Ind. Eng. Chem. Res. 2009, 48, 1203–1207
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Modeling Ideal and Nonideal Hydrocracking of Paraffins Using the Single-Event Lumped Parameter Hybrid (SELPH) Model Juan C. Chavarrı´a-Herna´ndez† and Jorge Ramı´rez*,†,‡ UNICAT, Departamento de Ingenierı´a Quı´mica, Facultad de Quı´mica, UNAM Cd. UniVersitaria, D.F., Me´xico, and Instituto Mexicano del Petro´leo, Eje Central La´zaro Ca´rdenas 152, D.F., 07730, Me´xico
The SELPH (single-event lumped parameter hybrid) model previously developed was used to simulate hydroconversion of n-octane and n-undecane over a wide range of operating conditions, in order to cover both ideal and nonideal hydrocracking behavior. The fundamental kinetic parameters used in the simulations were estimated previously from n-octane hydroconversion experimental data. Results of simulations demonstrate that predictions of the model for the effect of (i) operating pressure, (ii) reaction temperature, (iii) chain length of feed hydrocarbon, and (iv) hydrogen-to-hydrocarbon inlet molar ratio on the ideal (and nonideal) character of hydrocracking are in complete agreement with the general trends reported in the literature. The model allowed identification of intervals of the operating variables in which product selectivities are a unique function of total conversion, i.e., an ideal hydrocracking region, while, in the region of nonideal hydrocracking, the model accurately describes the changes of product selectivities as a function of operating conditions. Introduction Hydrocracking is a key process encountered in the oil refinery industry to convert relatively heavy oil feedstocks into lighter more valuable transportation fuels and lubricating oils.1 Hydrocracking is commonly carried out over bifunctional metal/ zeolite catalysts in the presence of high partial pressures of hydrogen. According to the widely accepted bifunctional mechanism,2,3 hydrocracking starts with adsorption of saturated hydrocarbons in the micropores of the zeolite, followed by dehydrogenation on the metal sites to produce unsaturated species. The olefins formed migrate to the acid sites of the catalyst, where they are protonated to produce carbenium ions, which in turn undergo acid-catalyzed rearrangements and cracking reactions. After deprotonation of the new carbenium ions and the later hydrogenation of the olefins on metal sites, lighter saturated products with a higher degree of branching are desorbed from the surface of the catalyst. Hydrocracking allows isomerizing n-alkanes into monobranched and multibranched alkanes to a high extent before the cracking reactions become important. If the aim of the process is focused on the production of feed isomers rather than on cracking, the process is referred to as hydroisomerization.4 The extent of the isomer formation in hydrocracking is determined by a number of variables, among which the most important is the acid/metal balance of the catalyst.5,6 The higher the (de)hydrogenation activity of the metal compared to the acid strength of the catalyst, the higher the isomer production. If the hydrogenating component of the catalyst is strong enough, quasiequilibrium of the (de)-hydrogenation reactions is reached, and the acid-catalyzed reactions are the rate-limiting steps.7 These circumstances correspond to the so-called ideal hydrocracking conditions, which is characterized by an apparent independence of product distributions with regard to the operating conditions.8 On the other hand, if (de)-hydrogenation is not at quasiequilibrium, these reactions could be the rate-determining steps. Under these conditions, the formation of feed isomers decreases * To whom correspondence should be addressed. E-mail: jrs@ servidor.unam.mx. † UNAM. ‡ Instituto Mexicano del Petro´leo.
since cracking reactions become important even at very low conversions. Nonideal hydrocracking can occur if the metal component of the catalyst is a weak hydrogenating function,9,10 but there are some other variables favoring nonideal behavior. It has been found that lower pressures, higher temperatures, longer chain length of feed hydrocarbons, and very high hydrogen to hydrocarbon inlet molar ratios enhance nonideal hydrocracking.7,11 In examining the ideal character of hydrocracking, a plot of conversion toward feed isomers against total conversion (see Figure 3 as an example) is quite useful.7 In such plots, the upper curve corresponds to ideal hydrocracking in which isomerization is maximized, while the maximum of the curves lowers down as deviation from ideal hydrocracking behavior becomes higher. Modeling the hydrocracking process is not an easy task due to the enormous number of products and the complexity of reaction schemes even if the feed is single paraffin. By the end of the last century, Froment and co-workers12-14 developed the single-event methodology to describe hydrocracking in terms of elementary isomerization and cracking reaction steps, by assuming quasi-equilibration of the (de)-hydrogenation reactions (except in recent work).15 The SELPH kinetic model, whose simulation results are discussed in this paper, is based upon the single-event methodology, but without assuming (de)-hydrogenation at quasi-equilibrium. In this way, the model is capable of describing ideal and nonideal hydrocracking behavior. In contrast to the fundamental single-event rate coefficients used to describe the acid-catalyzed reactions, (de)-hydrogenation reactions are modeled using lumped rate coefficients. The combination of the two approaches results in a hybrid model that takes its name from the nature of the kinetic parameters involved: single-event lumped parameter hybrid (SELPH) model.9 SELPH Model and Kinetic Rate Coefficients The development of the kinetic equations of the SELPH model is reported in a previous work,16 in which the values of the single event and lumped kinetic parameters were estimated from n-octane experiments, under ideal and nonideal hydrocracking conditions over a 0.25 wt % Pt/USY zeolite. The values
10.1021/ie800639n CCC: $40.75 2009 American Chemical Society Published on Web 12/12/2008
1204 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 1. Kinetic Rate Coefficients15 Used in the Simulations of n-C8 and n-C11 Hydroconversion single-event parametera
A0, h-1a
Ea, kJ mol-1a
* kPCP (s;s) * kPCP (s;t) * kPCP (t;t) * kCr (s;s) * kCr (s;t) * kCr (t;s)
3.45 × 1014 1.77 × 1015 5.91 × 1012 4.73 × 1016 1.08 × 1012 1.73 × 1021
60.8 71.6 51.7 82.6 25.4 92.0
lumped parametera
A0, h-1a
Ea, kJ mol-1a
* kdh-P11 * kdh-P8 * kdh-P7 * kdh-P6
8.3 × 1017 5.21 × 1016 2.8 × 1013 3.1 × 108
31.2 30.2 25.5 26.3
K0 (MPa-1)
physisorption parameter
1.0 × 10 6.24 × 10-2
KL_C11 KL_C8 a
∆Hads, kJ mol-1
-1
Figure 1. Simulated isomerization conversion of n-octane over Pt/US-Y as a function of total conversion under ideal hydrocracking conditions at 453 K (circles), 473 K (triangles), and 493 K (squares), and at 2.0 MPa (white symbols), and 5 MPa (shaded symbols).
79.9 79.6
Composite parameters.
Table 2. Ranges of P, T, and (H2/HC)° Used for the Simulations single feed
P, MPa
T, K
(H2/HC)°, mol/mol
n-octane n-undecane
0.2-8 0.3-10
433-598 423-573
0.3-100 0.5-100
of the kinetic rate constants as well as the adsorption parameters used in the simulations are shown in Table 1. Due to the fundamental nature of the single-event kinetic coefficients,17 they were assumed to be independent of the feed paraffin, and the estimates from n-octane were used in the simulations for n-undecane hydroconversion. Next, some of the SELPH-model kinetic equations that will be used in the explanations of the following section are rewritten.16 The (de)-hydrogenation reactions were modeled according to eq 1, in which cPi and cOj are the concentrations of pseudo-paraffins and pseudo-olefins respectively; pH2 is the partial pressure of hydrogen; K′dh,Pi is the equilibrium dehydrogenation constant, and k*dh,Pi is a composite (de)-hydrogenation rate coefficient given by eq 2. In eq 2 ctM is the total metal sites concentration; cMOj is the pseudo-olefin concentration on metal sites, while KMOj and KMPi are the adsorption constants for pseudo-olefins and pseudo-paraffins over metal sites.
(
* rdh,Pi ) -kdh,P cPi i
* kdh,P ) i
cOj· pH2 K′ dh,Pi
)
kdh,Pi · K PMi · cM t 1+
∑ i
K PMi · cPMi +
∑ j
K OMj · cOMj
(1)
(2)
The general expression for the rate of isomerization and cracking steps is written in terms of the fundamental parameters of the single-event theory12 according to eq 3, in which k′ is the rate constant for a single isomerization or cracking event, m and n are the types (secondary or tertiary) of the reactant and product carbenium ions, ne is the number of single events of the elementary step, and cIi+ is the adsorbed concentration of the reacting carbenium ion: rIj+ ) k′(m;n) · ne · cIi+
(3)
The concentration of individual carbenium ions appearing in eq 3 can be expressed (without assuming (de)-hydrogenation at quasi-equilibrium) according to eq 4, in which cOk is the adsorbed concentration of the olefins with skeletal structure analogous to that of the carbenium ion related; cH+ is the free
Figure 2. Simulated isomerization conversion of n-undecane over Pt/US-Y as a function of total conversion under ideal hydrocracking conditions at 453 K (circles), 473 K (triangles), and 493 K (squares), and at 2.5 MPa (white symbols), and 5 MPa (shaded symbols).
acid sites concentration, while kPr(m) and kDe(m;Ok) are the rate constants for elementary protonation and deprotonation steps, respectively. cIi+ ) KPr ⁄ De,k · cOk · cH+ )
kPr(m) ·c ·c kDe(m;Ok ) Ok H+
(4)
Results of Simulations Hydroconversion simulations for n-octane and n-undecane were performed separately under the range of operating conditions summarized in Table 2. For both paraffins the intervals of the variables allowed the prediction of transition from ideal to nonideal hydrocracking or vice versa. To analyze the effect of the manipulated variables on the ideal character of hydrocracking, a series of isomerization conversion versus total conversion plots were elaborated. In each plot one of the variables (P, T, or (H2/HC)°) was changed while the other two remained constant. The product distributions calculated with the model follow the general trends reported in the literature. Consider as an example the maximum conversion toward isomers of the feed paraffin calculated for n-octane and n-undecane under ideal hydrocracking conditions. The values calculated with the SELPH model for these maximums were 47% and 34%, respectively, according to Figures 1 and 2. These percentages coincide surprisingly well with the reported ex-
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Figure 3. Simulated isomerization conversion of n-octane over Pt/US-Y as a function of total conversion at 493 K, (H2/HC)° ) 10, and at: 4 MPa ()), 1.7 MPa (s), and 0.6 MPa (- -).
Figure 5. Simulated adsorbed olefin concentrations as a function of total pressure for n-C11 hydroconversion over Pt/US-Y at 493 K, (H2/HC)° ) 10, and % conversion ) 10: n-C11 olefins ()), monobranched-C11 olefins (s), and multibranched-C11 olefins (- -).
Figure 4. Simulated isomerization conversion of n-undecane over Pt/US-Y as a function of total conversion at 493 K, (H2/HC)° ) 10, and at 4 MPa ()), 1.8 MPa (s), and 0.7 MPa (- -).
perimental values of 46%,18 40%,8 and 32%8 for n-octane, n-decane, and n-dodecane, respectively, under ideal hydrocracking conditions, and using a Pt/USY catalyst similar to the one used in the obtention of the experimental data16 for the estimation of the kinetic parameters used in this work. Ideal Hydrocracking Predictions. Simulations corresponding to high total pressures (above 1.8 MPa for n-C8 and 2.0 MPa for n-C11), low to medium temperatures (440-520 K for both reactants), and medium to high hydrogen to hydrocarbon molar ratios (above 2 for both reactants) gave the same product distribution as a function of conversion for each paraffin, according to ideal hydrocracking behavior. This is illustrated in the plots of Figures 1 and 2 for n-octane and n-undecane, respectively. Operating Pressure Effect. The effect of total pressure on the ideal character of hydrocracking is shown in Figures 3 and 4 for n-C8 and n-C11, respectively. Both plots show that, as total pressure decreases, a lower maximum in the curve is obtained, and higher deviations from ideal hydrocracking are observed. This effect can be explained in terms of adsorbed concentrations of olefins calculated with the model. As an example, Figure 5 shows the simulated concentrations of normal, monobranched, and multibranched olefins with 11 carbon atoms, as a function of total pressure at a conversion level of 10%. On increasing the total pressure, the concentration of branched olefins decreases progressively, while the concentration of normal olefins related to the feed paraffin increases, and this effect is more pronounced at pressures below 3 MPa, i.e., in the nonideal
Figure 6. Simulated adsorbed olefins concentrations as a function of conversion for n-C11 ideal hydroconversion over Pt/US-Y at 493 K, 3 MPa, and (H2/HC)° ) 10: n-C11 olefins ()), monobranched-C11 olefins (s), and multibranched-C11 olefins (- -).
hydrocracking region. As a consequence of the latter and according to eqs 3 and 4, at higher pressures the concentrations of branched carbenium ions directly related to branched olefins decreases too, while the concentrations of linear ions with the same skeletal structure of normal olefins increases. Since branched carbenium ions are responsible for the cracking steps and linear carbenium ions are more likely to undergo isomerization reactions, cracking (nonideal hydrocracking) is favored at lower pressures, while isomerization (ideal hydrocracking) is enhanced at higher pressures. Temperature Effect. By increasing the reaction temperature, the rate of (de)-hydrogenation reactions and the rate of carbenium ion reactions increases. However, the effect is more pronounced for the acid-catalyzed transformations, and particularly for the secondary-secondary and tertiary-secondary cracking steps, since the activation energy of these steps is the highest as can be appreciated in Table 1. An additional effect can be identified by considering that at higher temperatures the values of the equilibrium (de)hydrogenation constants appearing in eq 1 is higher too. It is clear that higher values of these constants favor olefins formation and hence the production of the carbenium ions with analogous skeletal structure. Figure 6 shows the evolution of pseudo-olefins concentrations as a function of conversion for ideal hydro-
1206 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009
Figure 7. Simulated isomerization conversion of n-octane over Pt/US-Y as a function of total conversion at 2.0 MPa, (H2/HC)° ) 10, and at 473 K ()), 543 K (s), and 573 K (- -).
Figure 9. Simulated isomerization conversion of n-C8 (two upper curves) and n-C11 (three lower curves) over Pt/US-Y as a function of total conversion at 5 MPa, 453 K and at (H2/C8)° ) 20 ()), (H2/C8)° ) 0.9 (s), (H2/C11)° ) 20 (- - -), (H2/C11)° ) 1.2 (- - -), and (H2/C11)° ) 0.8 (- - -). Table 3. Number of Elementary Reaction Steps for Hydroconversion of Normal Paraffins
Figure 8. Simulated isomerization conversion of n-undecane over Pt/US-Y as a function of total conversion at 2.2 MPa, (H2/HC)° ) 10, and at 473 K ()), 553 K (s), and 583 K (- -).
cracking of n-undecane. As can be seen in the figure, at conversions above 10%, concentrations of branched olefins are higher than those for normal olefins. Since (de)-protonation reactions are at quasi-equilibrium, formation of branched carbenium ions responsible for the cracking steps follows analogous concentration profiles. As a result, the higher production of olefins at higher temperatures causes an increase in the formation of branched carbenium ions at medium and high conversion levels, enhancing cracking reactions and hence nonideal hydrocracking behavior. Moreover, the comparative profiles for the olefin concentrations under nonideal hydrocracking conditions were found to be quite similar to those for ideal hydrocracking shown in Figure 6, with the difference that for nonideal hydrocracking the concentrations of branched olefins become important even at lower conversion levels. The combination of the described kinetic and thermodynamic effects is clear: higher temperatures favor nonideal hydrocracking behavior as can be corroborated in Figures 7 and 8 for the hydroconversion of n-C8 and n-C11, respectively. (H2/HC)° Effect. The effect of the hydrogen to hydrocarbon inlet molar ratio was observed only at low values of this variable. As (H2/HC)° increases, the availability of hydrogen rises, producing an increase of the hydrogenation reactions rates given by eq 1, thus enhancing ideal hydrocracking behavior. The negative effect reported by Thybaut et al.11 at very high values of (H2/HC)° was not observed in this analysis, since the adsorption of hydrocarbons on the active sites of the catalyst
feed
DH
PCP
Cr
PCP/DH
Cr/DH
Cr/PCP
n-C8 n-C9 n-C11 n-C14
58 114 384 1725
149 322 1177 5424
15 36 138 629
2.57 2.82 3.07 3.14
0.26 0.32 0.36 0.37
0.10 0.11 0.12 0.12
was assumed negligible, i.e., the denominator of eq 2 was approximated to unity. Figure 9 shows the effect of (H2/HC)° on the ideal character of hydrocracking at low values of this variable. The simulation results show that above a value of (H2/ HC)° of ∼2 for the two feeds, i.e., n-C8 and n-C11, ideal hydrocracking conditions can be reached provided the temperature and pressure are chosen appropriately. Carbon Number Effect. The simulation results indicate that ideal hydrocracking is favored for lighter paraffins. It was found for example that for single n-octane and n-undecane feeds, with the same hydrogen-to-hydrocarbon inlet ratio and at the same temperature (100 mol/mol and 538 K, respectively), a pressure above 2 MPa is required for n-undecane to follow ideal hydrocracking behavior, while a value of 1.8 MPa is enough for the case of n-octane, indicating that higher pressures are required for longer paraffins to behave according to ideal hydrocracking. On the other hand, it was found that, at 5 MPa with a hydrogen-to-hydrocarbon inlet molar ratio of 100 for both reactants, deviations from ideal hydrocracking starts at a temperature of 520 K in the case of n-undecane, while at the same conditions n-octane hydrocracking follows ideal behavior, indicating that higher temperatures are required for lighter paraffins to behave according to nonideal hydrocracking. In addition, the results in Figures 1 and 2 indicate that hydroisomerization and hence ideal hydrocracking is favored for lighter paraffins since the maximum of isomerization formation for n-octane (47%) is greater than for n-undecane (34%) under ideal hydrocracking conditions. The effect of carbon number can be explained by making the following considerations: for longer chain paraffins the number of elementary reactions on acid sites increases faster than the number of elementary reactions on metal sites as shown in Table 3. As a consequence, the rates of isomerization and cracking reactions increase faster than the rate of (de)hydrogenation reactions for longer paraffins. Moreover, the ratio of the number of elementary cracking-to-PCP-isomerization steps is about 0.1 and slightly higher for longer paraffins.
Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1207
Additionally, adsorption parameters have higher values for paraffins with higher carbon number, and hence longer paraffins are more reactive than the lighter ones. The overall effect is that nonideal hydrocracking behavior is favored for paraffins with higher carbon number.
Acknowledgment We acknowledge financial support from the CONACyT (Me´xico)SECYT (Argentina) program. Ref: J110.470/2005. J.C.Ch. acknowledges the scholarship granted by CONACyT-Me´xico. Literature Cited
Conclusions The SELPH kinetic model, whose simulations results are discussed in this work, was the first single-event kinetic model explicitly developed for description of the nonideal hydrocracking behavior. The incorporation of the molecular approach for the acid-catalyzed reactions confers the kinetic model the advantages of (i) giving detailed information about the production of intermediate and observable species as reaction proceeds, and (ii) using fundamental and hence feed-independent kinetic coefficients, even though the confirmation of this statement requires additional work. The trends in the product distributions simulated for ideal and nonideal hydrocracking of n-octane and n-undecane are in complete agreement with experimental reports published in the open literature. Since the simulations for n-undecane were performed using the fundamental parameters estimated from n-octane experiments, the results constitute evidence supporting that single-event rate coefficients retain their fundamental character and independence of the feed paraffin, although the SELPH model combines fundamental rate constants with lumped rate coefficients for the (de)hydrogenation reactions. The results of the simulations and the product distribution trends encountered in the sensitivity analysis, as well as the fitting of the model to the experimental data used in the estimation of the parameters,16 demonstrate the capabilities of the SELPH model to describe with accuracy the effect that variations in (i) reaction temperature, (ii) operating pressure, (iii) chain length of feed hydrocarbon, and (iv) hydrogen-to-hydrocarbon inlet molar ratio have on the ideal and nonideal character of hydrocracking, and hence, on the resulting product selectivities. Moreover, the detailed information of the concentrations of intermediate species provided by the model can be used to analyze and better understand the effect caused by changes in the operating variables on the underlying molecular processes and on the observable macroscopic transformations. The simulation results are indicative of the feasibility of occurrence of nonideal hydrocracking, highlighting the importance of the development of models like the one presented here, that consider nonideal behavior in their kinetic equations, in order to achieve more accurate and realistic descriptions of nonideal hydrocracking processes. Even though the model was tested only for the hydroconversion of paraffins, it constitutes a powerful tool that can be refined and further developed to include other reactions in order to predict the behavior of complex industrial reaction systems.
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ReceiVed for reView April 20, 2008 ReVised manuscript receiVed October 20, 2008 Accepted October 21, 2008 IE800639N
