Ind. Eng. Chem. Res. 2009, 48, 3791–3801
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A Two-Phase Reactor Model for the Hydrocracking of Fischer-Tropsch-Derived Wax Klaus Mo¨ller* Process Modelling and Optimisation Group, Department of Chemical Engineering, UniVersity of Cape Town, PriVate Bag, 7701, Rondebosch, South Africa
Philip le Grange and Carlo Accolla C*Change, DST Centre of Excellence in Catalysis, Department of Chemical Engineering, UniVersity of Cape Town, PriVate Bag, 7701, Rondebosch, South Africa
A two-phase reactor model that describes the hydrocracking of Fischer-Tropsch-derived wax (eC80) has been developed that combines elementary hydrocracking kinetics and vapor-liquid equilibrium (VLE) with the design equations for an ideal fixed-bed reactor. The kinetics of the reaction considers each carbon number as an independent species in which all structural isomers and (de)hydrogenation steps are in chemical equilibrium. β-Scission cracking is rate-controlling for each carbon number; thus, an increase in reaction rate with increasing carbon number is observed. The VLE is described by a Peng-Robinson equation of state, and phase equilibrium is maintained at all locations down the reactor by simultaneous solution of the VLE within the reactor design equations. The model has only one adjustable rate constant: the β-scission rate constant, which controls the conversion. Meanwhile, the selectivity has no adjustable parameters and is controlled completely by the kinetic model and VLE. Results show that the VLE is responsible for the improved selectivity to diesel (C10-C20) with increasing temperature, decreasing pressure, and increasing H2:hydrocarbon feed ratio. These results are supported by experimental two-phase data. The model is able to predict the product distribution of a typical hydrocracking feed to the Shell Middle Distillate Process qualitatively. 1. Introduction Legislation and market-related demand for cleaner diesel can be met using coal- and gas-based Fischer-Tropsch (F-T) technology.1-4 Table 1 and Figure 1 show that the diesel selectivity, which, here, is denoted by the C10-C20 fraction, of the F-T process is only 39 wt % at R values in the range of 0.85-0.90. The diesel yield can be improved to >60 wt % when the F-T process is run at R > 0.95 and the wax is then hydrocracked to diesel.4 The wax consists of mainly linear alkanes C30+ and is free of aromatic, sulfur, and nitrogen compounds. Therefore, the hydrocracking of F-T wax to diesel provides an opportunity for the development of new technologies. The wax stream represents a relatively “clean” feed; therefore, only one-step mild hydrocracking is necessary to achieve a high diesel yield and prevent overcracking.5 Typical operating conditions are 250-350 °C and 40-50 bar. The hydrocracking reaction pathway,6-13 in the presence of H2, can be represented by -H2
x
C-shift
alkanes(n) a alkenes(n) a carbenium ions a β-scission
+H2
isomers(n) f alkenes(i) + alkanes(j) a alkanes(i, j) overall: CnH2n+2 + H2 f CiH2i+2 + CjH2j+2 (where i + j ) n) (1)
The reaction happens over bifunctional catalysts, with the metal function being responsible for the hydrogenation/dehydrogenation, and the acid function being responsible for the isomerization and cracking. Nevertheless, when hydrocracking carbon numbers between C10 and C17, similar activation energies and * To whom correspondence should be addressed. E-mail:
[email protected].
increasing intrinsic reaction rates are observed with increasing carbon number.4 This indicates that, as a first approximation, the hydrocracking can be represented by a single event. These patterns in the hydrocracking were recognized by Archibald et al.14 and formulated into a semilumped model by Stangeland.15 The single events concept10-13,16-24 has been developed extensively to represent the elementary steps in the reaction pathway, including adsorption and Langmuir-Hinshelwood (LH)-type kinetics. This elegant technique leads to millions of reaction steps (e.g., C15 and C25 have 4347 and 30 million paraffinic isomers, respectively) and soon becomes impractical for even moderately sized hydrocarbon molecules, without some form of lumping.23,25 Two general approaches are used to reduce the kinetic mechanism into practically useful forms. The method Martens and Marin,23 which uses structural classes, which requires user input, and the method of Vale´ry et al.,13 which uses a lateral-chain decomposition method that can be automated. However, a very important feature of these approaches is that the number of unknown rate constants is minimized (one for each family of elementary steps) and the kinetics parameters are feedstock-independent. Numerous other techniques based on lumping have been attempted (for example, grouping by carbon number or continuous mixtures based boiling point),26 but these all are dependent on feed type and require extensive calibration each time the feed is changed. The hydrocracking reaction conditions typically result in the presence of gas and liquid phases in the reactor, in addition to the adsorbed phase, which occurs in the catalyst pores. Early reactor models do not address the presence of a liquid phase in the reactor,15-17,19,20,26-29 although it has been shown to play an important role in the hydrocracking of long-chain hydrocarbons.4,26 More-recent reactor models12,13,23,30-32 have alluded to the interaction between the gas, liquid, and adsorbed phases.
10.1021/ie801350p CCC: $40.75 2009 American Chemical Society Published on Web 03/10/2009
3792 Ind. Eng. Chem. Res., Vol. 48, No. 8, 2009
It has been shown30 that the adsorption selectivity of linear alkanes from the liquid phase is unity; hence, the presence of a liquid phase eliminates the influence of adsorption on reactivity and selectivity. This is contrary to gas-phase reactor conditions, in which adsorption influences the reactivity and selectivity as a result of the adsorption selectivity. It is generally assumed that the (de)hydrogenation steps are fast, giving maximum isomer yields. This is termed ideal hydrocracking. Therefore, the selectivity is almost independent of catalyst type, very similar to the data presented in the Shell Middle Distillate Synthesis (SMDS) process.4 Thybaut et al.33 argued that this is not always the case and is dependent on operating conditions and the catalyst metal:acid activity ratio; this is termed nonideal hydrocracking. Nonideal hydrocracking is favored under conditions of decreased total pressure, increased temperature, increased molar hydrogen:hydrocarbon inlet ratio, and longer hydrocarbon chain lengths. This has only been studied in the gas phase up to C16. More-recent work by Kumar and Froment12 extended this concept for vapor-liquid systems with carbon numbers up to C33. There are few literature sources that provide experimental data for two-phase hydrocracking and even less for wax hydrocracking.4,12,13,21,32,34 In particular, data giving selectivity (or yield) as a function of conversion at constant conditions, or selectivity at constant conversion over various operating conditions is not available in the literature. Therefore, the data that can be used for model verification are not readily available and generally are grouped by carbon number. The cetane number, which is a parameter of interest, can thus not be inferred from the product distribution, although it is reported.34 The model of Pellegrini et al.32 categorized data by carbon number and distinguishes between normal paraffins or isoparaffins. The vapor-liquid equilibrium (VLE), which is held constant between integration steps, is described by the Soave-Redlich-Kwong equation of state (SRK-EOS), which was extrapolated up to C70. The model approximates β-scission reactions by allowing cracking only on the central C-C bond while other species reactivities are generated with a reaction rate probability distribution. Thus, for example, C9 can only be formed from C17, C18, and C19. It is not possible to form C9 via all the other possible intrinsic reaction steps applicable to C12+ species. Langmuir adsorption is accounted for in both liquidand vapor-phase reactions using regressed constants. However, the liquid-phase Langmuir parameters vary with carbon number, contrary to those reported in the literature.30 To improve the model prediction, “different multiplying factors”32 to the vapor and liquid phases are used. The predictability of the model declines as conversion increases above 70%. Vale´ry et al.13 incorporated isomerization and β-scission kinetics to describe the hydrocracking of squalane. Hydrogenation (or dehydrogenation) and phase equilibrium is assumed, but it is not clear if VLE is embedded in the model. Kumar and Froment,12 in addition, also include the (de)hydrogenation kinetics and phase mass-transfer resistance and therefore provide the most complete hydrocracking model to date, implemented up to C32. This model is able to investigate the influence of nonequilibrium in the (de)hydrogenation step. These models provide qualitative prediction of experimental data (C16,12 C3013); however, the prediction over wide ranges of temperature and pressure or larger carbon numbers is not verified. The objective of this work is to develop a hydrocracking model that sacrifices complexity but retains the primary building blocks and kinetic expressions, in an attempt to provide a simple, quick estimation of up to C120 wax hydrocracking performance.
Figure 1. Anderson-Schulz-Flory (ASF) product distribution obtained during Fischer-Tropsch (F-T) processing, as a function of the chain growth probability (R).
Figure 2. Schematic diagram of the two-phase reactor model. Table 1. Calculated Product Distributions as a Function of Chain-Growth Probabilitya Content (wt %) chain-growth probability, R
C20
0.80 0.85 0.90 0.95 0.98 0.99
62.4 45.6 26.4 8.60 1.60 0.40
31.80 38.9 37.1 19.8 4.90 1.40
5.80 15.50 36.57 71.70 93.50 98.20
a
Data taken from ref 2.
The model will be based on elementary β-scission kinetics applied to paraffin species lumped by carbon number in an ideal co-current reactor configuration with two-phase flow coupled by equilibrium. The model intends to elucidate the influence of VLE on activity and selectivity by studying a model C80 compound that is free of any distortions due to lumping. The quality of the model will be assessed using experimental data from the literature. 2. Model Development Assumptions (see Figure 2): (1) β-Scission cracking of carbon number lumps adequately represents the kinetic pathway and the reactivity change with carbon chain length. (2) The (de)hydrogenation and isomerization reactions are in equilibrium, and the β-scission reaction rate remains unaffected by these species. (3) Reactions are first order, with respect to the liquid phase concentrations of the hydrogen and hydrocarbons.
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reactions that follow thereafter, with the final products being C3-C5 fragments. This assumes that the type A-C skeletons are equally distributed throughout the carbon skeleton, with each configuration having the same probability of undergoing β-scission. This leads to increases in reaction rate with increasing carbon number, because of the increase in the number of β-scission active centers on the carbon skeleton. The reaction rate expressions take the form given by eq 2: n
L ri(C L) ) C HL 2[k1(C i+3 - C Li ) + k2(2 -
∑C
L j
- (i - 7)C Li )]
j)i+4
(2)
Figure 3. Simplified represenation of the hydrocracking reaction pathway.
(4) The reaction occurs in two phases, vapor and “pseudoreactive” liquid, in which the liquid-filled catalyst pore is incorporated into the liquid phase. (5) The vapor and liquid phase are in equilibrium, which can be adequately represented by a Peng-Robinson equation of state (PR-EOS). (6) An ideal isobaric, isothermal, co-current trickle-bed reactor in which the catalyst always remains homogeneously wetted. (7) There are no gas film or pore diffusion limitations. 2.1. Reaction Kinetics. In the development of the kinetic equations, it has been assumed that the β-scission is the ratecontrolling step, as shown in Figure 3. All other steps are assumed to be either fast or at equilibrium, which seems to be the case for longer-chain hydrocarbons.7-9,11 The rapid isomerization of the carbenium ions over strong acid sites provides a pool of hydrocarbon species with 1°, 2°, and 3° carbon atoms that are essentially in equilibrium. For carbon numbers of
