Modeling Analysis of the Fischer-Tropsch Synthesis in a Stirred-Tank Slurry Reactor

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1 2330 Ind. Eng. Chem. Res. 2004, 43, Modeling Analysis of the Fischer-Tropsch Synthesis in a Stirred-Tank Slurry Reactor Gang Wang, Yi-Ning Wang, Jun Yang,, Yuan-Yuan Xu, Liang Bai, Hong-Wei Xiang, and Yong-Wang Li*, Group of Catalytic Kinetics & Theoretical Modeling, State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan , People s Republic of China, and Department of Chemistry, Jinan University, Guangzhou , People s Republic of China On the basis of recent detailed kinetics models, a multicomponent model for the Fischer-Tropsch synthesis in a stirred-tank slurry reactor is developed to interpret the essential bulk effects that enhance the deviations of hydrocarbon product distribution from the standard Anderson- Schulz-Flory (ASF) model. It is found that the reactor model with kinetics excluding olefin readsorption and secondary reactions (ORSR) on the catalyst surface could not predict the correct trends observed in experiments, while that using the kinetics models including ORSR effects could well interpret these two deviations from the ASF distribution. The important notation pointed out is that ORSR is greatly enhanced by less volatility of heavier hydrocarbons in a multiphase reactor, which produces significant deviations from the ASF distribution in experiments, namely, the increasing chain growth factor and decreasing olefin-paraffin ratio with increasing carbon number. In addition, the experimentally proven fact that the addition of olefins in the feed could enhance the yields of hydrocarbons heavier than the added olefins is well interpreted by this simulation. Introduction As a route converting synthesis gas to liquid fuels or chemical feedstocks, Fischer-Tropsch synthesis (FTS) has been an interesting topic in catalyst development as well as process scale-up. 1-9 For considering the efficiency of a specified Fischer-Tropsch process, understanding the selectivity of the synthesis reaction system over the defined catalyst and in the designed reactor is of great importance because of the wide product spectrum of FTS, which may dramatically change with operation condition changes. 2,4,10,11 It is well-known that the FTS selectivity to various products (with different carbon numbers or in different states, namely, paraffins, olefins, and oxygenates) is closely related to the catalysts used, 3,6,12 namely, the catalystspecific selectivity. For a certain catalyst, the factors on influencing the selectivity of the catalyst could be classified as kinetically intrinsic and nonintrinsic. The intrinsic factors are those directly from the catalyst surface, and the nonintrinsic factors are those causing a change in the working environment of the catalyst surface. In literature up until now and back to very early studies, this point has not been well addressed in the explanation of experimental results, which are now believed to be in mixed situations with both intrinsic and nonintrinsic factors involved For a basic FTS mechanism understanding, Anderson 16 described the product distribution in terms of the chain growth factor (R) as the well-known Anderson- Schulz-Flory (ASF) law defined, and the ASF law has been a standard for explaining the experimental results. 4,11-17 However, there are some major deviations * To whom correspondence should be addressed. Tel.: Fax: ywl@sxicc.ac.cn. Chinese Academy of Sciences. Jinan University. in the experimental results from the ASF distribution. A couple of studies showed that the chain growth factor does not remain constant. 2,9,13,18-20 Another major deviation from the ideal ASF distribution is that the olefin-paraffin ratio of the hydrocarbon products in FTS deceases approximately in an exponential relationship of the carbon number. 2,10,20,21 The phenomenon of nonsingle-r distribution has been intrinsically interpreted in terms of the dual-site theory. 13,14,22 It was noticed that the two phenomena could not be justified by the dual-site theory. 2 Beyond the complex surface reactions in a FTS process, the factors in bulk at different levels (catalyst particles or pores and the reactor media) have proven to be significant in bending of the ideal ASF curves. 2 The fundamental implications are even more complicated because of the fact that it is practically not possible to exclude the bulk effects (solubility, diffusivity, and the parameter nonuniform effect in a reactor) when FTS reaction experiments are made. Very recently, Puskas and Hurlbut 15 argued that different microscopic kinetic environments are the only reasonable cause for the double-r distribution. However, the double-r distribution can be observed in a stirredtank slurry reactor (STSR) or a spinning-basket reactor, where the working environment of the catalyst is uniform. It is generally agreed that FTS reactions are extremely complex and that olefin readsorption and secondary reactions (ORSR) can significantly modify the product distribution. It has been well-known that primary FTS products, R-olefins, can reabsorb on the catalyst surface and undergo ORSR. 2,17,23-27 van der Laan and Beenackers 2 reviewed different opinions for explaining the observed phenomenon of nonsingle-chain growth factors and /ie CCC: $ American Chemical Society Published on Web 04/15/2004

2 catalyst particles are uniformly distributed in the reactor owing to the typical small size for the slurry-phase FTS; (3) the reactor is at steady state; (4) reactions take place in the liquid phase only; (5) the reactor is operated isothermally and isobarically; (6) diffusion limitation in catalyst pores is negligible. Model equations are derived based on the mass balances. For convenience of calculation, dimensionless forms are formulated as follows: Gas phase: Ind. Eng. Chem. Res., Vol. 43, No. 10, Figure 1. Relationship between kinetics and reactor models. concluded that the dependence of the product distribution on ORSR imposed the most reasonable interpretation. The ORSR occur for all of the olefinic FTS products with different chain lengths, and it has experimentally been observed that the extent of ORSR is dependent on the chain length of olefins It has been proposed that the ORSR dependence on the chain length might be correlated with some of bulk effects, namely, diffusion behaviors, solubilities, and physisorption behaviors. 25,27,32,33 For the FTS kinetics aspect, 10,34-39 Lox and Froment 34 developed a detailed kinetics model based on several sets of elementary reactions. However, ORSR were not taken into account in their model. van der Laan 10 made an attempt to include bulk effect enhanced ORSR in their kinetics model to describe the experimental phenomenon. This treatment progressed significantly but mixed several bulk effects in a kinetics model that is generally expected to be intrinsic for the events occurring on the catalyst surface in order to formulate a kinetics base for a reactor modeling. Nowicki et al. 39 and Schulz and Claeys 38 assumed that ORSR took place on the different active sites and developed detailed kinetics models, in which the effect of solubility was also considered empirically. Several detailed kinetics models considering ORSR have recently been developed in our group with the comprehensive understanding of the complicated kinetics in FTS. 35,36 From the viewpoint of chemical reaction engineering, bulk effects should be considered in a reactor model, and a kinetics model should be intrinsic. The well-defined interface between a kinetics model and a reactor model is essential to get a deep insight for the discrimination of the role of intrinsic factors and nonintrinsic ones for the two deviations from the ideal ASF distribution (Figure 1). On the basis of available detailed kinetics models, a reactor model is established in a manner similar to that of published ones 37,40-43 to study the product distribution modified by ORSR with the enhancement of bulk effects. The behaviors of these models are validated by comparing model predictions with several key experimental trends related to FTS selectivity. The ORSR effect on the final FTS products is discussed. u G0 y i,0 - u G y i - St G,i( y i - x m i i) ) 0 (1) Overall stream: u L0 x i,0 - u L x i + u G0 y i,0 - u G y i + β m r i ) 0 (2) Gas-phase total concentration: n y i ) 1 (3) i Liquid-phase total concentration: n x i ) C L,t /C G0,t (4) i where the definitions of group variables and parameters are written as follows: y i ) C G,i /C G0,t (5) x i ) C L,i /C G0,t (6) u G ) U G /U G0 (7) u L ) U L /U G0 (8) St G,i ) k L,i al/u G0 (9) β m ) M c /U G0 C G0,t S (10) 2N c + 2 nonlinear algebraic equations (1)-(4) with 2N c + 2 unknowns (x i, y i, u G, and u L ) are numerically solved by a hybrid iteration method, which is available in MINPACK library. 44 Mass-transfer coefficients are added for application to the situation where the mass-transfer resistance is significant. However, it is generally agreed that masstransfer resistance is negligible and the gas-liquid equilibrium can be reached in a laboratory STSR. In this study mass-transfer coefficients are therefore set large enough to approximate the experimental cases. For calculation of Henry coefficients, the liquid phase is assumed to be a pseudocomponent, with the average carbon number updated in each run. 45 Henry coefficients are estimated for CO, H 2,CO 2,H 2 O, N 2, and C 1 -C 3 hydrocarbons using correlation developed by Marano and Holder 45 and for other components in terms of the extrapolation using the saturated vapor pressures of pure components: Reactor Model and Numerical Procedures A multicomponent reactor model for FTS in a STSR is based on the assumptions given as follows: (1) gas and liquid phases are assumed to be perfectly mixed because of turbulence caused by the impeller; (2) H (n) (n) (n+1) P sv H (n+1) ) P sv m i ) C G,i ) H i C L,i C L,t RT (11) (12)

3 2332 Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 Table 1. Comparison of Detailed Kinetics Models authors mechanism experimental conditions and catalyst reactor Lox and Froment 34 CO insertion alkyl mechanism and Fe-Cu-K catalyst at T ) K, FBR a CH 2 insertion alkyl mechanism P ) MPa, H 2/CO feed ratio ) , and space velocity ) NL kg -1 cat s -1 Wang et al. 35 CO insertion alkyl mechanism Fe-Cu-K catalyst at T ) K, FBR a P ) bar, H 2/CO feed ratio ) , and space velocity ) h -1 Yang et al. 36 CO insertion alkyl mechanism, Fe-Mn catalyst at T ) K, FBR a CH 2 insertion alkyl mechanism, and CH 2 insertion alkylidene mechanism P ) MPa, H 2/CO feed ratio ) , space velocity ) NL kg -1 cat s -1 van der Laan 10 CH 2 insertion alkyl mechanism Fe-Cu-K-SiO 2 catalyst at T ) 523 K, P ) MPa, H 2/CO feed ratio ) , and space velocity ) NL kg -1 cat s -1 STSR a FBR ) fixed-bed reactor. The source for extended Antoine equation coefficients used in estimating the saturated vapor pressure is API Project 44 Table The liquid density is computed using the procedures suggested in API Technical Data BooksPetroleum Refining. 47 The liquid total concentration is obtained using eq 13. C L,t )F L /M L (13) The critical properties and specific gravities of pure components at 15.6 C are required in the computation of the density of the liquid phase. For the components CO, H 2,CO 2,H 2 O, N 2, paraffins C 1 -C 30, and olefins C 2 - C 20, data are from the Aspen Plus PURE11 data bank, and for other components, data are from the extrapolation of the ABC method (for details, see the appendix). 48 The diameter and length of the reactor are 9 and cm, respectively, and the loading weight of the catalyst is 20 g. Results and Discussion The available detailed kinetics models were established for different catalysts with different experimental conditions. 10,34-36 It should be noticed that model parameters may depend on catalysts as well as experimental conditions. Table 1 summarizes the specific conditions for these kinetics models. Yang s model has the characteristic considering the ORSR in the mechanism development stage and excluding the bulk effects in the final kinetics equations, while the other models empirically mixed the bulk effects in the kinetics equations without considering a mechanism consequence, and the bulk factors included in the present reactor model have no influence on these empirical models. In addition, it can be seen that the catalysts and operation conditions used are varied with the models. Nevertheless, some general experimental trends for FTS selectivity are expected to be predicted by these mechanism-based models. To validate this, two well-tested experimental trends, namely, the product distribution over the carbon number and the dependence of the olefin-to-paraffin ratio on the carbon number, are compared with available experimental results, which reflect the most important characteristics in FTS selectivities. As shown in Figure 2, the typical FTS product distribution curve from an STSR has reflected Figure 2. Comparison of calculated and experimental product distributions (reaction conditions: T ) 523 K, P ) 1.5 MPa, H 2/ CO ) 0.67, GHSV ) 1.4 Nm 3 kg cat -1 h -1 ). the deviation from the ASF distribution. The results from kinetics models show that the models with ORSR could qualitatively reproduce the bended distribution curve, while those without ORSR could not. In addition, the kinetics model from Yang et al. has proven to fit well all of the distribution curves obtained from kinetics experiments in a micro-fixed-bed reactor. 36 The dependence of the olefin-to-paraffin ratio on the carbon number has been observed in both fixed-bed and STSR reactors. 2,10,20,21,36 This basic (but deeply hidden) experimental observation is simulated as shown in Figure 3. The experimental trend presented in Figure 3 is from the experiments of van der Laan in a STSR reactor. 10 To validate the bulk effect on ORSR, the simulation results with and without bulk effects are presented in Figure 4 for Yang s model. It is clear that the mechanism-based kinetics model from Yang et al. can only produce the correct trend in the olefin-toparaffin ratio when the bulk effects are considered, and van der Laan can also produce the experimental trends having no resolution in the role of the bulk effect, while the one without ORSR cannot. As discussed above, the experimental phenomena, namely, the so-called double-r distribution and the exponential decrease of the olefin-to-paraffin ratio with an increase in the carbon number, are basically due to

4 Ind. Eng. Chem. Res., Vol. 43, No. 10, Figure 3. Comparison of calculated and experimental olefin-toparaffin ratios (reaction conditions: T ) 523 K, P ) 2.0 MPa, H 2/ CO ) 0.67, GHSV ) 2.0 Nm 3 kg cat -1 h -1 ). Figure 5. Olefin molar fraction as a function of the carbon number (reaction conditions: T ) 523 K, P ) 1.6 MPa, H 2/CO ) 0.67, GHSV ) 2.24 Nm 3 kg -1 cat h -1 ). Figure 4. Comparison of the calculated and experimental olefinto-paraffin ratios (reaction conditions: T ) 585 K, P ) 3.02 MPa, H 2/CO ) 2.04, GHSV ) Nm 3 kg cat -1 h -1 ). the ORSR enhanced by bulk effects. The scenarios can be depicted as follows: It is noticed in our simulation that the superficial gas velocity is approximately 3 or 4 orders of magnitude higher than that in the liquid phase, implying much longer residence times of the products in the liquid phase than those in the gas phase. Most of the heavy olefins stay in the liquid phase because of less volatility (Figure 5), reabsorbing on the catalyst surface to incorporate into the growing carbon chain or initiate a new chain propagation process before leaving the reactor, which significantly enhances the yields of heavy hydrocarbons compared to those predicted by the standard ASF law. On the contrary, most of the light olefins leave the reactor with the gaseous stream once produced. However, it should be noticed that the gas and liquid phases in the bulk of a fixed-bed reactor have similar residence times because of the fact that the FTS waxes are instantly carried by the gas flowing through the reactor, while those in the catalyst pores are significantly different, and an apparent difference between the residence times for the gas and liquid flow exists in a Figure 6. Comparison of calculated product distributions at different temperatures (reaction conditions: P ) 2.0 MPa, H 2/CO ) 1.0, GHSV ) 1.68 Nm 3 kg -1 cat h -1 ). STSR. In a STSR, the high molecular weight olefinic products in the heavy wax phase have many more choices to undergo ORSR than those with low molecular weight flow out of the reactor. The situation in a STSR may be summarized as the volatility-enhanced ORSR. For a fixed-bed reactor, however, the similar situation making the heavy olefinic FTS products have more choices to undergo ORSR can only be caused by different residence times of the olefinic FTS products in catalyst pores, namely, the diffusion-enhanced ORSR. 25 To explore the complexity of FTS reaction systems, our simulation has pointed out a comprehensive direction. To get a better understanding in this direction, systematic experiments and simulation studies are still needed, for which the mechanism-based kinetics model (Yang et al.) will play a proper role. To study the effects of parameters in Yang s model on the product distribution, simulations using Yang s model are carried out. It is found that high temperature and high H 2 /CO ratio have favorable effects on the formation of light hydrocarbons, which is comparable with experimental findings (Figures 6 and 7). 2,11,16 The mechanism consequence is that the high temperature promotes the desorption, the high H 2 /CO ratio leads to

5 2334 Ind. Eng. Chem. Res., Vol. 43, No. 10, 2004 Figure 7. Comparison of calculated product distributions at different H 2/CO ratios (reaction conditions: T ) 553 K, P ) 2.0 MPa, GHSV ) 1.68 Nm 3 kg -1 cat h -1 ). Figure 9. Calculated inhibition of the cofed butene on the selectivity of methane at different H 2/CO ratios (reaction conditions: T ) 543 K, synthesis gas pressure ) 2 MPa, GHSV ) 2.24 Nm 3 kg -1 cat h -1 ). leading to a weak hydrogenation behavior and lower methane formation rate. 2,23,27,28 On the other hand, the addition of an olefin in the feed changes the FTS behaviors on the catalyst surface due to ORSR. The cofed olefins absorb on the catalyst surface and initiate the new process of chain propagation, consuming more chain building blocks, -CH 2 -, according to the carbide mechanism 2,53-55 and thus forming more hydrocarbons heavier than the cofed olefin and, consequently, leaving less -CH 2 - building blocks for the formation of those products lighter than the cofed olefin. Conclusions Figure 8. Comparison of the calculated formation rates as a function of the carbon number with and without the cofed pentene (reaction conditions: T ) 523 K, synthesis gas pressure ) 2.0 MPa, H 2/CO ) 0.67, GHSV ) 1.68 Nm 3 kg -1 cat h -1 ). a strong hydrogenation environment for lowering the olefinic product selectivity, and both conditions suppress the chain growth reactions. Simulation is carried out to study the effect of the addition of olefins in the feed on the product distribution. As illustrated in Figure 8, for hydrocarbons lighter than the cofed olefin, formation rates are suppressed, while the formations of the hydrocarbons heavier than the cofed olefin are enhanced. The enhancements on the yields of the hydrocarbons heavier than the co-fed olefin havebeenobservedinmanyexperimentalstudies. 14,24,27,28,49-52 With respect to suppression of those lower than the cofed olefin, most of the studies concentrated on inhibition of the selectivity to methane. 24,49,50,52 The simulated results reproduce this phenomenon as shown in Figure 9. The addition of olefins will enrich the olefinic species in the reaction system, leading to enhanced ORSR for the olefins with longer chains than the added ones in general. On the one hand, the addition of olefins will suppress the adsorption of hydrogen on catalyst surfaces because of the strong competitive adsorption of olefins, The present study has proposed a systematic approach in understanding the nature of experimentally observed FTS selectivity behavior. A well-defined kinetics model for such a simulation study needs to be basically free of mixing with bulk factors that should be considered in a classical reactor model. Different from other available kinetics models, Yang s kinetics model has not only included the important ORSR mechanism but also kept the intrinsic character. This detailed kinetics model can well predict important FTS selectivity features, namely, the non-asf product distribution and the dependence of the olefin-to-paraffin ratio on the carbon number. Simulations on the basis of the detailed kinetics model have been conducted to explore the fundamental consequences of the complex selectivity behavior of FTS processes. Supported with many experimental findings, it is found that the essential aspect of the non-asf product distribution and the dependence of the olefinto-paraffin ratio on the carbon number is related to the ORSR in the FTS mechanism at the catalyst surface scale. However, bulk effects at the reactor scale, to a large extent, enhance ORSR, leading to significant deviations of FTS selectivity from the standard ASF law and especially the experimentally observed dependence of the olefin-to-paraffin ratio on the carbon number. For a STSR system, the bulk effects are mainly contributed by the mobilities/volatilities of the widely distributed olefinic FTS products, which can undergo ORSR.

6 Ind. Eng. Chem. Res., Vol. 43, No. 10, Table 2. Parameters for Critical Temperatures and Pressures of Hydrocarbons a Y a b c d e T c, K paraffin olefin P c, MPa paraffin olefin a n ) carbon number. Table 3. Parameters for the Specific Gravity of Hydrocarbons a parameter paraffin olefin a b c d e f a n ) carbon number. Acknowledgment Financial support from the Chinese Academy of Sciences (Project No. KGCX1-SW-02), National Ministry of Science and Technology of China via 863 plan (Project No. 2001AA523010), Shanxi Natural Science Foundation ( ), and National Natural Sciences Foundation of China (Project No ) is gratefully acknowledged. The support from Alexander von Humboldt Foundation to Y.-W.L. is also greatly acknowledged. Appendix: Parameters for the Properties of Hydrocarbons See Table 2. See Table 3. Y ) a - b exp[-c(n + d) e ] M w SG ) a + e(n - d) - f exp[-b(n - d) c ] (A1) (A2) Nomenclature a ) gas-liquid interfacial area per expanded slurry, m -1 C ) molar concentration, mol m -3 D r ) reactor diameter, cm H ) Henry s coefficient, MPa k L ) mass-transfer coefficient, m s -1 L ) reactor length, cm M c ) weight of the catalyst used, g M L ) number-average molecular weight, kg mol -1 M w ) molecular weight, g mol -1 m ) Henry s coefficient, dimensionless N c ) component number r ) reaction rate, mol kg -1 cat s -1 R ) universal gas constant, J mol -1 K P ) pressure of the reactor, MPa P sv ) saturated vapor pressure, MPa S ) cross section of the reactor, m 2 SG ) specific gravity, eq A2 St G ) Stanton number, eq 9 T ) temperature of the reactor, K U ) superficial velocity, m s -1 u ) dimensionless superficial velocity, eqs 7 and 8 x ) dimensionless liquid molar concentration, eq 6 y ) dimensionless gas molar concentration, eq 5 Y ) critical pressure (bar) or temperature (K), eq A1 Greek Symbols R)chain growth factor β m ) kinetic coefficient, (mol kg -1 cat s -1 ) -1 F)liquid density, kg m -3 Superscripts and Subscripts 0 ) inlet c ) critical G ) gas phase L ) liquid phase i ) component index t ) total n ) carbon number p ) paraffin o ) olefin * ) catalyst surface Literature Cited (1) Kölbel, H.; Ralek, M. 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