Kinetic Modelling of the Influence of H 2 S on Dibenzothiophene Hydrodesulfurization in a Batch System over Nano-MoS 2

In this work, the possibility of enhanced activity during the hydrodesulfurization of dibenzothiophene over certain nano-MoS 2 catalyst due to the presence of H 2 S was examined by focusing on the reaction kinetics. With H 2 S generated in situ, the overall reaction followed the autocatalytic rate law; while in the absence of H 2 S the kinetics indicated a pseudo-first-order reaction. H 2 S appears to modify the relative contributions of parallel hydrogenation and desulfurization reactions by drastically increasing the hydrogenation rate. Kinetic models were developed that describe the hydrodesulfurization reaction at various H 2 S concentrations, and the kinetic parameters and adsorption equilibrium constants associated with this process were estimated by fitting the experimental data. The results suggest that the promotion and/or inhibition of hydrodesulfurization by H 2 S likely result from the same overall reaction mechanism.

conditions, the sulfur substrate species must be reacted under the presence of H 2 S. Many studies based on either fixed bed systems or batch reactors have reported drastic suppression of the catalysis of the HDS reaction involving both model sulfur compounds and real feed stocks in the presence of H 2 S [7] [8] [9] [10]. Such behavior is well-known in this area of research where the consensus catalysts are subjected to seriously lose their overall activity because of H 2 S. The extent of activity reduction is varied and highly dependent on the catalyst identity where the established reaction network of sulfur substrate is important.
However, interesting results concerning the HDS of dibenzothiophene (DBT) and 4,6-dimethyldibenzothiophene were recently reported [11] [12], which showed that H 2 S may actually promote the HDS activity of some certain MoS 2 class catalysts. To the best of our knowledge, such results are interesting and yet there is surprisingly a lack of literature on following and widely investigating this point. Thus, kinetic modeling that thoroughly describes this approach is needed.
The overall catalytic activity and selectivity appear to be dependent on the concentration of H 2 S in the reaction media. Overall, it is evident from the results to date that H 2 S somehow modifies the chemical nature of the active sites in this reaction. To investigate the catalyst activity promotion phenomenon by H 2 S and to determine the adsorption equilibrium constants, the present work performed a number of DBT HDS experiments in conjunction with a MoS 2 catalyst under various conditions, and derived detailed kinetic models to assist in understanding the reaction mechanism.

Experimental
A model MoS 2 catalyst was prepared by a heat treatment procedure previously described in the literature [11]. Briefly, a precursor of ammonium heptamolybdate tetrahydrate (NH 4 ) 6 Mo 7 O 24 ·4H 2 O were subjected to a gradual thermal annealing till reaching to 850˚C under a stream of H 2 S/H 2 (10% v/v) gas. After synthesis, the catalyst was milled using zirconia balls and then sulfided at 400˚C and 1 atm under a 10% v/v H 2 S/H 2 gas mixture flowing at 100 sccm in preparation for the experimental trials. All reactions were carried out in a 100 ml batch-type micro-autoclave from which aliquots were withdrawn at specific time intervals, using 100 mg of the catalyst for each trial. The feed consisted of 1 wt% DBT in decane although, in some experiments, 500 mg Cu powder was also added as a H 2 S scavenger to establish the initial kinetics without matrix interference [13]. The use of this type of reactor allowed the effects of the reaction matrix and operating conditions to be examined. All reactions were performed at 340˚C and an initial H 2 pressure of 3 MPa. The H 2 S concentration in the reaction mixture was

Results and Discussion
The major products detected following the HDS of DBT were biphenyl (BP), cyclohexylbenzene (CB), partially hydrogenated DBT (HDBT) and H 2 S. As noted, various H 2 S concentrations were employed during the HDS reaction, and

Kinetics
Several assumptions and simplifications were involved in the kinetics calculations. Firstly, the HDS of DBT was assumed to proceed primarily by DDS and HYD, as in Scheme 1.
Scheme 1. Intermediate products formed during the HDS reaction of DBT.
In addition, CB was assumed to result mainly from partially-hydrogenated DBT, and so the formation of this product will be promoted by H 2 S, in agreement with prior reports [5] [6]. The effect of the H 2 pressure on the reaction rate was neglected because H 2 was added in excess and so could be included in the intrinsic rate constant. Two active sites were considered, one for HYD and the other for DDS, according to the equations (all symbols and parameters are identified either in the notation section or in the text): and In this case, the concentration of hydrogenation sites (π H ) will be affected by the presence of H 2 S while the concentration of σ D sites remains almost unaffected.
Two scenarios were considered, consisting of the HDS reaction of DBT with and without H 2 S.

Kinetic Model for HDS with a Negligible H2S Concentration
Some prior studies have shown that the HDS of DBT is a pseudo-zero-order reaction [14] [15], while others have determined that this is a pseudo-first-order reaction [7] [12] [16] [17] [18]. As discussed below, the results of the present study agree with the latter behavior and so the analysis in this paper is predicated on pseudo-first-order kinetics. Based on mass balances of the reaction components, rate equations were adapted to quantitatively describe the product distributions.
These equations (details of which have been previously published [19]) are: Advances in Chemical Engineering and Science The reaction rate in the absence of H 2 S was well represented by the pseudo-first order relationship in Equation (4), and a plot of the data is presented in Figure 3. Here the fit of the experimental points to this equation is confirmed by the high regression factor. Equations (5) and (6) were used to fit the experimental results for the reaction intermediates, which required the iteration estimation of only two variables (k 1 and k 2 ). Each data fitting was performed using the Mathcad software package and employing non-linear methods via sequential iterations until convergence. Figure 4 plots the concentrations of the intermediate species against reaction time and also shows the fits obtained using Equations (5) and (6), which confirm the validity of the model. Fitting the experimental data with the model allowed the rate constants to be determined, which in turn enabled an estimation of the contribution of intermediates B and C to and The apparent kinetic parameters determined in this manner are provided in Table 1. The model used in this work was based on a version of the Langmuir-Hinshelwood mechanism, and so the rate equations for the HYD and DDS reactions were: By substitution, it is possible to obtain the equations: and Once the individual apparent rate constants were found, the equilibrium adsorption constants could be compared. The experimental data were fit according to Equations (11)-(13), as shown in Figure 5. Using the apparent rate constants for the parallel reactions determined from the previous calculations, the adsorption equilibrium constants for the substrate on the σ and π sites were predicted and the values are provided in Table 2.

Kinetic Model for HDS in the Presence of H2S, Promotion Model
Data regarding the product distributions are the primary means of validating Under these conditions, the promotional effect of the H 2 S was determined to involve a physical reversible process and was associated with the nature of the catalyst. In the existing of H 2 S, the hydrogenation reaction products were predominant, as can be seen by comparing Figure 4 and Figure 6, and so the activity of this route was obviously increased. The effect of H 2 S can be discussed in terms of its concentration in the reaction feedstock. Because the reaction is carried out in a batch system, a classical treatment of the autocatalytic-like kinetics leads to the equations: and   Here, R t is the total reaction rate and k ts is the overall rate constant under this conditions. In the present trials, the sum total of the moles of DBT and H 2 S at any given time remained constant, and so we can write: Equation (15) can be rearranged after integration to: ( ) which, after rearrangement and substitution, becomes: The DDS route is not considered to be affected by the presence of H 2 S, and so we have: This indicates a special case in which the reaction rate exhibits autocatalytic-like behavior. In an autocatalytic process, one of the reaction products is involved in the catalytic mechanism and so should be included in the rate law.
During HDS over the present MoS 2 catalyst, the reaction rate was found to be promoted by H 2 S, and thus this species may affect both the potential and the nature of the active catalytic sites. Therefore, the overall rate in the presence of H 2 S that is generated in situ, R ts , can be represented as: where R ts is the overall reaction rate. The correlation associated with Equation (21) is depicted in Figure 8 and shows a suitable fit to the experimental data.
Based on the constants estimated from both the classical treatment and the data analysis using Equations (19)-(21), the adsorption equilibrium constant associated with H 2 S can be determined, and the results of such calculations are provided in Table 2.

Analysis of the Kinetic Data
In model simulations, as the constants utilized in the model remain limited in number then the validity of model to be adopted increased. To minimize the number of constants included in our kinetic model, we first calculated reaction parameters based on the proposed model of Equations (5) and (6), and then estimated the fraction of each intermediate product that participates in the reaction, followed by manipulating the kinetic treatments once more according to the promotion model. From these calculations, the ratio of the DBT adsorption equilibrium constant for π sites to that for σ sites was found to be close to unity.
Thus, there was no preferential adsorption of the reactant on either active site when using the present catalyst. It should be noted that the adsorption equilibrium constants were estimated to have this limited value K σ or K π ≤ 0.01 and that the ratio of K π /K σ ≈ 1. Based on prior research regarding HDS reactions and the kinetic parameters estimated in this study, it is possible to analyze the experimental data as follows.

First Stage
When the HDS reaction was performed in the absence of H 2 S, the data could be fitted with a model recently developed by our group in which all the reaction products are included in the rate equations (that is, Equations (4)- (6)). This model was subsequently used to simulate the experimental data shown in Figure   4 and a reasonable agreement between the experimental values and the simulation can be seen. The estimated values predicted by this model are presented in Table 1. If the HDS process proceeds as a pseudo-first-order reaction, then this

Second Stage
If the H 2 S generated in situ remains in the reaction mixture, a kinetic rate curve corresponding to autocatalytic behavior is obtained, as is evident in Figure 7 and Figure 8. In this case, models based on Equations (17) and (21) were applied to simulate the experimental data for the overall reaction, and these pre-

Third Stage
In presence of an excess of H 2 S, a part of this species modifies the potential active sites while the rest is essentially not involved in the reaction. This scenario is quite similar to that in an actual refinery performing HDS. The catalyst may be involved in the reaction in a manner which is kinetically similar in nature to that found in the first stage section. The model discussed above in relation to the first stage can also be applied to describe this reaction, and the associated kinetic data are listed in Table 1. It is interesting to observe that the H 2 S has an effect following the first dose, such that the reaction proceeds as though the H 2 S undergoes self-promotion. Thereafter, with increases in the H 2 S concentration in the feedstock, its primary effect remains almost unchanged and the reaction behaves kinetically as a pseudo-first-order process. This effect can possibly be attributed to the formation of new active sites created by the H 2 S. After an equilibrium is achieved, at which point the H 2 S has modified all possible potential active sites, the reaction proceeds normally through the participation of the two kinds of active sites. Thus, the self-promotion effect induced by H 2 S is basically temporary and is associated with the modification of active sites up to saturation. Another point to note is that an excess of H 2 S induces neither further promotion nor inhibition of the catalytic activity, Figure 9. These results emphasize that H 2 S acts as a promoter possibly by increasing the efficiency of active sites, by increasing the number of sites, or by both mechanisms.

Inhibition and Promotion
At present, there is a lack of full information regarding the effect of compounds such as H 2 S and organic nitrogen compounds on catalytic behavior during HDS over unsupported bulk MoS 2 catalysts. The presence of H 2 S evidently inhibits the Advances in Chemical Engineering and Science DDS reaction of polyaromatic refractory sulfur containing compounds but has little impact on the HYD pathway. This detrimental effect on activity is apparent when employing conventional catalysts. As an example, an inhibition effect was reported in reactions using conventional CoMo/Al 2 O 3 catalysts, and was also reported to be reversible [7]. The present results concerning the MoS 2 catalyst show a remarkable enhancement of the HYD route upon the addition of H 2 S.
Two kinetic models are proposed: one in the absence of H 2 S and the other with H 2 S in the reaction medium at moderate levels. H 2 appears to be essential to the HDS process and may play a specific role in modifying the potential active sites that become two independent types: for the HYD and DDS reactions. The experimental results in the absence of H 2 S can be reasonably described by the model based on Equations (4)- (6). In contrast, in the presence of H 2 S, the occurrence of HYD is promoted and the overall catalytic activity is enhanced. This improvement in the activity is obviously due to the increased rate of the HYD reaction.
The effect of H 2 S on kinetics leads to the hypothesis that H 2 S interacts chemically with the catalyst by creating new highly active HYD sites. The good agreement of the experimental results with the non-linear numerical fitting supports this hypothesis.
Thus, H 2 S is believed to act as a reagent to create a fixed number of potential HYD active sites. These sites can be modified either by H 2 or H 2 S. While H 2 modification of the active sites leads to two distinct types of sites for the two routes, H 2 S modifies the active sites to selectively promote the HYD reaction.
The efficiency of the HYD active sites created by H 2 S is likely much more pronounced than those generated by H 2 . The present results and the fitting models also suggest the potential for mutual interconversion of the newly created active sites. Egorova et al. [5] reported that H 2 S has a positive effect on the cleavage of C-N bonds. It is unclear if this effect is due to the sulfidation state of the catalyst or to the participation of H 2 S in the reaction mechanism, although the authors suggest the latter. The present study supports this hypothesis too. This unique behavior of H 2 S in conjunction with this particular bulk MoS 2 catalyst during