oref ) homologous series of reference olefin pcp ) protonated-cyclopropane branching Pi ) paraffin i pr ) protonation Rik+ ) ion k issued from paraffin i r ) reactant q ) activated complex Superscripts ads ) adsorbed eq ) equilibrium g ) gas l ) liquid pcp ) protonated-cyclopropane branching
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ReceiVed for reView June 23, 2008 ReVised manuscript receiVed January 23, 2009 Accepted January 24, 2009 IE800974Q
