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1 Model test set up methodology for HDS to improve the understanding of reaction pathways in HDT catalysts Paulo, D. 1,2 , Guichard, B. 2 , Delattre, V. 2 , Lett, N. 2 , Lemos, F. 1 1 Instituto Superior Técnico, Chemical and Biological Engineering Department, Lisbon, Portugal. 2 Institut Français du Pétrole Énergies nouvelles, Catalysis and Separation Division, Catalysis by Sulfides Department, Solaize, France. Abstract In this present work, the hydrodesulfurization (HDS) of 4,6-dimethyldibenzothiophene (4,6-DMDBT) was studied over three CoMo/Al 2 O 3 catalysts (dried, calcined and additive impregnated) in a fixed-bed reactor under standard conditions close to those usually used in diesel fuel hydrotreating following particularly the HYD and DDS pathways behaviors. The main focus was to identify some strong differences in behavior between the various catalysts and evaluate the effect of H 2 S, NH 3 and H 2 partial pressures on their relative catalytic performances. It was found by experimental and modelling results that, at standard conditions, the additive impregnated catalyst performs better and was less impacted by H 2 S adsorption than dried and calcined. Though, in the presence of high amounts of H 2 S, the additive impregnated showed to be the one differing mostly from H 2 S partial pressure. In addition, the study on the impact of nitrogen-based compounds (quinoline) revealed that all three catalysts are similar inhibited. In the same way, modifying the partial pressure of H 2 was found to enhance the activity of all catalysts, especially the HYD pathway. A more detailed study and additional experimental tests should be performed in order to improve the understanding on the relation between quinoline and H 2 S within the deep HDS of 4,6-DMDBT and to further develop the kinetic model created. Keywords: Diesel; middle distillates; 4,6-DMDBT; CoMo/Al 2 O 3 ; inhibition effect. 1 Introduction In order to decrease pollution caused by automobile vehicles, the sulfur content in diesel fuel has been drastically reduced over the years as witnesses the restrictive regulations. However, refining industries are processing heavier feedstocks and facing an increasing demand on fuels so, a better performance from the hydrodesulfurization (HDS) catalysts is required. The commercial catalysts commonly used for HDS reactions are molybdenum sulfides promoted by cobalt or nickel and supported over alumina. Nevertheless, if one aims to improve their performances, it is now necessary to identify precisely the limitations. It can be achieved by characterizing deeply the catalyst, using powerful tools or by carrying a kinetic study to identify the main limitation, inhibiting and activating parameters. To do so, it is necessary to evaluate the catalyst in representative conditions witnessing the way it will have to work in real conditions. In the HDS of middle distillates, as sulfur conversion increases the remaining species are mostly dibenzothiophenes. As 4,6-DMDBT, these compounds are very difficult to decompose. Moreover, these compounds are decomposed through two main and distinct pathways namely, hydrogenation (HYD) and direct desulfurization (DDS). Furthermore, the presence of the methyl groups on 4,6-DMDBT highly limits the reactivity and leads the HDS to selectively process through the hydrogenating route compared to the DDS one. The objective of this work was focused on the comprehension of the HDS mechanism on various representatives CoMo catalyst types in order to study the deep HDS of middle distillates in the range of operating conditions dedicated to the low pressure HDS.

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Page 1: Model test set up methodology for HDS to improve …...Model test set up methodology for HDS to improve the understanding of reaction pathways in HDT catalysts Paulo, D.1,2, Guichard,

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Model test set up methodology for HDS to improve the understanding of reaction pathways in HDT catalysts

Paulo, D.1,2, Guichard, B.2, Delattre, V.2, Lett, N.2, Lemos, F.1

1 Instituto Superior Técnico, Chemical and Biological Engineering Department, Lisbon, Portugal. 2 Institut Français du Pétrole Énergies nouvelles, Catalysis and Separation Division, Catalysis by Sulfides Department, Solaize, France.

Abstract

In this present work, the hydrodesulfurization (HDS) of 4,6-dimethyldibenzothiophene (4,6-DMDBT) was studied over three CoMo/Al2O3 catalysts (dried, calcined and additive impregnated) in a fixed-bed reactor under standard conditions close to those usually used in diesel fuel hydrotreating following particularly the HYD and DDS pathways behaviors. The main focus was to identify some strong differences in behavior between the various catalysts and evaluate the effect of H2S, NH3 and H2 partial pressures on their relative catalytic performances.

It was found by experimental and modelling results that, at standard conditions, the additive impregnated catalyst performs better and was less impacted by H2S adsorption than dried and calcined. Though, in the presence of high amounts of H2S, the additive impregnated showed to be the one differing mostly from H2S partial pressure.

In addition, the study on the impact of nitrogen-based compounds (quinoline) revealed that all three catalysts are similar inhibited.

In the same way, modifying the partial pressure of H2 was found to enhance the activity of all catalysts, especially the HYD pathway.

A more detailed study and additional experimental tests should be performed in order to improve the understanding on the relation between quinoline and H2S within the deep HDS of 4,6-DMDBT and to further develop the kinetic model created.

Keywords: Diesel; middle distillates; 4,6-DMDBT; CoMo/Al2O3; inhibition effect.

1 Introduction In order to decrease pollution caused by

automobile vehicles, the sulfur content in diesel fuel has been drastically reduced over the years as witnesses the restrictive regulations. However, refining industries are processing heavier feedstocks and facing an increasing demand on fuels so, a better performance from the hydrodesulfurization (HDS) catalysts is required.

The commercial catalysts commonly used for HDS reactions are molybdenum sulfides promoted by cobalt or nickel and supported over alumina. Nevertheless, if one aims to improve their performances, it is now necessary to identify precisely the limitations. It can be achieved by characterizing deeply the catalyst, using powerful tools or by carrying a kinetic study to identify the main limitation, inhibiting and activating parameters. To do so, it is necessary to evaluate the catalyst in representative conditions witnessing the way it will have to work in real conditions. In the HDS of middle distillates, as sulfur

conversion increases the remaining species are mostly dibenzothiophenes. As 4,6-DMDBT, these compounds are very difficult to decompose. Moreover, these compounds are decomposed through two main and distinct pathways namely, hydrogenation (HYD) and direct desulfurization (DDS). Furthermore, the presence of the methyl groups on 4,6-DMDBT highly limits the reactivity and leads the HDS to selectively process through the hydrogenating route compared to the DDS one. The objective of this work was focused on the comprehension of the HDS mechanism on various representatives CoMo catalyst types in order to study the deep HDS of middle distillates in the range of operating conditions dedicated to the low pressure HDS.

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2 Methodology 2.1 Catalysts Three types of catalysts were prepared – CoMo-A,

CoMo-B and CoMo-C. All used catalysts are CoMo trilobe extrudates supported on γ-alumina. In order to process to their catalytic evaluation, their length has been calibrated between 2 and 4 mm for hydrodynamic considerations.

These catalysts were prepared by three common stages: active phase impregnation (dry impregnation), maturation (in air atmosphere for 1,5 hours) and drying (at 90°C for 24 hours).

CoMo-A was the only catalyst used directly on the catalytic tests after drying phase. CoMo-B was calcined under air at 450°C, for 120 minutes, and to produce CoMo-C catalyst, an organic solution was added as an additive, at pore volume, which was then dried under nitrogen flow at 140°C and two hours to preserve the organic compound but eliminating the solvent. The catalysts samples (4 cm3) were loaded with silicon carbide in the reactor to ensure good thermal diffusion in the catalyst bed. They were sulfided in situ in the reactor using a sulfidation feedstock containing DMDS, xylene and cyclohexane. This mixture was injected at a starting temperature of 40ºC. After 3h, the temperature was raised to 350ºC at a 1,7ºC/min rate and was maintained at 350ºC for 1h, before decreasing to 290ºC at a 1,5ºC/min.

2.2 Reaction Conditions

For this study, the HDS of 4,6-DMDBT was carried out in a high-pressure fixed-bed microreactor (length: 18,2 cm; inner diameter: 1 cm) at 290-310 ºC, under 3 MPa (ratio H2/HC=240) of total pressure after in situ sulfidation. The feedstock established for standard conditions contained: 4,6-DMDBT (0,66 wt.%) dissolved in cyclohexane (57,14 wt.%) and xylene (40,00 wt.%), then dimethyl disulfide (1,20 wt.%) and quinoline (1,00 wt.%) were added to generate H2S and NH3, respectively .

In order to evaluate the effect of H2S the quantity of DMDS in the liquid feedstock was increased to 2,00 wt.%. Then, to study the influence of the NH3 partial pressure, one used the experimental results determined on previous works (feedstock containing 0,50 wt.% of quinoline) and the experimental tests done along the present work (feedstock containing 1,50 wt.% of quinoline). For all cases, the composition of the other compounds was maintained by adjusting the amount of cyclohexane.

Finally, the effect of the H2 partial pressure was studied by increasing the total operating pressure from 3 to 4 MPa. To maintain the composition of the

other compounds constant the ratio H2/HC was increased from 240 to 320. The tests with CoMo-A, CoMo-B and CoMo-C were performed at different LHSV - 4 h-1, 3 h-1, 6,5 h-1, respectively.

2.3 Analysis

The effluents were analyzed by a gas chromatography (GC). The starting oven temperature was 50°C and then increased to 67ºC at a 15ºC/min rate, prior to increasing to 290ºC at a 30ºC/min rate, in order to separate the produced organic compounds. The analytic results obtained from the GC allowed determining the conversion of the liquid feedstock. Hence, to obtain the HDS conversion of 4,6-DMDBT (%𝑋!,!!!"!#$) the following equation was used:

%𝐗𝟒,𝟔!𝐃𝐌𝐃𝐁𝐓 =

𝐧𝐏𝐫𝐨𝐝𝐮𝐜𝐭𝐬  𝐨𝐟  𝟒,𝟔!𝐃𝐌𝐃𝐁𝐓  𝐜𝐨𝐧𝐯𝐞𝐫𝐬𝐢𝐨𝐧𝐧𝟒,𝟔!𝐃𝐌𝐃𝐁𝐓,𝐭𝐨𝐭𝐚𝐥

×𝟏𝟎𝟎 (Eq. 1)

In addition, the conversion of 4,6-DMDBT through

both HYD (%𝑋!"#) and DDS (%𝑋!!") pathways were calculated by the following equations:

%𝑿𝑯𝒀𝑫 =

𝒏𝑯𝒀𝑫𝒏𝟒,𝟔!𝑫𝑴𝑫𝑩𝑻,𝒕𝒐𝒕𝒂𝒍

×𝟏𝟎𝟎 (Eq. 2)

%𝑿𝑫𝑫𝑺 =𝒏𝑫𝑫𝑺

𝒏𝟒,𝟔!𝑫𝑴𝑫𝑩𝑻,𝒕𝒐𝒕𝒂𝒍×𝟏𝟎𝟎 (Eq. 3)

In Eq. 2 and Eq. 3, 𝑛!"# and 𝑛!!"

represent the number of moles of HYD products and DDS product produced during the catalytic test, respectively.

2.4 Kinetic Study

In this study, the kinetic model was created in the software ReactOp Cascade®, considering the decomposition of 4,6-DMDBT through three main pathways: HYD, DDS and HDA. Thus, the following reactions were inserted in the kinetic model.

With A – 4,6-DMDBT, B – HYD products and C – DDS product.

Then, the results obtained from the experimental tests performed were inserted into the software in order to establish the kinetic model and understand how the H2S, NH3 and H2 partial pressures influence the decomposition of 4,6-DMDBT. With the kinetic model established, the reaction rate constant (𝑘) and

A  !!"# B (Eq. 4)

A  !!!" C (Eq. 5)

C  !!"# B (Eq. 6)

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the activation energy (𝐸!) were calculated. Finally, to determine the kinetic partial order for each component, the logarithm of the reaction rate constant was plotted as function of the logarithm of the partial pressure of H2S, NH3 and H2.

3 Results and Discussion 3.1 Impact of H2S partial pressure

CoMo-based catalysts are known for being inhibited by H2S [1] [2]. In this study, the results showed the same tendency as HYD pathway has proven to be strongly inhibited (Figure 1), at high H2S partial pressure. The experimental tests concerning CoMo-A and CoMo-B at standard conditions (1,20% DMDS) were performed in previous works.

Figure 1 - HYD conversion of 4,6-DMDBT as function of temperature for

the three catalysts prepared. In the graph, full lines represent the 1,2 wt.% DMDS feed and gapped lines represent the 2 wt.% DMDS.

Moreover, as CoMo-C is the catalyst with the lowest activation energy, the almost negligible effect of H2S may confirm that, in additive impregnated-type catalysts, the adsorption of H2S is much weaker than on the other catalysts tested. However, the results found for the additive impregnated catalyst are difficult to discuss as it shows a low activity compared to the others. Thus, this test should be redone with a lower LHSV.

Concerning the results obtained for the DDS pathway, for all catalysts the selectivity on hydrogenolysis products was enhanced (Figure 2), with higher H2S partial pressure which is in disagreement with literature [2] [3].

A possible explanation for why all catalysts exhibit higher DDS conversion, with higher H2S partial pressure, could be the existence of two distinct and specific active sites each of them being selective for one of the two reactions considered. Thus, H2S would adsorb favourably on the hydrogenolysis centers or closed to them and, at some point, would change the structure of these active sites.

Other explanation, which can be pointed out, is the fact that the catalysts used in this study have much more molybdenum (up to 20 wt.% MoO3) than the catalysts averagely used [2] [4] [5]. Therefore, the catalysts prepared probably exhibit much more dispersed active phase due to the recent way of preparation. However, one cannot confirm this assumption because it is not possible to characterize the catalysts from the literature. So, it is possible that the catalysts prepared, in this study, contain more active sites than the catalysts stated in literature.

Figure 2 – DDS conversion of 4,6-DMDBT as function of temperature for

the three catalysts prepared. In the graph, full lines represent the 1,2 wt.% DMDS feed and gapped lines represent the 2 wt.% DMDS.

Therefore, it is possible that to reach full saturation of the catalytic surface, by H2S adsorption, and consequent inhibition of the S-edges, where supposedly hydrogenolysis reaction takes place [6], the H2S partial pressure should have to be higher. Eventually, the operating conditions presented in the literature were not the same as the conditions used in this study. In fact, regarding the feedstock composition, most part of the previous studies in this subject did not use quinoline into their model feedstock in order to evaluate the effect of H2S on HDS [2] [3]. Hence, one could also suggest that there is an indirect effect within the DDS pathway if H2S is introduced in the presence of quinoline.

3.2 Impact of NH3 partial pressure

The following results (Figure 3) show the difference between the chosen standard conditions and the condition with less concentration of quinoline. These experimental tests at lower concentration were performed in previous works as well as the tests with CoMo-A and CoMo-B at standard conditions (1,00% quinoline).

As one can see in Figure 3, the HYD conversion increased for all three catalysts with a lower NH3 partial pressure. In other words, a higher amount of quinoline increases the inhibition effect within the

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hydrogenation reaction in all catalysts which is in agreement with literature [5]. In addition, it is also clear that the most impacted catalyst was the additive impregnated.

Figure 3 – HYD conversion of 4,6-DMDBT as function of temperature for the three catalysts prepared. Full lines represent the 0,5 wt.% Quinoline model approximation and gapped lines represent the 1,0 wt.% Quinoline (standard

conditions).

In Figure 4 are presented the results concerning the DDS conversion. For CoMo-A and CoMo-B, the DDS conversion slightly decreased, for high temperatures, when using a feedstock containing a low quinoline concentration.

Figure 4 – DDS conversion of 4,6-DMDBT as function of temperature for

the three catalysts prepared. Full lines represent the 0,5% Quinoline model approximation and gapped lines represent the 1,0% Quinoline (standard

conditions). So, it seems that there was a slight inhibition of the

DDS pathway. Therefore, this fact is in agreement to what was found in literature [5]. It is also noticeable that, for both dried and calcined catalysts there was a similar impact of NH3 partial pressure. This may again point out the similar adsorption of inhibitory compounds by these two catalysts. Additionally, literature reports that DDS is more inhibited by quinoline than HYD [5]. However, at this level, this fact was not seen in the results as there was a higher apparent inhibition on the hydrogenation reaction, for all three catalysts (Figure 3). The only experimental

work showing a stronger effect of nitrogen compounds on HYD was actually obtained with piperidine [3].

Ma et al. [7] and Turaga et al. [8] have also found from molecular modeling experiments, that the inhibition effect caused by nitrogen-based compounds could be stronger for HYD route.

3.3 Impact of H2 partial pressure

In Figure 5 are shown the performances concerning the HYD pathway from the catalytic test performed with a total working pressure of 40 bar. The experimental tests concerning CoMo-A and CoMo-B at standard conditions (30 bar) were performed in previous works.

Figure 5 – HYD pathway conversion as a function of the temperature for

different catalysts and total pressures, full lines represent the 30 bar and gapped lines represent the 40 bar conditions.

Concerning the results obtained, one can see that the decomposition of 4,6-DMDBT through HYD route increases with the increasing of H2 partial pressure. This fact is supported by most part of the results found in literature [3] [4] [9].

However, throughout the experimental test of the calcined catalyst (CoMo-B) there were some problems, at 300°C, associated with the data exploitation in the GC. So, one may consider that at this temperature the conversion through HYD pathway would be higher attending to the tendency of the experimental results. Thus, this test should be redone in order to better evaluate the influence of H2 partial pressure on the calcined catalyst.

In Figure 6 are shown the performances concerning the DDS pathway from the catalytic test performed with a total working pressure of 40 bar. Looking at the results, as mentioned previously, the DDS conversion for CoMo-B catalyst may not be correct taking into account that at 300°C there were some problems with the GC. Nevertheless, there is a clear decrease on the DDS conversion. The only way to explain this tendency should be to assume that

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HDA pathway consecutive to DDS is enhanced. The same results were found for CoMo-A.

For the additive impregnated catalyst, the decrease on DDS conversion is not as high as the one found for the other catalysts.

Figure 6 – DDS pathway conversion as a function of the temperature for

different catalysts and total pressures, full lines represent the 30 bar and gapped lines represent the 40 bar conditions.

In fact, for high temperatures, one can see a slight increase. However, these results might be bias considering the high LHSV used (low conversion rates). Indeed, this test should be redone, with a lower LHSV (higher contact time) in order to evaluate how the activity of additive impregnated catalyst is influenced by this working conditions than for the standard ones.

3.4 Kinetic Modelling

For the three catalysts, a kinetic study was performed regarding the several tested conditions. The aim was to better understand the difference in the catalytic performances by changing the H2S, NH3 and H2 partial pressures.

To evaluate the inhibition and activation effect caused by each partial pressure in each individual reaction pathway, the logarithm of the reaction constant rate determined by the modeling program was plotted as function of the logarithm of the partial pressure of H2S, NH3 and H2. Thus, the slopes obtained represent the kinetic partial orders concerning the HYD, DDS and HDA pathways.

As previewed from the majority of the works published in literature, H2S has a negative impact on HYD pathway for all three catalysts [2] [10].

Moreover, looking particularly to the results obtained for the hydrogenation routes (HYD and HDA), one can see that the additive impregnated catalyst was the most inhibited, comparing with the other two catalysts. Surprisingly, this conflicts with the fact that the additive impregnated was the one with

the lowest activation energy attributed to a lower H2S partial pressure effect. Additionally, this may be linked to the fact that, at low H2S partial pressure, the catalytic surface coverage of the dried and calcined catalysts by H2S was already high. Thus, for a higher H2S partial pressure, they would be much less affected than the additive impregnated catalyst.

Table 1 - Kinetic partial orders with respect to H2S

As can be seen in Table 2, the HYD pathway was greatly inhibited for all three catalysts by NH3 partial pressure. Regarding the results obtained for DDS, one can notice that the kinetic orders are negative, for the three catalysts, although the experimental results show an increase on DDS selectivity for the higher NH3 partial pressure. Actually, this probably an artefact linked to the HDA inhibition that provides higher DDS selectivity, but in appearance. Nevertheless, DDS is less inhibited than HYD. Regarding literature, this difference in the inhibition between DDS and HYD is possible, as shown by [7] and [8]. Actually, some experimental work carried out with quinoline in presence of H2S show that the HDN rate is highly impacted by H2S [11]. So the remaining quinoline could be hold responsible for the high inhibition of HYD, being known that quinoline undergoes HDN mainly by hydrogenation.

Table 2 – Kinetic partial orders with respect to NH3

As previewed, increasing H2 partial pressure has a positive impact on HYD pathway for all three catalysts (Table 3). Moreover, it appears that the hydrogenation reaction for both dried and calcined catalysts is more promoted by the H2 partial pressure than for the additive impregnated. Concerning the DDS pathway, one can point out that the changes in values found were almost negligible.

Catalyst HYD DDS HDA

CoMo-A -0,9 1,1 -1,1

CoMo-B -0,9 0,8 -1,1

CoMo-C -1,1 0,7 -1,6

Catalyst HYD DDS HDA

CoMo-A -1,6 -0,7 -2,0

CoMo-B -1,6 -0,8 -2,0

CoMo-C -1,5 -0,4 -1,9

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Table 3 – Kinetic partial orders with respect to H2

Furthermore, the values obtained could be result of

two made assumptions: - First, the acid S-H groups, present in the

catalyst active sites, may be inhibited by H2 thus leading to a lower DDS rate;

- Secondly, one may also consider that these results could be due to the lack of experimental points and the error associated to the model fitting.

As a consequence, at this point, one considered that DDS pathway was not modified by the H2 partial pressure.

4 Conclusion and Perspectives In this study, the main focus was to evaluate the

deep HDS of middle distillates in the range of operating conditions dedicated to the low pressure HDS with sulfided CoMo-based catalysts.

Three CoMo-based catalysts were prepared and catalytic tests were performed in order to compare their performances within the same range of temperature and HDS global conversion. Moreover, the inhibiting and promoting effects of H2S, NH3 and H2 on the three catalysts were compared and discussed for each HDS pathways, namely HYD and DDS.

Regarding the effect of the partial pressure of H2S, the three catalysts were inhibited similarly by H2S. Nevertheless, only the hydrogenation seems to be inhibited while DDS appears to be promoted. These results strongly disagree with the literature and could be due to the working conditions, the molybdenum amount and/or the partial pressure of nitrogen. Concerning the impact of nitrogen-based compounds (quinoline), it was found that the three catalysts undergo a strong inhibition over both pathways and especially the hydrogenation, in agreement with some literature data. Finally, concerning the effect of H2, the catalysts showed a quite similar promoting impact although the additive impregnated was slightly less enhanced. All in all, the conditions in which the additive impregnated catalyst would relatively perform

the best compared to non-additivated catalysts were with high NH3 partial pressure, low H2 partial pressure and relatively low H2S partial pressure.

As perspectives for this study, an improvement regarding the kinetic model created should be done in order to fully understand the HDS of 4,6-DMDBT within the model feedstock considered. The following propositions should be taken into account:

- The decomposition of quinoline should be

introduced into the kinetic model to conclude if quinoline inhibits more than NH3 or if there is some cross effect with H2S;

- A lower amount of 4,6-DMDBT should be introduced into the model feedstock in order to study the adsorption/desorption relation between the 4,6-DMDBT and the catalytic surface. Some other perspectives, regarding the hypothesis

made to explain the promoting effect over DDS with high H2S partial pressure, should also be considered. On one hand, the same tests should be redone for all three catalysts decreasing the amount of MoO3 within the catalysts and/or increasing the H2S partial pressure, in order to directly compare the results with literature. On the other hand, the amount of H2S could be increased to a higher extent to observe if some inhibition occurs, providing a more accurate H2S partial order. Finally, all the experimental tests performed should be redone replacing the CoMo/Al2O3 catalysts by NiMo/Al2O3 or even without promoter (Mo/Al2O3). This would allow understanding if the promoter used has an impact on the kinetic mechanism of the 4,6-DMDBT HDS.

References

[1] S. Texier et al., J. Catal., vol. 223, 404-418, 2004.

[2] V. Rabariohela-Rakotovao et al., Appl. Catal. A, vol. 306, 34-44, 2006.

[3] M. Egorova et al., J. Catal., vol. 241, 162-172, 2006.

[4] J. Kim et al., Ener. & Fuels, vol. 19, 353-364, 2005.

[5] C. Kwak et al., Appl. Catal. A, vol. 35, 59-68, 2001.

[6] P. Moses et al., J. of Catal., vol. 248, 188-203, 2007.

[7] X. Ma et al., Ener. & Fuels, vol. 9, 33-37, 1995. [8] U. Turaga et al., Catal. Today, vol. 86, 265-

275, 2003.

Catalyst HYD DDS HDA

CoMo-A 1,0 -0,5 1,0

CoMo-B 1,0 -0,4 1,0

CoMo-C 0,7 -0,3 0,4

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[9] K. Al-Dalama et al., E. & Fuels, vol. 20, 1777-1783, 2006.

[10] X. Li et al., J. Catal., vol. 250, 283-293, 2007.

[11] C. Satterfield, I. Eng. Chem. Des., vol. 20, 53, 1981.