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. 2019 Dec 9;4(26):22237–22244. doi: 10.1021/acsomega.9b03707

Thermodynamic Equilibrium Analysis of Product Distribution in the Fischer–Tropsch Process Under Different Operating Conditions

Junjie Chen 1,*, Cheng Yang 1
PMCID: PMC6933804  PMID: 31891107

Abstract

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Thermodynamic equilibrium analysis is necessary to provide a fundamental understanding of the distribution of the products formed in the Fischer–Tropsch process. The thermodynamic equilibrium distribution of the products formed at constant temperature and pressure was studied based on the minimization of the total Gibbs free energy of the system. The effects of temperature, pressure, and feed ratio on the product distribution were investigated under typical operating conditions. The distribution of the total products obtained from the reactions of added ethylene or ethanol was also studied. The results indicated that the products formed in a state of thermodynamic equilibrium follow Anderson–Schulz–Flory’s general polymerization distribution at carbon numbers greater than about three. Both olefins and paraffins are primary products and there are essentially no alcohol and water at high degrees of conversion when the conditions for thermodynamic equilibrium are satisfied. The olefins formed in the Fischer–Tropsch process consist essentially of propylene. The product distribution is very sensitive to feed composition, and to temperature and pressure to a lesser extent. The product spectrum can be described broadly by the probability of chain growth relative to chain termination. This parameter decreases with increasing temperature, the feed ratio of hydrogen to carbon monoxide, and after the addition of ethanol to the feed, but increases with increasing pressure and after the addition of ethylene to the feed. An increase in reaction temperature results in a shift in selectivity towards low carbon number hydrocarbons and more hydrogenated products.

1. Introduction

As the major component of natural gas, methane has attracted increasing attention in recent years. The primary chemical reactions of methane are steam reforming to synthesis gas, oxidation, and halogenation.1,2 The quest for an efficient process to convert methane efficiently to high value-added chemicals is motivated by the ever-increasing demands placed on them as well as recently discovered rich reserves of methane. Direct conversion into high value-added chemicals can be realized either nonoxidatively via methane dehydroaromatization3,4 or oxidatively via oxidative coupling of methane.5,6 Alternatively, methane can be catalytically converted to C2 and higher hydrocarbons via an indirect route, and this process is usually carried out in two steps. Methane is converted into synthesis gas containing carbon monoxide and hydrogen in a steam reforming process or in a partial oxidation process,7,8 followed by final conversion to higher hydrocarbons. Synthesis gas can also be produced from other sources, such as coal, biomass, and virtually any hydrocarbon feedstock, by reaction with steam, oxygen, or carbon dioxide.9,10 The production of hydrocarbons from synthesis gas is usually referred to as the Fischer–Tropsch process.11,12 Catalysts used in this process are typically comprised of a catalytically active metal from one of Group VIIIB elements.13,14 In particular, iron,15,16 cobalt,17,18 nickel,19,20 and ruthenium21,22 have been extensively used as the catalytically active materials for the Fischer–Tropsch process. Cobalt and ruthenium are particularly effective for the catalytic conversion of synthesis gas to primary hydrocarbons having five or more carbon atoms.23,24

The main products formed in the Fischer–Tropsch process range from methane to higher alkanes and aliphatic alcohols.25,26 The process is critical to the production of liquid fuels and chemicals from carbonaceous feedstock.27,28 Despite the research that has been done to date, the need exists for further improvement in commercial Fischer–Tropsch processes.29,30 For example, a great deal of effort has been made to develop more efficient Fischer–Tropsch reaction systems and catalyst systems, which will eventually lead to an increase in the selectivity for high-value hydrocarbon products from the Fischer–Tropsch processes.31,32 In particular, iron, cobalt, and ruthenium based catalysts have been developed for use in various reactor types,33,34 and much progress has been made in preparation technology.35,36

There is a significant difference in the distribution of the hydrocarbon products formed from different Fischer–Tropsch reaction systems.37,38 The selectivity to the desired product depends upon the conditions under which the Fischer–Tropsch process is performed.39,40 Accordingly, it is highly desirable to improve the selectivity to the desired high-value liquid fuels and chemicals, such as primarily hydrocarbons having five or more carbon atoms. These hydrocarbons, which correspond to gasoline or diesel products, are expected to be in great demand. Traditional methods produce a range of hydrocarbon products,41,42 which can be characterized by the Anderson–Schulz–Flory distribution, irrespective of catalyst type.43,44

Recent studies suggested that thermodynamic equilibrium analysis is necessary to provide a fundamental understanding of the distribution of the products formed in the Fischer–Tropsch process, and the importance of such a product distribution should not be underestimated.45,46 This thermodynamic method offers greater flexibility for complex problems for which the pathways of the Fischer–Tropsch reactions are unclear. Furthermore, this thermodynamic equilibrium distribution may have important implications for the improvement in the selectivity of the desired products. However, further studies are needed to determine the distribution of the Fischer–Tropsch products formed in a state of thermodynamic equilibrium.

In this study, the thermodynamic equilibrium distribution of the products formed in the Fischer–Tropsch process was investigated at constant temperature and pressure. The effects of different operating conditions on product distribution were evaluated using a thermodynamic equilibrium calculation on the basis of the minimization of the Gibbs free energy. The distribution of the total products obtained from the reactions of added ethylene or ethanol was also studied. The objective of this study was to determine the thermodynamic equilibrium distribution of the products formed in the Fischer–Tropsch process under different operating conditions. Particular emphasis was placed on determining how the carbon number product distribution depends on various operating conditions.

2. Results and Discussion

The primary compounds involved in the products may be primary olefins in the C2–C15 range,47,48 normal paraffins in the C1–C15 range, normal alcohols in the C1–C8 range, water, and carbon dioxide.49,50 In all of the cases studied herein, complete conversion of carbon monoxide and hydrogen is assumed, and all the products are in the vapor phase. The effects of different operating conditions on product distribution are investigated under typical operating conditions using the equilibrium modeling method described later.

2.1. Effects of Temperature and Pressure

The effect of changing temperature on the distribution of Fischer–Tropsch products is studied. The results obtained for different temperatures are presented in Figure 1, wherein the distribution of the product is expressed as a function of the number of carbon atoms. The temperatures of the product mixture considered here are 510, 525, and 540 K, respectively, the pressure is 1.5 MPa, and the usage ratio is 0.7. The usage ratio typically varies between 0.5 and 1.0 for iron-based catalysts and has been found to be about 0.7, obtained from the majority of the results available.51,52 The logarithm of the mole fraction of the total organic products is plotted against the number of carbon atoms.

Figure 1.

Figure 1

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Distribution of the total products at different temperatures. The logarithm of the mole fraction of the total organic products is plotted against the carbon number. The temperatures of the product mixture are 510, 525, and 540 K, respectively, the pressure is 1.5 MPa, and the usage ratio is 0.7.

At each temperature of the thermodynamic equilibrium system, there is a linear relationship between the number of carbon atoms and the concentration of the C4 plus products. An increase in reaction temperature results in a shift in selectivity towards low carbon number hydrocarbons, as depicted in Figure 1. This shift in selectivity is consistent with the relative stability of the products. Therefore, low carbon number hydrocarbons are thermodynamically favored at high temperatures. Chain growth probability is somewhat sensitive to the reaction temperature. More specifically, this parameter decreases from 0.72 to 0.68 when the temperature of the thermodynamic equilibrium system increases from 510 to 540 K. Chain growth probability decreases with increasing temperature, which is in consistence with the experimental results available in the literature.47,48 In addition, the ratio of the amount of C3 product to that of C2 product increases with increasing temperature, which is also in consistence with the experimental results available in the literature.47,48 This ratio indicates the extent of the reincorporation of C2 product.47,48

The Fischer–Tropsch reactions are assumed to be carried out under different pressure conditions, and the effect of changing pressure on the distribution of Fischer–Tropsch products is investigated. The results obtained for different pressures are presented in Figure 2, wherein the distribution of the product is expressed as a function of the number of carbon atoms. The temperature of the product mixture is 540 K, and the usage ratio is 0.7. The pressures used in the Fischer–Tropsch process are 0.38, 0.75, and 1.5 MPa, respectively, and thus pressure variations are significant. The results indicate that high carbon number hydrocarbons are thermodynamically favored at high pressures. Chain growth probability is somewhat sensitive to pressure. More specifically, this parameter varies from 0.56 at a pressure of 0.38 MPa to 0.68 at a pressure of 1.5 MPa.

Figure 2.

Figure 2

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Distribution of the total products at different pressures. The temperature of the product mixture is 540 K, the usage ratio is 0.7, and the pressures are 0.38, 0.75, and 1.5 MPa, respectively.

Irrespective of the temperatures and pressures considered herein, the products formed in a state of thermodynamic equilibrium follow Anderson–Schulz–Flory’s general polymerization distribution at carbon numbers greater than about three, as predicted in Figures 1 and 2. The Fischer–Tropsch synthesis may be viewed as a simple polymerization reaction, and the monomer is carbon monoxide or a C1 species derived from it. Schulz53,54 derived an equation for the distribution of molecular weights of polymers obtained by a free radical polymerization process, i.e., through a one-by-one addition of monomer to a growing chain. If there is a constant probability of chain growth, the Schulz distribution function is generally applicable. Flory55 and Anderson56 continued efforts to account for the products formed by chain branching, to derive theoretical distribution functions for various types of macromolecular formation, and to develop chain growth mechanisms. The polymerization process can be described by the Anderson–Schulz–Flory distribution if the chain growth probability is assumed to be independent of the chain length.

2.2. Effect of Feed Ratio

The usage ratio defined in eq 1 is equal to the feed ratio of hydrogen to carbon monoxide, as a complete conversion of hydrogen and carbon monoxide is assumed in the Fischer–Tropsch process. The results obtained for different feed ratios are presented in Figure 3, wherein the distribution of the product is expressed as a function of the number of carbon atoms at a specified temperature and pressure. The temperature of the product mixture is 540 K, the pressure is 1.5 MPa, and the feed ratios of hydrogen to carbon monoxide considered here are 0.6, 0.7, and 0.8, respectively.

Figure 3.

Figure 3

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Distribution of the total products at different feed ratios of hydrogen to carbon monoxide. The temperature of the product mixture is 540 K, the pressure is 1.5 MPa, and the feed ratios are 0.6, 0.7, and 0.8, respectively.

There is difference in the distribution of the products formed under different feed ratio conditions, as depicted in Figure 3. For each feed ratio of hydrogen to carbon monoxide, there is a linear relationship between the number of carbon atoms and the concentration of the C4 plus products. Corresponding to each feed ratio, chain growth probability is determined based on the C4 plus products. Chain growth probability is very sensitive to feed ratio. This parameter decreases from 0.76 at a usage ratio of 0.6–0.58 at a usage ratio of 0.8. Chain growth probability is 0.68 at a usage ratio of 0.7, which is the average reported in the literature.51,52 When the whole system is at thermodynamic equilibrium at the specified temperature and pressure, the selectivity to methane is between 0.4 and 0.6 in the Fischer–Tropsch product stream.

The selectivity to methane depends on the conditions under which the Fischer–Tropsch process is performed, for example, the feed ratio of hydrogen to carbon monoxide, as depicted in Figure 3. An increase in the feed ratio of hydrogen to carbon monoxide results in a shift in selectivity toward low carbon number hydrocarbons, especially towards methane. In all of the cases studied herein, complete conversion of carbon monoxide and hydrogen is assumed, as described above. Under the specified conditions, the selectivity to methane is relatively low due to low feed ratios of hydrogen to carbon monoxide used in this study. This has important implications for the improvement in the selectivity of the desired products. Higher feed ratios of hydrogen to carbon monoxide tend to favor the formation of methane, i.e., methanation, as depicted in Figure 3. This is particularly undesirable. For practical applications, however, a variety of feed ratios can be used for the Fischer–Tropsch process.11,12 The optimum feed ratio of hydrogen to carbon monoxide is about 1.8–2.1 for cobalt-based catalysts.13,14 Iron-based catalysts can tolerate lower feed ratios due to intrinsic water–gas shift reaction activity of iron-based catalysts.57,58 Nickel-based catalysts can also be used, but tend to favor the formation of methane,59,60 especially under high-feed ratio conditions.

2.3. Formation of Alcohols and Water

The amount of alcohols formed in the Fischer–Tropsch process is predicted by Newton’s method. Interestingly, the products resulting from the Fischer–Tropsch synthesis contain essentially no alcohols at high degrees of conversion, when the conditions for thermodynamic equilibrium are satisfied for the reaction system. Therefore, alcohols are not favored as products under the specified conditions, and the product distribution depicted in Figure 3 is entirely that of normal paraffins and primary olefins. This offers an explanation for the results available in the literature,47,48 in which the amount of alcohol formed in the Fischer–Tropsch process has been found to decrease with decreasing space velocity. It is worth noting that low space velocities enable the distribution of the products to approach chemical equilibrium.

When the conditions for thermodynamic equilibrium are satisfied, the amount of water predicted by Newton’s method is essentially zero at high degrees of conversion. It has been found that only a small amount of water formed over an iron-based catalyst,47,48 as it is apparently limited by the water–gas shift reaction. This reaction favors the formation of hydrogen and carbon dioxide rather than that of carbon monoxide and water vapor at the temperatures considered here, given the fact that the conversion of reactants to products becomes less favorable with increasing reaction temperature61,62 due to the exothermic nature of the Fischer–Tropsch reactions.

2.4. Formation of Olefins

The amount of olefins formed in the Fischer–Tropsch process will vary depending on the way in which the process is carried out.47,48 To better understand the distribution of the products, the effect of the reaction temperature is investigated on the basis of the minimization of the Gibbs free energy. The predicted mole fractions of olefins at each carbon number as a function of the number of carbon atoms at different temperatures are depicted in Figure 4. The temperatures of the product mixture considered here are 525 and 540 K, respectively, the pressure is 1.5 MPa, and the usage ratio is 0.7.

Figure 4.

Figure 4

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Olefin mole fractions obtained at each carbon number at different temperatures. The temperatures of the product mixture are 525 and 540 K, respectively, the pressure is 1.5 MPa, and the usage ratio is 0.7.

The results indicate that Fischer–Tropsch products contain a certain amount of olefins, in all of the cases studied herein, with the amount dependent to some extent on the conditions used. The low carbon number hydrocarbons formed in the Fischer–Tropsch process are fairly olefinic. The products contain varying amounts of olefins depending on the temperature employed. An increase in reaction temperature results in a shift in selectivity towards more hydrogenated products, as depicted in Figure 4. This shift is consistent with the relative stability of the products. The amount of olefins present in the products is quite different from each other. The concentration of C2 olefinic products is low, the concentration of C3 olefinic product is high, and the concentration of high-molecular-weight olefinic products in the C4–C10 range is essentially constant. Therefore, the olefins formed in the Fischer–Tropsch process are predominantly primary olefins, consisting essentially of propylene, under the specified conditions. On the other hand, the amounts of olefins decrease with decreasing temperature. Therefore, higher temperature operation favors an olefinic product.

2.5. Effect of Ethylene or Ethanol to the Feed

There exists evidence that some species such as olefins and alcohols may become incorporated into growing chains,63,64 but the extent to which this occurs seems to vary greatly with reaction conditions.65,66 The distribution of the total products formed in the Fischer–Tropsch reactions of added ethylene or ethanol is studied using the equilibrium modeling method described later.

When the reaction system is in a state of thermodynamic equilibrium, the effect of the addition of ethylene to the feed on the distribution of the total products is depicted in Figure 5. The temperature of the product mixture is 540 K, the pressure is 1.5 MPa, and the usage ratio is 0.7. High carbon number hydrocarbons become more thermodynamically favorable after the addition of ethylene to the feed, and the presence of ethylene suppresses the conversion of carbon monoxide to methane through hydrogenation. Both of them are in consistence with the experimental data available in the literature.67,68 In addition, the presence of ethylene effects the chain growth probability. More specifically, this parameter varies from 0.68 in the absence of ethylene to 0.8 with a molar ratio of ethylene to carbon monoxide 0.2:1. Therefore, chain growth probability is very sensitive to the addition of ethylene to the feed. The addition of ethylene to the feed of carbon monoxide and hydrogen enhances the formation of propylene. Overall, ethylene acts as an effective chain initiator, as the presence of ethylene enhances the formation of high carbon number hydrocarbons.

Figure 5.

Figure 5

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Distribution of the total products after the addition of ethylene to the feed. The temperature of the product mixture is 540 K, the pressure is 1.5 MPa, and the usage ratio is 0.7.

On the other hand, the effect of the addition of ethanol to the feed on the distribution of the total products is depicted in Figure 6. Low carbon number hydrocarbons become more thermodynamically favorable after the addition of ethanol to the feed, and the presence of ethanol enhances the conversion of carbon monoxide to methane through hydrogenation. In addition, the presence of ethanol also affects the chain growth probability. More specifically, this parameter varies from 0.68 in the absence of ethanol to 0.56 with a molar ratio of ethanol to carbon monoxide 0.2:1. Therefore, chain growth probability is also very sensitive to the addition of ethanol to the feed. After the addition of a small amount of ethanol to the feed of carbon monoxide and hydrogen, however, the formation of alcohols with greater than two carbons is enhanced in the Fischer–Tropsch process. This is because ethanol also acts as a chain-growth initiator.69,70 Overall, the distribution of the total products is greatly affected by the addition of ethylene or ethanol to the feed.

Figure 6.

Figure 6

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Distribution of the total products after the addition of ethanol to the feed. The temperature of the product mixture is 540 K, the pressure is 1.5 MPa, and the usage ratio is 0.7.

3. Conclusions

The thermodynamic equilibrium distribution of the products formed in the Fischer–Tropsch process was studied based on the minimization of the Gibbs free energy. The following major conclusions can be drawn from this study.

  • The products formed in a state of thermodynamic equilibrium follow Anderson–Schulz–Flory’s general polymerization distribution at carbon numbers greater than about three.

  • Both olefins and paraffins are primary products. The olefins formed in the Fischer–Tropsch process are predominantly primary olefins, consisting essentially of propylene.

  • Product distribution and chain-growth probability are very sensitive to feed composition, and to reaction temperature and pressure to a lesser extent. An increase in the reaction temperature results in a shift in selectivity towards low carbon number hydrocarbons and more hydrogenated products.

  • The presence of ethylene or ethanol greatly affects the chain growth probability and both of them function as chain initiators.

  • Chain growth probability decreases with increasing temperature and the feed ratio of hydrogen to carbon monoxide but increases with increasing pressure. This parameter decreases after the addition of ethanol to the feed, but increases after the addition of ethylene to the feed.

  • Alcohols and water are thermodynamically unfavored at high degrees of conversion when the conditions for thermodynamic equilibrium are satisfied.

It is worth noting that a general distribution has been determined for the total products formed in the Fischer–Tropsch process, which is completely independent of the reaction mechanism and catalyst used. This general distribution is important to identify the difference in performance between different catalysts, and trends in product selectivity, through the comparison with the product distributions determined by experiment.

4. Development of the Model

The chemical mechanism of the Fischer–Tropsch synthesis is still being debated. This synthesis process involves a series of chemical reactions, and the overall chemical reaction can be expressed as

4. 1

in which U is the overall usage ratio of the Fischer–Tropsch reactions, and ai, bi, ci, d, and e are the undetermined stoichiometric coefficients of the products formed in the Fischer–Tropsch process. The products are assumed to be normal paraffins, primary olefins, normal alcohols, water, and carbon dioxide, as defined in the above equation. Paraffins constitute a specific type of reaction product of the Fischer–Tropsch synthesis included within the hydrocarbons. Paraffins generally do not react further under conditions applicable to the Fischer–Tropsch synthesis.71,72

Thermodynamic equilibrium analysis is of significant importance to determine the product distribution, as it can provide significant insight into the compositions and properties of complex mixtures,73,74 on the basis of the minimization of the Gibbs free energy.75,76 Therefore, thermodynamic equilibrium analysis is performed to determine the distribution of the products formed in the Fischer–Tropsch process under different operating conditions. The flexibility of the equilibrium modeling method used in this study is due to the ease with which the distribution of the products formed in the complex reaction system can be determined without needing to specify each chemical reaction equation, as noted above. When the conditions for all mechanical, chemical, and thermal equilibrium are satisfied, the reaction system is in a state of thermodynamic equilibrium.77,78 Therefore, the intensive properties of the product mixture are homogeneous. Global thermodynamic equilibrium is assumed in this study, and thus intensive properties such as temperature, pressure, concentration, and density are homogeneous throughout the whole thermodynamic system.

The important criterion for chemical equilibrium is that the Gibbs free energy is minimized for the overall chemical reaction proceeded at constant temperature and pressure. Therefore, the Fischer–Tropsch reactions are assumed to be carried out at constant temperature and pressure. It is possible to determine the distribution of the products formed in the Fischer–Tropsch process, based on the thermodynamic equilibrium at which the Gibbs free energy for the overall chemical reaction is minimized. To determine this distribution, it is required to minimize the total Gibbs free energy of the product mixture at thermodynamic equilibrium:

4. 2

in which G is the total Gibbs free energy of the product mixture at thermodynamic equilibrium under the particular conditions, Ni is the number of moles of each species, and Gi is the Gibbs free energy of species i in the product mixture.

The mass balance constraints are given for a single-phase reaction by

4. 3

in which Mk is the number of moles of element k fed to the thermodynamic reaction system, nk,i is the number of atoms of element k in species i, and Ni is the moles of species i leaving the system.

To minimize the total Gibbs free energy of the product mixture, Newton’s method is employed with the NASA computer program Chemical Equilibrium with Applications (CEA) developed by Gordon and McBride.79,80 Thermodynamic data are included with this program for reaction products and reactants. The thermodynamic data provided with the CEA program are in the form of least-squares coefficients. These data, in formatted form, are processed by subroutine UTHERM and stored for further use in the unformatted form. Thermodynamic data are expressed as temperature-dependent values. The amount of data for the thermodynamic properties of chemical species involved in the Fischer–Tropsch process is very large. Thermodynamic data are readily available through the CEA program and therefore are not provided herein. To obtain the Gibbs free energy of species i in the product mix as defined in eq 2, the ideal gas thermodynamic properties are corrected by using the Soave–Redlich–Kwong equation of state.81,82

The distribution of the products can be represented by

4. 4

in which Mn is the mole fraction of all the products having n carbon atoms, n is the number of carbon atoms in the chain, and α is the probability of chain growth relative to chain termination. Chain growth probability is defined as

4. 5

in which rp and rt are the rates of propagation and termination, respectively.

The mole fractions of the products formed in the Fischer–Tropsch process are usually plotted on a semilogarithmic scale,83,84 as chain growth probability can be determined from the slope of such a plot in the following form

4. 6

The logarithmic form of the above equation is a convenient way to characterize the distribution of the total products because a plot of log Mn is linear with the number of carbon atoms.

Mathematical models are of significant importance in the natural sciences such as chemistry.85 Validation of the model is carried out by comparing the numerical results with the experimental data available in the literature.86 Validation of a mathematical model means that the model within its domain of applicability possesses a satisfactory range of accuracy consistent with the intended application of the model.87,88

The experimental conditions are given as follows: the temperature of the product mixture is 536 K, the pressure is 1.48 MPa, and the feed ratio of hydrogen to carbon monoxide is 0.7. Computational simulations are carried out with the model using the same set of conditions to check the accuracy of the model by comparison with the experimental data. The comparison results are presented in Figure 7, wherein the distribution of the total products formed in the Fischer–Tropsch process, on the basis of methane-free products, is expressed as a function of the number of carbon atoms. The results obtained from the model are in good agreement with the experimental data.

Figure 7.

Figure 7

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Comparison of the distribution of the total products formed in the Fischer–Tropsch process, on the basis of methane-free products, at each carbon number with the experimental data available in the literature.86 The temperature of the product mixture is 536 K, the pressure is 1.48 MPa, and the feed ratio of hydrogen to carbon monoxide is 0.7.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 51506048).

The authors declare no competing financial interest.

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