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Ind. Eng. Chem. Res. 2005, 44, 3402-3411
Two Severity Indices for Scale-Up of Steam Cracking Coils Kevin M. Van Geem, Marie-Franc¸ oise Reyniers,* and Guy B. Marin Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281 (S5), B-9000 Gent, Belgium
A direct experimental scale-up method is presented for steam cracking of hydrocarbon feedstocks. It is based on the “severity” concept but uses two severity indices instead of one to unambiguously characterize the product yields for a given feedstock. Reaction path analysis suggests that the combination of the ethylene/ethane yield ratio and the methane yield characterizes the complete product spectrum. Simulation results for n-butane cracking in a pilot plant reactor, a Lummus SRT-1 reactor, and a 4-2-1 split coil reactor confirm that the same product spectrum is obtained for identical values of both indices in the different reactor geometries although the process conditions differ strongly. The soundness of the approach is further corroborated by experimental results obtained from a pilot plant reactor and a small scale Uno-Quattro coil. This approach is only valid when similar feedstocks are used. A rule of thumb is that the highest PIONA weight fraction for a feedstock cannot deviate by more than 5% of the corresponding value for the reference feedstock. Stronger deviations in feedstock composition lead to larger differences between the product spectra. 1. Introduction Steam cracking of hydrocarbons is the main process for the production of almost all valuable base chemicals, especially for ethylene and propylene production. The process is carried out in reactor coils with a diameter between 0.03 and 0.15 m and a length of maximum 100 m placed in large furnaces. Feedstocks range from ethane to complex mixtures such as naphthas, gas oils, and even vacuum gas oils (VGOs). Steam is added to the hydrocarbon feedstock to decrease the coke deposition in the reactor coil and to increase the light olefin selectivity. Short residence times (0.1-1 s) and high coil outlet temperatures (up to 900 °C) are typically applied because they positively influence the ethylene yield. The operating conditions vary strongly along the reactor coil. The temperature rises fast from 600 °C at the reactor inlet to 850 °C at the outlet while the pressure drops from about 0.3 MPa to atmospheric pressure. The reactor effluent is rapidly quenched in a few milliseconds in the transfer line exchanger (TLE) to 350 °C to avoid losses of valuable light olefins by secondary reactions.1,2 High Reynolds numbers (Re > 250 000) and heat fluxes to the reactor (50-100 kW m-2) are characteristic in an industrial steam cracker. Scaling-up steam cracking coils is a difficult task. Two possible methods are commonly applied: mathematical modeling and direct experimental scale-up.3 Mathematical modeling is probably the most attractive solution because it has the advantage that once the model is developed, results can be easily gathered and computer simulations take only a limited time.4 Although there is a general consensus about the free radical mechanism, several different types of kinetic models are used and developed to simulate the steam cracking process. A distinction can be made between three different types of models: empirical, global, and detailed kinetic models. For industrial practice, only the last category is able to provide enough flexibility and accuracy, but develop* To whom correspondence should be addressed. Tel.: 32 9 264 45 17. Fax: 32 9 264 49 99. E-mail:
[email protected].
ing such a detailed reaction network is a major challenge. On one hand, the size of the reaction network can become huge, as the number of reactions and species increases exponentially with the average carbon number of the feedstock.5 On the other hand, developing these reaction networks implies that both the thermochemistry and kinetic parameters are known. Moreover, fundamental kinetic models work with a detailed feedstock composition, and obtaining this information for naphthas, gas oils, and VGOs is not straightforward. Therefore, direct experimental scale-up is still an interesting option. A commonly applied direct scale-up method is based on the “severity” concept. Scale-up is then performed based on experimental data obtained at the same severity.6,7 This approach is used not only for scale-up but also for control of process conditions. Ideally, in industry, one would like to have a single controllable measure of the severity of the cracking that is independent of the scale of the reactor and that can function as a variable that can be set in order to obtain the desired product spectrum. For this reason, the propylene over ethylene yield ratio (P/E ratio) is still used in industrial practice. However, a single severity index does not unambiguously characterize the products yields.8 In the present contribution reaction path analysis is applied to find a set of independent severity indices that is able to uniquely determine the product spectrum and that directly relates to a settable variable, such as the dilution, the coil inlet pressure (CIP), or the coil outlet temperature (COT). 2. Selection of Severity Indices Product yields depend on process conditions such as temperature, feedstock, dilution, total pressure, and residence time. The temperature profile and the partial pressure profile of the reactants in the reactor directly determine the reaction rates and, hence, characterize the product yields. Other process conditions such as residence time or dilution influence the product yields via the temperature profile and/or the partial pressure. The total pressure and the dilution influence the partial
10.1021/ie048988j CCC: $30.25 © 2005 American Chemical Society Published on Web 04/02/2005
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pressures in an obvious way. Van Damme et al.9 and Plehiers and Froment10 showed that there exists a strong correlation between the residence time and the established temperature profile. These showed that cracking at lower residence times requires higher temperatures to achieve a desired conversion, implying that, at lower residence times, reactions with a high activation energy are favored (that is, C-C and C-H β-scission reactions), resulting in a higher selectivity to light olefins. In addition, the selectivity to heavier products such as aromatics will be lower, as they are formed by addition reactions with relatively low activation energies. Also, the definition of the residence time θ in eq 1 suggests that the residence time is not an independent variable but that it is a function of the temperature and the pressure profile in the reactor.
θ)
∫dθ ) ∫
1 dV ) Q
pt dV FtRT
∫
(1)
As there is only a weak correlation between the temperature profile and the partial pressure profile, at least two severity indices are required to characterize the product yields: one providing a measure for the temperature and the other providing a measure for the reactants’ partial pressure in the reactor coil. For a given feedstock, a judicious selection of the latter could possibly allow to account for the partial pressures of all the mixture components and, hence, in combination with a severity index characterizing the temperature profile, completely determine the product yields. 2.1. Severity Index Accounting for the Temperature. In view of the endothermic character of the steam cracking process, it is obvious that higher conversions are coupled to higher temperatures. Hence, the most concise measure for the temperature is the feedstock conversion or a severity index that correlates well with the conversion. One of the main problems of using the feedstock conversion is that its definition is straightforward for single components only and even then its use is not trivial; for example, the conversion cannot exceed 100% while the product distribution still changes. These drawbacks have led to the definition of several other severity indices, for example, the methane yield, the propylene over ethylene yield ratio, the equivalent reactor volume, and so forth. According to Froment and co-workers, the best measure for the conversion is the equivalent reactor volume.1,11-13 The equivalent reactor volume, VE, is the volume of an isothermal and isobaric reactor that operates at a reference temperature, TR, and a reference pressure, pR, yielding the same conversion as the actual reactor with its temperature and pressure profile. The
VE )
pT
[ ( E
∫0V ptRTR exp - Ra T1 - T1R
)]
dV
(2)
equivalent reactor volume meets all the requirements for an appropriate severity index, as its relation with conversion is independent of the operating conditions, the reactor geometry, and the feed composition.13 In addition, unlike the conversion, the equivalent reactor volume does not have an upper limit. However, it requires knowledge of the temperature and pressure profile, which is seldom the case in industry. Hence, other severity indices seem more appropriate. Reaction
Figure 1. Elementary steps in the reaction of a component S via Rice-Herzfeld pyrolysis.14 Simplified reaction network used for the selection of a severity index that is an appropriate measure for the temperature. [kC-C is the reaction rate coefficient of a C-C scission reaction, kab is the reaction rate coefficient of a hydrogen abstraction reaction, and kβ is the reaction rate coefficient of a β-scission reaction.] Table 1. Characteristic Values for the Activation Energy of the Different Types of Reactions Involved in Steam Cracking
reaction type
activation energy (kJ mol-1)
hydrogen abstraction (formation of primary radical) hydrogen abstraction (formation of secondary radical) hydrogen abstraction (formation of tertiary radical) β-scission of radical (C-C bond breaking) β-scission of radical (C-H bond breaking) addition isomerization
50 40 30 120 170 20 50
path analysis is applied to select a severity index that correlates well with the temperature in the reactor. A detailed description of the steam cracking process is only possible using a fundamental reaction network involving hundreds of species and thousands of elementary reactions. However, the qualitative features can be presented by a simplified network. The reaction scheme proposed by Nigam et al.14 in Figure 1 for the RiceHerzfeld pyrolysis of a single component S is used to find an appropriate measure for the conversion. From the previous paragraphs, it is obvious that this index will then also be a good measure for the temperature in the reactor. According to Rice and Herzfeld, steam cracking of hydrocarbons proceeds through a free-radical mechanism where three important reaction families can be distinguished: (1) carbon-carbon and carbonhydrogen bond scissions in molecules without radical character and the reverse radical-radical recombinations; (2) hydrogen abstraction reactions, both intra- and intermolecular (Isomerization reactions are intramolecular hydrogen abstractions.); (3) radical addition to olefins and the reverse β-scission of radicals, both intraand intermolecular (Cyclization reactions are intramolecular additions.). In Table 1, characteristic values for the activation energies are given for the different types of reactions from these families. Hydrogen abstraction reactions and addition reactions are bimolecular reactions that have low activation energies. β-Scission reactions are monomolecular reactions with high activation energies. Hence, high temperatures and low pressures favor β-scission reactions, while low temperatures and high pressures favor addition reactions and hydrogen abstractions. Three different types of products are formed via the intermediate µ- and β-radicals in the simplified reaction network of Figure 1: primary products (P1), products formed via hydrogen abstraction reactions (H-β), and products formed via recombination reactions. The yields of the latter are generally negligible under standard cracking conditions. In the scheme, a distinction is made between two different types of radicals: β-radicals with a β-character and µ-radicals with a µ-character.15 µ-Rad-
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Table 2. Values of the Reaction Rates for All C-C Scission Reactions and All Hydrogen Abstraction Reactions during the Cracking of Pure n-Hexane. reaction rate (mol m-3 s-1) 5% reactor 50% reactor 95% reactor length length length ∑i ri(C-C scission reactions)a 3.42 × 10-1 1.71 × 10-1 5.45 × 10-2 ∑i ri(Hydrogen abstractions)b 65.05 4.83 2.39 a ∑ r (C-C scission reactions) ) the sum of the reaction rates i i of all C-C scission reactions of hexane. b ∑i ri(Hydrogen abstractions) ) the sum of the reaction rates of the hydrogen abstraction reactions by all radicals.
icals react in unimolecular β-scission reactions only. Large radicals formed directly from the feed molecules mainly have a µ-character. This does not imply that µ-radicals do not take part in reactions such as hydrogen abstractions or addition reactions, but their reaction rate via these types of reactions is much lower than the reaction rate via β-scission. Isomerization reactions are also possible for µ-radicals, but after isomerization a β-scission again takes place. The reaction rate of these isomerization reactions is generally more than 1 order of magnitude higher than the reaction rate of the subsequent β-scission. β-Radicals are mainly short radicals with five or less carbon atoms that undergo bimolecular reactions such as hydrogen abstractions and addition reactions. These β-radicals are not only species such as the hydrogen (H•) and the methyl (CH3•) radicals, that do not have any other reaction possibility, but also the ethyl (C2H5•), propyl (C3H7•), vinylic (C2H3• and vC3H5•), and allylic (C3H5• and C4H7•) radicals. All the above-mentioned small radicals except the hydrogen and the methyl radicals also have a µ-character. However, compared to the β-character, the µ-character is less pronounced and becomes important only at higher temperatures. The reason is that radicals such as the ethyl radical and the but-1-en-3-yl radical have no C-C bond in the β-position but only have a C-H bond. Scission of this C-H bond has a very high activation energy, that is, 170 kJ mol-1, and, hence, becomes important only at high temperatures. Consequently, these radicals have a β-character at low temperatures while, at high temperatures, they have both a β-character and a µ-character. The elementary steps in the simplified reaction scheme suggest that two reactions are equally important in determining the conversion: the hydrogen abstraction reactions and the C-C scission reaction of the feed molecule. However, the reaction rate of the hydrogen abstraction reaction is significantly higher than the reaction rate of the C-C scission reaction of the feed molecules. The latter is illustrated in Table 2, where the sum of the reaction rates of all hydrogen abstraction reactions and the sum of the reaction rates of all C-C scission reactions are given at different positions in the reactor for the cracking of pure n-hexane. In the steady state, the rate of initiation and the rate of termination are equal, and the kinetic chain length, defined by the ratio of the rate of propagation to the rate of termination, is equal to the ratio of the rate of propagation to the rate of initiation. For steam cracking of hydrocarbons under standard cracking conditions, a kinetic chain length in the order of 100 can then be expected (see the results in Table 2). Hence, the reaction rate of the hydrogen abstraction reactions determines the conversion of the feed component S. The reaction rate of the C-C scission reactions versus the recombination reac-
Figure 2. Set of elementary steps for the Rice-Herzfeld pyrolysis of a single component S. Reaction network used to identify a severity index that is a reliable measure for the reactants’ partial pressures. [kC-C is the reaction rate coefficient of a C-C scission reaction, kab1 and kab2 are the reaction rate coefficients of hydrogen abstraction reactions, kad is the reaction rate coefficient of an addition reaction, and kβ1, kβ2, and kβ3 are the reaction rate coefficients for the β-scission reactions.]
tion determines the global radical concentration and, thus, the concentration of β-radicals that can abstract a hydrogen from the feed molecule S. Although this conclusion might seem trivial, it is not; it indicates that the yields of the products formed via hydrogen abstraction reactions of feed molecules, that is, the products H-β in the reaction scheme, are directly related to the conversion. One of those products is methane; methane is almost entirely produced from hydrogen abstractions with methyl radicals. This suggests that the methane yield can be considered as an excellent measure for the conversion and, hence, as stated in the previous section, for the temperature in the reactor. However, the methane yield is not entirely independent of the reactants’ partial pressures. Van Camp et al.13 showed experimentally that the methane yield does indeed depend on the reactants’ partial pressures, but the dependence is not strongly pronounced. At low severities, that is, methane yields
