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Ind. Eng. Chem. Res. 2006, 45, 4554-4557
Network Generation of Oligomerization Reactions: Principles Denis Guillaume* Institut Franc¸ ais du Pe´ trole, BP 3, 69390 Vernaison, France
Oligomerization of light olefins produces gasoline or fuels. The kinetic network involves thousands of species and even more reactions. To develop a microkinetic model, the preliminary generation of a mechanism, as detailed as possible, is necessary. The classical single event network generation algorithm does not handle an exhaustive large oligomerization network. To be able to generate the network, qualitative a priori information on the kinetic rate scales are introduced. Principles of the new generation distinguish quasi-equilibrium reactions and rate determining steps (from a generation point of view). Each type of reaction is generated step by step. During the generation step of the equilibrium reactions, every possible reaction of this kind, initiated from the already generated species, is created, building sets of species that are linked by one or several reactions. During the generation step of the rate determining step reactions, the new species are linked by only one new reaction. This algorithm was only applied for the generation of alkylation and a cracking reaction and allowed in a few steps the generation of approximately 80 000 species. Introduction Refining processes generally involve complex feedstocks consisting of several hundreds or thousands of molecule species. However, a large number of the processes, catalytic reforming, isomerization, FCC, hydrocracking, ..., are acid catalyzed. The chemistry of carbenium ions is well-known1 and computer tools were developed to generate the reaction network and to model the kinetics of the whole network.2,3 The so-called “single events” theory allowed the description of very large networks with few parameters. For some processes (hydrocracking and reforming), lumped models are possible, which simplifies drastically the network generation. For hydrocracking reactions and with the assumptions of equilibrium for species with the same carbon atom numbers and same branching numbers, the generation of the network became even unnecessary and the kinetic model could be established directly.4,5 Oligomerization of light olefins is a process that converts light olefin into gasoline, kerosene, and fuel. Considering the experimental data, no single event lumped model by carbon number is possible because isomerization reactions are not at equilibrium. Thus, network generation is necessary. This network has to be limited because of the exponential growth of the network with the carbon number of the products. A limitation by the maximum carbon atom number of the products is insufficient for generating a network with classical tools due to computer limitations (storage size and efficiency of the algorithm). These tools had to be improved in order to take into account new typical species of the oligomerization reactions and in order to generate a representative network, tractable for building a kinetic model. Two kind of rules for generating limited complex network can be distinguished: species-based or reaction-based generation. The first are characterized by species considerations: what kind of species are allowed (size) or needed (key species)? Termination criteria based on the species rank6 or seeding with molecules7 also exist. The second type of rule is characterized by reaction considerations: which reactions are allowed? Criteria are based on * To whom correspondence should be addressed. E-mail:
[email protected]. Tel.: +33 4 78 02 26 67.
the reaction rate8 or “on the fly” sensitivity analysis.9 The solution proposed hereafter can be viewed as a combination of these two groups, while qualitative kinetic information is used by the modified algorithm for choosing the sequence of reactions and as a kind of rank-based criterion is used to choose how many sequences have to be generated. The generation principles explained further were developed for molecules with a maximum of 16 carbon atoms but can be easily extended to any carbon number. Chemistry Olefin oligomerization on acid catalysts is done via elementary steps involving carbenium ions.1 Olefins are protonated on the catalyst and form carbenium ions. These ions can isomerize to form new ions with the same carbon atom number, can alkylate to form new ions with a higher carbon atom number, or crack to form new olefins and new ions with a lower carbon atom number (Figure 1). Single event theory, developed for the modeling of kinetic modeling of refining processes,2,3 makes large use of computer tools for generating a detailed exhaustive network for hydrocracking, reforming, FCC, and isomerization processes. These tools are modified in order, first, to take into account the characteristic properties of alkylation reactions and species and, second, to generate the most representative and detailed network. Specifities of Alkylation Generation The computer code for the generation of complex networks that were developed in the framework of the single events theory is structured in several sections and libraries of procedures. The main section contains the algorithm that controls the generation of the species and which kinds of reactions are allowed. The other procedures are dedicated to the treatment of each species and reaction: e.g., computer description and coding of species and reactions and checking of the feasibility of a reaction. For hydrocracking and reforming, the procedures considered classically that the alkyl groups on the main chain of each molecule were only methyls or ethyls. Alkylation of olefins leads to more compact molecules with several other alkyl groups. It is obvious that alkyl groups such as tert-butyl, 2-methylpropyl, 1-methyl-
10.1021/ie0510019 CCC: $33.50 © 2006 American Chemical Society Published on Web 05/19/2006
Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4555 Table 1. Additional Alkyl Patterns for Oligomerization up to C16a
Figure 1. Reactions on the acid sites.
propyl, and n-butyl have to be added, because they are directly formed by the addition of isobutene and n-butene to a carbon chain. However, due to the different cracking and alkylation reactions that recombine molecules, more alkyl groups have to be considered. To be able to generate a network up to C16, 16 new alkyl groups (Table 1) were added (limited to 5 carbon atoms) and the computer code was modified for recognizing and treating them. Extension to higher carbon atom number (>16) requires the addition of alkyl groups to this library and slight modification of the code. The modification of the molecule description and treatment is necessary before the modification of the rules to generate these molecules. For the present case, the maximum carbon atom number of the heaviest molecules was fixed arbitrarily to 5. This corresponds to the longest possible linear alkyl groups for a C16 molecule. Once this parameter was fixed, the library of all alkyl groups (with at most 5 carbon atoms) was determined and the code was enriched (Table 1). For further developments, an analysis of the possible patterns should be carried out. Shape selectivity could also be introduced during the generation in order to not generate some patterns of molecules. This could also participate in the reduction of the size of the global reaction network. Principles of Generation After modification of the alkyl groups library, a larger number of molecules of at most 16 carbon atom number can generated. However, not all possible reactions were generated and a limitation on their number had to be introduced. With this limitation, a network was generated (Table 2). At this point of the modeling, no quantitative information on the reaction rate is available because kinetic parameters have to be fitted on the experimental data. So, a quantitative method 9 based on the kinetic parameters cannot be applied directly. However, acid-based catalysis is well-known and there is some qualitative knowledge on the relative rate of the elementary steps for some reactions.10,11 Especially, tertiary-tertiary reactions are known to be much faster than other reaction types (Table 3). This was experimentally verified by the higher reactivity of isobutene compared to that of n-butene on amorphous silica alumina.12 Moreover, tertiary-tertiary alkylation reactions starting from isobutene seem to be much closer to the equilibrium than other reactions. Our proposal for generating a network is to introduce qualitative information that leads the way and order in which the species are generated. For that, a priori kinetic information has to be translated in terms of generation rules and introduced into the algorithm. To achieve this goal, we introduce kinetic qualitative notions in the code, that will have analogous signification for the generation rules (computer code) and for the kinetic information (evolution of species). We
a R represents the main chain of the molecule. The main chain is determined in order to be the longest and most branched chain of the molecule.
distinguish several kinds of reactions: very fast (at equilibrium), fast (close to equilibrium), and slow (far from equilibrium) (Table 4). The key concept is to generate the network step by step, considering each possible reaction in a consecutive kinetic scheme so that the generated species appear at different stages, analogously to primary products, secondary products, and so on. That means that all species that are at quasi-equilibrium appear simultaneously. They are linked by fast reactions. Species that are not at equilibrium appear consecutively at the next algorithm step and so on (Figure 2). This notion is different
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Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006
Figure 2. Step by step generation. Table 2. Network Size Evolution
olefins carbenium ions protonation deprotonation hybride shift methyl shift PCP branching beta scission alkylation a
Table 5. Principles of Step Generation
C8
C12
C16a
92 69 135 135 86 0 0 23 23
3726 2934 5832 5832 4212 0 0 1817 1817
47 000 65 000 51 409 60 373 45 770 0 0 34 937 56 919
step 2n step (2n - 1)
a
b
protonation deprotonation hybride shift alkylation t,t beta scission t,t (on every species)
alkylation s,t & t,s beta scission s,t & t,s (on species step (2n - 1))
protonation deprotonation hybride shift (on every species)
Table 6. Summary of Steps 1-4a
Termination rank: maximum number of one species 65 000.
Table 3. Relative Rates of Hydrocracking
Modes11,13
beta scission type
ions
relative rate
A B1 B2 C D
t-t s-t t-s s-s s-p
170-1050 2.8 1 0.4 ∼0
Table 4. Rates and Network rate
very fast
olefins carbenium ions protonation deprotonation hybride shift methyl shift PCP branching beta scission alkylation a
fast
step 1
step 2
step 2 bis
step 3
step 4
29 30 43 43 28 0 0 17 17
143 123 219 219 152 0 0 1 31
154 130 454 454 314 0 0 3 33
27 059 20 891 41 833 41 833 29 548 0 0 6 811 6 811
79 867 61 679 125 977 125 977 92 220 0 0 6 929 15 368
Reactions are generated at each step.
slow
reaction
double bond t-t alkylation, s-t/t-s alkylation, isomerization t-t cracking s-t/t-s cracking reactions network step exhaustive (species exhaustive (species nonexhaustive with the same at equilibrium) (creation of structure) seeds)
from that of the species/rank-based criterion.6 However, it could be considered as a rank-based criterion, if we consider the number of slow reaction generation steps necessary to create a molecule as a rank. The step of fast reaction generation will be the generation of the exhaustive tertiary-tertiary reactions from the current set of species, and the step with the slow reaction generation will be the rank-based step that generates seeds for further reactions. Reactions that will be considered at equilibrium are protonation, deprotonation, and hybride shift reactions. This leads to an equilibrium of olefins with the same structure (double bond isomerization at equilibrium). The fast reactions are the tertiary-tertiary steps (cracking and alkylation). This explains why isobutene direct alkylation products appear very quickly and do not seem to depend on contact time. Tertiary-secondary, secondary-tertiary, and secondary-secondary are slow reactions. In our simplified generation, secondary-secondary reactions are considered to be very slow and are taken into account only for the conversion of n-butene where they are necessary
as starting reactions (no tertiary-tertiary, secondary-tertiary, or tertiary-secondary reaction can occur from n-butene only). The main algorithm is modified in order to generate these steps alternatively (Table 5). Odd steps (2n - 1) are dedicated to the generation of the fast reactions, starting from the available molecules. The step continues until no more tertiary-tertiary reactions are possible on every species, former and new species included. Very fast reactions (hybride shift, protonation, and deprotonation) are generated simultaneously and exhaustively. The set of molecules generated is complete: no new tertiarytertiary alkylation reaction can be added once this step is achieved. Even steps (2n) are dedicated to the generation of slow reactions. The step is achieved when all the species generated at step (2n - 1) have been processed for creating new species (2n) by tertiary-secondary or secondary-tertiary alkylation/cracking and all new species have been processed for the generation of double bond isomers (no alkylation or cracking on these new species). Network Networks are generated from initial molecules that can be considered as seeds. The maximal size of the generated species is 16 carbon atoms. Results presented further (Table 6) concern the generation of a network from a feed constituted of isobutene,
Ind. Eng. Chem. Res., Vol. 45, No. 13, 2006 4557
Conclusions
Table 7. Cumulative Number of Olefins by Carbon Number olefins
step 1
step 2
step 2 bis
step 3
step 4
C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 total
0 3 0 0 0 2 0 0 0 6 0 0 0 18 29
0 3 0 0 0 14 0 0 0 30 0 0 0 96 143
0 3 0 0 0 25 0 0 0 30 0 0 0 96 154
0 3 3 9 21 57 119 117 356 972 1 117 2 394 6 213 15 678 27 059
1 3 5 13 27 62 139 291 643 1 623 3 664 7 478 19 071 46 847 79 867
Generation of complex networks for acid catalyzed reactions of oligomerization requires the use of adapted computer tools. The addition of qualitative kinetic information to the algorithm allows the generation of a network. The key principle is to translate rate scales in terms of generation rules. This is done via alternative steps that generate consecutively fast and slow reactions in order to form a pseudo “slow-reaction-based criterion”. Extension to skeletal isomerization and the kinetic modeling on the generated network has not yet been done. Work is in progress for comparing the network with experimental data and for building a kinetic model for simulation purposes. Acknowledgment is made to A. Forestie`re and K. Surla from IFP-Lyon for fruitful discussion.
Table 8. Network Comparison
olefins carbenium ions protonation deprotonation hybride shift methyl shift PCP branching beta scission alkylation a
C16a
C16b
47 000 65 000 51 409 60 373 45 770 0 0 34 937 56 919
79 867 61 979 125 977 125 977 92 220 0 0 13 740 22 179
Classical. b Step generation.
butene-1, and butene-2. The numbers of olefins and carbenium ions are cumulated at each step, leading to growing numbers. Protonation, deprotonation, and hybride shift numbers increase monotonically because they are generated at each step (no comparison to a library of already generated reactions) for the whole set of species. Skeletal isomerization by alkyl shift is deactivated and, so, set to zero. Alkylation and beta scission are generated at each step. There are two consequences for this. For odd steps, the total numbers of alkylation and cracking reactions are equal due to the fact that forward and reverse reactions are generated at the same time, until no new reaction is possible. For even steps, alkylation and beta scission numbers are different because only direct reactions are considered (for each new seed, the reverse reaction will be created at step (2n + 2)). Detailed results for the olefin distributions (Table 7) show the explosion of the network from step 2 to step 3. During the first two steps, olefins are limited to direct products. During step 3, due to the many branched species of step 2 that can alkylate via tertiary-tertiary alkylation, the number of structures explode and the number of double bond isomerizations (hybride shift, protonation, and deprotonation) grows very quickly. The 79 867 olefins are linked by at most two slow reactions (considering cracking and alkylation only). This illustrates the high complexity of the network and the need for further reduction of the network in order to build a kinetic model. In Table 7, the 2 bis step corresponds to the only step where secondary-secondary reactions are allowed, to initiate reaction with the n-butenes, when the feed contains only these molecules. Comparison of the generated networks (Table 8) shows that many more olefins are generated with less alkylation/cracking reactions. The second network is more coherent because equilibrium reactions are generated (protonation/deprotonation) and the appearance of species in the network is similar to the appearance of products from a kinetic point of view (primary, secondary, tertiary, ...).
Literature Cited (1) 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.; NATO Adv. Study Institute Series, Series E; Sijthoff and Noordhoff: Alphen aan de Rijn, 1980; Vol. 39, pp 137-160. (2) Baltanas, M. A.; Froment, G. F. Computer Generation of reaction networks and calculations of product distributions in the hydroisomerization and hydrocracking of paraffins on Pt-containing bifunctional catalysts. Comput. Chem. Eng. 1985, 9 (1), 71-81. (3) 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. Ind. Eng. Chem. Res. 1989, 28, 899-910. (4) Martens, G. G.; Marin, G. B. Kinetics for hydrocracking based on structural classes: model development and application. AIChE J. 2001, 47 (7), 1607-1622. (5) Guillaume, D.; Surla, K.; Vale´ry, E.; Galtier, P.; Verstraete, J. Modelling of large acid-catalyzed reaction network: application to hydroisomerisation of squalane. Ind. Eng. Chem. Res. 2005, submitted for publication. (6) Broadbelt, L. J.; Stark, S. M.; Klein, M. T. Termination of computergenerated reaction mechanisms: species rank-based convergence criterion. Ind. Eng. Chem. Res. 1995, 34, 2566-2573. (7) Joshi, P. V.; Freund, H.; Klein, M. T. Directed kinetic model building: seeding as a model reduction tool. Energy Fuels 1999, 13, 877880. (8) De Witt, M. J.; Dooling, D. J.; Broadbelt, L. J. Computer generation of reaction mechanisms using quantitative rate information: application to long chain hydrocarbon pyrolysis. Ind. Eng. Chem. Res. 2000, 39, 22282237. (9) Klinke, D. J.; Broadbelt, L. J. Mechanism reduction during computer generation of compact reaction models. AIChE J. 1997, 43 (7), 18281837. (10) Martens, J. A.; Jacobs, P. A.; Weitkamp, J. Attempts to rationalize the distribution of hydrocracked producs, I. Qualitative description of the primary hydrocracking modes of long chain paraffins in open zeolites. Appl. Catal. 1986, 20, 239-281. (11) Martens, J. A.; Jacobs, P. A.; Weitkamp, J. Attempts to rationalize the distribution of hydrocracked producs, II. Relative rates of primary hydrocracking modes of long chain paraffins in open zeolites. Appl. Catal. 1986, 20, 283-303. (12) Picard, F.; Bertoncini, F.; Guillaume, D. Butenes oligomerization on amorphous silica alumina catalyst: structure of dimers consideration, submitted to Chem. Eng. Science. 2005. (13) Marcilly, C. Catalyse acido-basique: Application au raffinage et a` la pe´trochimie, Editions Technip. 2003, 215-217. (14) Martens, J. A.; Tielen, M.; Jacobs, P. A. Attempts to rationalize the distribution of hydrocracked producs III. Mechanistic aspects of isomerization and hydrocracking of branched alkanes on ideal bifunctional large-pore zeolite catalysts, Catal. Today 1987, 1 (4), 435-453.
ReceiVed for reView September 7, 2005 ReVised manuscript receiVed March 13, 2006 Accepted March 22, 2006 IE0510019
