A review of kinetics for Fischer-Tropsch synthesis

Yang Jun ^1,2
(¹Department of Chemistry, Jinan University, Guangzhou 510632 China;  ²State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan, 030001 )

3. MECHANISM OF FISCHER-TROPSCH SYNTHESIS
The FTS reaction considered here consists of surface steps in five categories: (1) the adsorption of reactants (H₂ and CO); (2) chain initiation; (3) chain propagation; (4) chain termination and desorption of products; (5) readsorption and secondary reaction of olefins^[2-5].
3.1 Chain initiation
A great number of surface species are involved in the chain initiation and chain propagation, and this leads to great difficulty to describe the Fischer-Tropsch kinetics. It is generally accepted that the chain initiation is started by the dissociation of the CO, and sequential hydrogenation to form CH, CH₂ and CH₃, namely as the "building block" of the hydrocarbon. However, for the further formation of hydrogenated carbon species, mechanism studies for FTS often assumed the formation of CH₂ and CH₃ species,^[2-5] while recent characterization and theoretical studies in energetics debate for the more possible formation of CH species on several transition metal surfaces.^[6,7]
3.2 Chain growth mechanism
There is generally an agreement that the FTS reaction is a surface polymerization reaction and the step that CH_x species couple with each other(C-C coupling) to form high-molecular hydrocarbon is the key step^[7-13]. Since the discovery of the process, the chain growth mechanism of FTS has been extensively studied and many results have been obtained^[7-13]. However, there is still in controversy about the mechanism of chain growth in the Fischer-Tropsch synthesis. The alkyl mechanism proposes that the reaction is initiated by the formation of a methyl species, and that chain growth takes place by the successive insertion of methylene into the metal-alkyl bond: ^[8]
CH₂s₁ + C_nH_2n+1s₁ = C_n+1H_2n+3s₁ + s₁        (5)
    The alkylidene mechanism proposes that the formation of the adsorbed ethylidene initiates the chain formation, and that chain growth is facilitated by methylene insertion into the metal-alkylidene bond:^[9]
CH₂s₁ + C_nH_2ns₁ = C_n+1H_2n+2s₁ + s₁            (6)
    Another mechanism assumes that chain growth is initiated by the adsorption of CO on the active sites already containing hydrocarbon intermediate and then by a sequence of hydrogenation:^[10]
CO + C_nH_2n+1s₁ = C_nH_2n+1-s₁-CO                   (7)
C_nH_2n+1-s₁-CO + H₂ = C_nH_2n+1-s₁-C +H₂O (8)
C_nH_2n+1-s₁-C +H₂ = C_nH_2n+1-s₁-CH₂                  (9)
    The alkenyl mechanism was proposed by Maitlis¹¹ as an alternative to the alkyl mechanism. This mechanism suggested that reaction is initiated by the formation of a surface vinyl species (-CH=CH₂) from a surface methyne (≡CH) and a surface methylene (=CH₂). Then chain growth occur through the insertion of a surface methylene (=CH₂) into a vinyl species to form a surface allyl species (-CH₂CH=CH₂) which sequentially isomerizes to a surface alkenyl (vinylic) species (-CH=CHCH₃). There is evidence that the sp²-sp³ carbon coupling involved in proposed chain propagation is kinetically favored over the sp³-sp³ carbon coupling required in the alkyl mechanism. However, most of the organometallic model systems used to support the mechanism have not used common FT catalysts, such as iron and cobalt and the key steps in the mechanism is not well established. In particular the isomerization of surface allyl species to alkenyl species has little precedent in model studies.
    Although there are a great number of evidences that obtained by using organometallic and surface science models to support the mechanisms mentioned above, the debate is still continued. In 2000, Overett^[12] gave a detailed review of the mechanisms (alkyl and alkenyl mechanisms) for the FTS and the evidence for these mechanisms. He suggested that it is possible that there is not one mechanism operating for the formation of all observed products due to the wide range of operation conditions for the FTS, and both alkyl and alkenyl intermediates may play an important role under various conditions.
    Recently, Ciobîcä ^[7,13] studied the chain growth mechanism of FTS over Ru catalyst by using periodic ab initio quantum chemical calculations and offer more atomic-level description of how specific steps are taken place. The results show that CH was the most stable of all C₁ surface intermediates and used as the primary monomer units for growing longer carbon chains rather than CH₂. Two chain growth mechanisms based on carbene-type mechanisms were proposed, in one mechanism the chain growth was initiated by addition of CH to growing alkylidene (RCH-)(R=alkyl) and another mechanism was initiated by addition of CH to growing alkyl (RCH₂-)(R=H or alkyl). It is concluded that the two mechanisms proposed can proceed in parallel and hydrocarbon chain can be formed via a few cycles of one mechanism and the few from the other, depending on the balance of hydrogenation and C-C coupling, since the two mechanisms share the same intermediate.
    In 2002, by means of extensive density functional theory (DFT) method, Liu^[6] studied the FTS and got the relative stabilities of many key intermediates. In their work, several C-C coupling mechanisms that likely to be involved, such as C+C, C+CH, C+CH₂, CH+CH, CH+CH₂, CH₂+CH₂, CH₂+CH₃ coupling, were compared quantitatively. The results show that the C+CH coupling has the lowest barrier of 0.43ev, whereas the well-regarded mechanism of CH₂+CH₃ possesses high reaction barriers. They suggested that chain growth in FTS may be following a C+CR pattern rather than CH₂+CH₂R pattern(R=H or alkyl).

4. MODEL OF PRODUCT DISTRIBUTION
In 1946, Herington^[2,20] first treated the molar distribution of hydrocarbons from Fischer-Tropsch Synthesis in terms of a polymerization mechanism. The same formulation was rediscovered by Anderson^[2,20] et al in 1951 and named as Anderson- Schulz-Flory (ASF) distribution. In the ASF model, the formation of hydrocarbon chains was assumed as a stepwise polymerization procedure, and the chain growth probability was assumed to be independent of carbon number.
                       (10)
    However, significant deviations from the ideal ASF distribution have been observed in many studies.^[2,14] Picher^[14] et al for the first time reported the deviations of experimental results from ASF distribution. The usual deviations of the distribution of the linear hydrocarbons are a relatively higher selectivity to methane, a relatively lower selectivity to ethane, an increase in chain growth probability with increasing molecular size, and an exponential decrease of olefin to paraffin ratio with increasing chain length in comparison to the ideal ASF distribution. Some authors^[2,15] interpreted the deviations from the standard ASF distribution by the superposition of two ASF distributions. They suspected the existence of two sorts of sites for the chain growth on the catalyst surface, and therefore proposed that each site might individually yield the ideal ASF distribution with different chain growth probabilities. However, this explanation cannot interpret the increase of the paraffin/olefin ratio with the chain length. On the basis of the experiments with co-fed olefins, it was noted that the re-adsorption and secondary reaction of olefins had a great influence on the products distribution of FTS. Some researchers^[16,17] proposed a more plausible explanation for these deviations and suggested that the occurrence of secondary reactions of the olefins caused the deviations from the ASF distribution. Kuipers^[17] et al. described the increase of physisorption strength of hydrocarbon at the catalyst interface with increasing chain length by . Iglesia et al^[16] developed a model describing the olefin re-adsorption effect enhanced by intra-particle and inter-particle transport processes. They suggested that the diffusion limitation within liquid-filled pores slowed down the removal of 1-olefins, which caused an increase of their residence time within the catalyst pores. In 1999, van der Laan^[2] studied the kinetics of the gas-solid Fischer-Tropsch synthesis over a commercial Fe-Cu-K-SiO₂ catalyst in a continuous spinning basket reactor. They proposed a product distribution model named as a-Olefin Readsorption Product Distribution Model (ORPDM), which combines a mechanistic model of olefin readsorption with kinetics of chain growth and termination on the same catalytic sites. The olefin readsorption rates depend upon chain length due to increasing physisorption strength on the catalyst surface and increasing solubility in FT-wax inside the catalyst pores with increasing chain length. With this model, the experimental observed relatively high yield of methane, relatively low yield of ethane and both the exponential decrease of olefin to paraffin ratio and the change of the chain growth probability with chain length can be predicted. However, in their model, the CO hydrogenation model and the olefin re-adsorption model were treated separately.

5. KINETICS OF FISCHER-TROPSCH SYNTHESIS
The FTS product is composed of a complex multi-component mixture of linear and branched hydrocarbons and oxygenated products, the majority of which are linear hydrocarbons.^[2] The FTS kinetics has extensively been studied, and many attempts have been made for the rate equations describing the FTS reactions.^[3-5] In most cases, the hydrocarbon products were lumped according to the carbon number of hydrocarbon molecules with an ideal Anderson-Schulz-Flory (ASF) distribution. Although a few of available kinetics models were developed based on the detailed mechanism of Langmuir-Hinshwood- Hougen-Watson (LHHW) type, ^[2-5] only two of them simultaneously considered both the syngas conversion rates and the hydrocarbon formation rates.
5.1 Lumped kinetics
In 1956, Anderson² proposed a rate expression which includes water inhibition:
(11)
    Huff and Satterfield² observed a linear decrease in the adsorption parameter in equation (10) with partial pressure of hydrogen and modified the equation (10) as the following form:
(12)
    Ledakowicz and Deckwer¹⁸ proposed a rate expression including CO₂ inhibition, because the water-gas-shift reaction will influence the reaction rate by altering the concentration of the reactants and products.
(13)
(14)
However, we recently have pointed out that the deficiencies existing in the conventional lumped models and those tailing syngas conversion rates with carbon number distribution formula when a comprehensive simulation is required. ^[5]
5.2 Detailed kinetics
Zimmerman and Bukur^[19] proposed a kinetic model for both the formation of linear hydrocarbons and the water-gas-shift reaction over an iron catalyst, in which the re-adsorption and secondary reaction of the 1-olefins was considered. With this model, the increase of the paraffin/olefin ratio with carbon number can be predicted. However, there are significant deviations between the mole fractions of hydrocarbon predicted and those of experiment, especially for methane and ethene.
    In 1993, Lox and Froment^[3,4] studied the FTS kinetics over a commercial precipitated iron catalyst. Based on the LHHW scheme, they developed seven sets of "elementary steps", from which detailed kinetic models were derived by assuming the carbide mechanism for the FTS and formate intermediate scheme for the WGS reaction. The rates of CO or H₂ consumption and product formation were unified in these models. Experimental data were regressed with large-scale nonlinear optimization approaches for determining the "best" kinetic parameters, and statistic analysis was applied to validate the feasibility of both models and parameters in them. The final model could describe the distribution of linear paraffins and olefins of FT synthesis obeying the ideal ASF distribution at the level of surface reaction. The formation rates of hydrocarbon are given by:
Paraffins:                 (15)
Olefins:                          (16)
Chain growth probability:                (17)
    However, the deviations, observed in many experiments, from the ideal ASF distribution were totally neglected in their models. Very recently, the authors have proposed a systematic approach for considering more complicated olefin re-adsorption phenomenon in kinetic modelling over a precipitated iron catalyst on the basis of similar ideas to those of Lox and Froment.^[3] Three kinetic models based on mechanism of CO insertion are established. The predicted product distribution fitted well with the experimental data obtained at temperature 493-542 K, pressure 10.9-30.9 bar, and H₂/CO 0.98-2.99 over an industrial Fe-Cu-K catalyst in a fixed bed reactor. The formation rates of hydrocarbon are given by:
Methane:                                    (18)
Paraffins:                     (19)
Olefins:                       (20)
Chain growth probability:                                            (21)
    In the above work only the CO insertion mechanism was examined. However, the CO insertion mechanism for chain growth has lost favor, because of the observation that most catalysts active for FT reaction also dissociate CO when it adsorbed on the surface at the FT temperature. In order to establish and test detailed mechanistic kinetics models for the Fischer-Tropsch system with considering much more possibilities in mechanism combinations than before, recently the authors^[20] establish 13 kinetic models by consideration of several plausible chain growth mechanisms, such as the alkyl and alkylidene mechanisms. The new mechanistic model, in which the olefin re-adsorption and secondary reactions are taken into account, leaves the transportation-enhanced olefin re-adsorption factor for further work in the combination of kinetics and the reactor simulations. Combining these FT model with three water-gas-shift model, finally 39 kinetic models are obtained. These kinetic models were scanned sequentially by genetic algorithm and conventional Levenberg-Marquardt method for finding the 'best' parameter values. The results showed that the FTS model on the basis of the alkylidene mechanism and the WGS model based on formate intermediate mechanism can describe both the distribution of paraffins and olefins and the consumption rates of the reactants well. Although primary, namely limited number of mechanism sets, from which only about 13 kinetics models were scanned, was considered, our optimal model for an industrial iron catalyst showed a better description for the non-ideal ASF distribution than that from Lox and Froment.
    The formation rates of the hydrocarbon for final model are given as:
    (22)
(23)
(24)
(25)
(26)
    As above shown, the chain growth probability and the readsorption factor of are the function of carbon number.

REFERENCES
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