Generalized kinetic model for iron and cobalt based Fischer–Tropsch synthesis catalysts: Review and model evaluation

Accepted Manuscript Title: Generalized Kinetic Model for Iron and Cobalt based Fischer-Tropsch Synthesis Catalysts: Review and Model Evaluation Author: Shabbir Mousavi Akbar Zamaniyan Mohammad Irani Mehdi Rashidzadeh PII: DOI: Reference:

S0926-860X(15)30115-0 http://dx.doi.org/doi:10.1016/j.apcata.2015.08.020 APCATA 15514

To appear in:

Applied Catalysis A: General

Received date: Revised date: Accepted date:

18-3-2015 10-8-2015 14-8-2015

Please cite this article as: Shabbir Mousavi, Akbar Zamaniyan, Mohammad Irani, Mehdi Rashidzadeh, Generalized Kinetic Model for Iron and Cobalt based Fischer-Tropsch Synthesis Catalysts: Review and Model Evaluation, Applied Catalysis A, General http://dx.doi.org/10.1016/j.apcata.2015.08.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Generalized Kinetic Model for Iron and Cobalt based FischerTropsch Synthesis Catalysts: Review and Model Evaluation Shabbir Mousavi, Akbar Zamaniyan*, Mohammad Irani and Mehdi Rashidzadeh

Department of Natural Gas Conversion, Gas Research Division, Research Institute of Petroleum Industry (RIPI), Tehran 14665-137, Iran

*Corresponding Author: P.O.Box : 14665-137, Tel: +98 (21) 48252336, Fax: +98 (21) 44739716 Email: [email protected]

Graphical abstract

Highlights  

 

A generalized mechanism was found that can be applied for FTS mechanism for both iron and cobalt based catalysts. A general rate equation was derived based on the proposed generalized mechanism. The general rate equation is evaluated for both iron and cobalt based catalysts. The general rate equation is capable to describe wide range of kinetic data for Co and Fe based catalysts simultaneously.

ABSTRACT

1

During the decades of kinetic studies over iron and cobalt based Fischer-Tropsch Synthesis (FTS) catalysts, various mechanisms and equations have been proposed with a wide diversity. Literature review indicates that neither general kinetic model nor the same shape for reaction rate equation has been proposed for FTS. In the present paper, a generalized mechanism was developed and verified against reported kinetic data for both iron and cobalt based FTS catalysts. Also it was shown that all various types of the proposed mechanisms can fall under the heading of one general mechanism. The proposed generalized macro kinetic model can be applied simultaneously to both iron and cobalt based FTS catalysts.

KEYWORDS: Mechanism; Fischer–Tropsch Synthesis; Kinetic Model; Catalyst;

1. INTRODUCTION The major fuel production is currently based on crude oil. The reserves of crude oil are limited and therefore, fuel production from other hydrocarbon sources attracted considerable amount of attention. The XTL (X to Liquid) process can produce fuel from any hydrocarbon containing materials like coal, natural gas, biomass, and even wastes. A typical XTL process involves feed to synthesis gas (syngas), syngas to syncrude and syncrude to product steps. The syngas to syncrude conversion is known as Fischer Tropsch Synthesis (FTS). A typical FTS is catalytic conversion of syngas to a mixture of predominantly linear alkanes and alkenes, with the product distribution displaying a recognizable pattern. ∶ :

+ (2 + 1) + 2

→ C

→ C

2

+

+

(1) (2)

ℎ

:

+ (2 − 1)

→ C

+ ( − 1)

(3)

In FTS, iron and cobalt based catalysts are of commercial interest. The mechanism and kinetics of FTS on iron and cobalt based catalysts has received significant attention. Many attempts have been made to describe the rate of reaction, either by tuning the kinetic data in an empirical equation or driving an equation based on mechanistic assumptions [1]. This leads to different and sometimes conflicting rate equations in literature meaning there are different and conflicting mechanisms which are unfavorable and unacceptable. It is interesting to propose one reaction rate equation that can cover all reported kinetic data for either cobalt and/or iron catalysts. Table 1 summarizes reported studies that claim to cover a range of kinetic data. From the Table 1, equation 1 proposed by Anderson-Dry [2, 3] and equation 2 proposed by Yates and Satterfield [4] were the first equations that have been studied and used extensively for iron and cobalt catalysts respectively [5]. Recently Botes et al. performed a macro-kinetic study for cobalt and iron FTS catalysts wherein operating conditions were systematically varied in a wide range [6, 7]. They found that equations 1 and 2 show systematic statistical deviations and therefore proposed different equations (equation 3 and 4) for cobalt and iron respectively. In another approach, van Steen and Schulz [8], performed experimental kinetic studies in a wide range of operating conditions for both iron and cobalt catalysts. They derived mechanistically one equation that could present experimental kinetic data for both catalysts (equation 5). But it must be noted that it predicts zero value for FTS rate in case of zero water partial pressure that is contrary to experimental observations [9]. Most recently, Ojeda et al. [10] used Density Functional Theory (DFT) to study FTS mechanism on Co and Fe surfaces. They came to the conclusion that iron and cobalt catalysts kinetic data can be presented with one 3

mechanism and reaction rate equation and so proposed equation 6. But equation 6, predicts non zero rate for zero hydrogen partial pressure that is not true conceptually. In this work, a generalized kinetic model (kinetic equation and mechanism) that can be applied to both iron and cobalt FTS catalysts was developed. In section 2, some of the most important aspects of FTS mechanism are discussed. In section 3, CO consumption rate is modeled (based on section 2 results), a mathematical procedure for evaluation of CO consumption rate is described and results are discussed. 2. FISCHER-TROPSCH SYNTHESIS MECHANISM Several transition metals are active in FTS. Vannice [11] found the following order for transition metals according to the average molecular weight of produced hydrocarbons: >

>

> ℎ >

> >

>

(4)

Pd, Pt and Ir are mainly selective for methanation and essentially produce methane. Ni as pure metal is very poor in FTS, however when the pressure is increased, it can show FT activity [12]. In other words; Ru, Fe, Co, Rh and Ni can be considered as FTS active metals. Pricewise, Co or Fe based catalysts are preferred for commercial scale but Ru and Ni are most attractive for academic research [13]. Previous studies confirm certainly that FTS is polymerization type reaction with step wise chain growth [14], but unlike other polymerization reactions, in FTS reaction the feed should be converted firstly to a monomer and initiator, then polymerize into the final hydrocarbon products. Thus the formation chemistry and form of monomer and initiator are the first points that must be addressed and noticed [15]. This behavior leads to a type of mechanism based on one path monomer and initiator formation. Recently another type of mechanism appears based 4

on two paths for initiation and propagation steps. In this section, two aforementioned mechanism types are presented and discussed. 2.1. MONOMER AND INITIATOR FORMATION CHEMISTRY During the decades, several assumptions for FTS monomer and initiator forms and formation chemistry had been made. The general form of the monomer and initiator can be defined as [13]: (5) Historically, the most important proposed monomers were: methylene (CH2), hydroxyl carbine (CHOH) and CO; that led to three mechanisms for FTS; carbide, the Enol and CO insertion mechanism respectively. Another mechanism proposed recently is “formate” mechanism [16]. The differences between proposed mechanisms arise from different assumptions for monomer and initiator forms and formation chemistry. In this regard, the formation chemistry dictates the form of monomer and initiator, so it is sufficient to be investigated. The previously proposed formation chemistry for monomers and initiators are shown in Table 2. As can be seen, different formation chemistry leads to different FTS mechanisms. In the next subsections, monomers and initiators formation chemistry and dependent FTS mechanism are discussed. 2.1.1 ENOL MECHANISM As shown in Table 2, CHOH is considered as monomer and initiator in Enol mechanism. Previous studies on Fe catalysts indicate that alcohols and aldehydes can initiate FT reaction [17] whereas they are weak initiators for Co catalysts [18]. Though alcohols can act as chain initiator, Tau et al. [19] found that they cannot act as propagators. In other words alcohols can act as initiator but not monomer. 5

Other studies on Fe and Co based catalysts showed that alcohols and aldehydes form alkoxide not CHOH [20-23] and initiation chemistry is well described by the alkoxide structure [22, 23]. These results indicate that alkoxide intermediate is responsible for the chain initiation not CHOH. On the other hand anionic polymerization chemistry confirms that alkoxides can act as nucleophilic initiators [24]. As a result for iron or cobalt catalysts, alcohols (or aldehydes) can form alkoxide structure that can act as chain initiators but they cannot create active monomer in the form of CHOH. 2.1.2. CO INSERTION MECHANISM As Table 2 indicates, in CO insertion mechanism, M-CO (CO adsorbed on active metal surface) was proposed as monomer, analogous to the hydroformylation mechanism [25]. Analogy with homogeneous studies supports this mechanism but it should be noted that there is a lack of experimental data to prove this mechanism in heterogeneous media [26, 27]. Thus it can be concluded that M-CO proposal as monomer is questionable. 2.1.3. FORMATE MECHANISM As Table 2 illustrates, in formate mechanism CO in gas phase acts as monomer via insertion into the O-H (O-R) bond of a surface hydroxyl (Alkoxy) group to form COOH (COOR). It was found that there is a very close relationship between CO partial pressure in gas phase and chain lengthening on the catalyst surface [16, 28, 29] so it was concluded that CO in gas phase acts likely as the inserting monomer. Frennet and Hubert [16] observed that during the early stage of reaction, the chain lengthening probability (α (

) is proportional to p

and it is not proportional to carbon surface coverage

). Thus they concluded that surface carbon cannot act as monomer and CO in gas phase acts

as monomer on Co-Cu catalyst. These results were confirmed later by Schweicher et al. on 6

Co/MgO catalyst [28]. Though these results show close relationship between CO in gas phase and chain lengthening process, but such relationship was not observed for Co/SiO2 [29]. The same results had been observed over Ni, Ni/SiO2, Ni/TiO2 and Ni/Al2O3 [30]. Therefore it seems that this relationship is support sensitive and support has a role in mechanism. As formate mechanism does not consider this role, it can be concluded that this mechanism does not able to predict FTS on all supports and is not general. In fact, there are strong evidences that indicate CHx acts as monomer in FTS [12, 31- 37] and that is discussed in the next section. 2.1.4. CARBIDE MECHANISM As shown in Table 2, in carbide mechanism CH2 is considered as monomer. In early days of FTS mechanism investigations, Fischer and Tropsch [38] proposed that carbides might be intermediates in FTS from the reaction of CO with active metals. The carbide is then reduced to CH2 as monomer. There are strong evidences that indicate carbide is involved in FTS. It is well known that several transient metals can dissociate CO to form metal carbides and the metals that do not dissociate CO easily (Cu, Pd, Ag, Ir, Pt, and Au) are almost inactive in FTS. Also the metals that dissociate CO easily and form too stable oxides (and carbides) are inactive in FTS too [39]. It should be noted that there are mainly two types of carbon on the surface; low temperature carbidic surface and high temperature graphitic bulk that indicate high and low activity toward hydrogenation respectively [13].

7

Although the low-temperature surface carbide is reactive toward hydrogenation, but there are evidences that show CH2 cannot self polymerize and needs initiator [12]. This led to carbide mechanism modification known as alkyl mechanism. 2.1.5. ALKYL MECHANISM Alkyl mechanism is the most widely accepted reaction pathway for formation of alkanes and alkenes [17]. As shown in Table 2, in Alkyl mechanism CH2 and CH3 (Alkyl) are considered as monomer and initiator respectively based on Brady and Pettit [12] work. They found that in the presence of inert gas, the primary product of CH2 was ethylene; so concluded that CH2 cannot polymerize alone. On the other hand in presence of H2, CH2 groups incorporate into hydrocarbons. From these observations they suggested that metal hydride and alkyl groups initiate the chain growth. But further studies showed that Alkyl mechanism is too simple to explain the FTS mechanism [40]. Barneveld and Ponec [40], in complete agreement with Vannice [11], found that C2+ activity for syngas was in the following order for active metals: >

> ℎ>

>

=0

(6)

It is expected that this behavior is observed for CH2 and CH, but they found that activity for the case of CH is different from CH2 and none of them follows the syngas one. This result indicates that FTS mechanism is not as simple as alkyl mechanism suggested. Recently, more complex Alkenyl and Alkylidene-hydride-methylidyne mechanisms have been developed. 2.1.6. ALKENYL MECHANISM

8

For Alkenyl mechanism in Table 2, instead of Alkyl, a vinyl (Alkenyl) surface species (-CH=CH2) resulting from coupling of CH and CH2 is considered as chain initiator. Therefore here both CH and CH2 are considered as intermediates in FTS. The alkenyl mechanism was initially developed by Maitlis and coworkers [31]. As evidence, they found that Fe, Co, Ru, and Rh on silica support gave similar product distributions with1alkenes as predominated products. This led to the conclusion that alkanes are secondary products from alkenes. In addition, after ethene-13C2 addition to syngas, the 1-alkene products had two adjacent 13C atoms at the alkyl ends. From these results they suggested that initiation took places via C2 surface species of a vinyl type (-CH=CH2). For initiation, the alkenyl mechanism was supported experimentally but in the case of propagation and termination, there is lack of experiments [41]. Also alkenyl mechanism cannot explain easily the presence of methyl branched products [41] and cannot predict alkanes as primary products [42]. 2.1.7. ALKYLIDENE-HYDRIDE-METHYLIDYNE MECHANISM As Table 2 illustrates, in the Alkylidene-hydride-methylidyne mechanism, CH+H instead of CH2 is considered as monomer. Initially developed by Ciobicǎ et al. [43], this mechanism does not need an Alkenyl isomerization step and it can explain alkanes as well as alkenes as primary products too. Recently, this mechanism was selected by Maitlis and Zanotti as the preferred mechanism for chain propagation [34]. Last but not the least, the D tracing analysis [35, 36] showed that propagation should take place by CH+H rather than CH2. According to this mechanism, the methyl branched hydrocarbons should be formed but it is not the case for ethyl or dimethyl branched hydrocarbons that is consistent with experimental data [36]. In other words, it seems that the 9

Alkylidene-hydride-methylidyne mechanism is the most general mechanism discussed so far to explain FTS mechanism. Though Alkylidene-hydride-methylidyne mechanism can explain initiation, chain growth and termination in FTS mechanism, but assumes that CO dissociation is direct in spite of recent studies that showed it is not direct and should be H-assisted (As discussed in Section 2.2). 2.2. TWO REACTION PATHS FOR THE FTS MECHANISM There is evidence that the FTS mechanism includes two reaction paths (two types of carbon containing intermediates leading to hydrocarbons); 1- From Steady State Isotopic Transient Kinetic Analysis (SSITKA) studies two reaction paths for FTS mechanism have been observed for Co catalyst [37]. 2- From SSITKA studies two reaction paths for methanation have been observed for Ni [44], Ru [45], Rh [46], Co [37, 47] and Fe [48, 49]. As it has been found that synthesis of methane and higher hydrocarbons are closely related [13, 37, 43, 47, 50, 51], so it can be concluded that similar two reaction paths mechanism may exist in FTS for all aforementioned active metals. Two mechanisms based on two reaction paths have been proposed in the literature; the CO Insertion-Carbide mechanism and the H-Assisted CO dissociation mechanism. 2.2.1. CO INSERTION-CARBIDE MECHANISM In this mechanism, proposed by Gaube and Klein [52, 53], it is assumed that CO insertion and alkyl mechanisms occur simultaneously. The mechanism proposal resulted from the well known superposition of two Anderson-Schulz-Flory (ASF) distributions or dual alpha FTS whereas it has been shown that dual alpha ASF is due to “dilution effect” resulted from reactor holdup [17]. 10

The incorporation of alcohols probes discussed in section 2.1.1 is the evidence mentioned for this mechanism, but as discussed earlier in section 2.1.1., the investigations reject this issue. On the other hand CO insertion is based on analogy without any experimental support [26, 27] and the D tracing analysis [35, 36] showed that propagation should take place by CH+H rather than CH2 (or CO). 2.2.2. H-ASSISTED CO DISSOCIATION MECHANISM One limitation of all mechanisms with CHx as monomer or initiator, is the fact that the direct CO dissociation rate is limited [54] and not sufficient even for methane formation [33]. One solution is the assumption of H-assisted CO dissociation where it is assumed that there are two paths for CO dissociation: Direct and indirect; as shown in Fig. 1. [10]. As can be seen, in this mechanism CH is considered as monomer that is consistent with the Alkylidene-hydridemethylidyne mechanism. DFT and isotope studies are the main evidence for this mechanism. DFT studies showed that direct CO dissociation has high activation barrier on the surface of Fe, Co and Ru catalysts [5558] contrary to the H-assisted one. Also Inverse H2-D2 isotope effect supports H involvement in CO dissociation [59]. Most recently it was found that size-dependent dissociation of carbon monoxide on Co nano-particles is related to H-assisted CO dissociation [60, 61]. Thus the H-assisted CO dissociation mechanism combined with Alkylidene-hydridemethylidyne mechanism is the most consistent with FTS mechanism than the others. But one major limitation in all mechanisms is no consideration of metal-support interaction. As discussed in the formate mechanism, support can affect FTS mechanism. Also it has been shown in literature that metal oxides can increase several times the CO dissociation and hydrogenation rates, so it is clear that this effect should be considered too. It will be discussed in section 3. 11

3. RESULTS AND DISCUSSION 3.1. MODELLING THE RATE OF CO CONSUMPTION Based on discussed mechanisms, the generalized kinetic rate equation is derived. The rate of CO consumption is summation of hydrocarbons and CO2 formation rates as following: −

=

+

(7)

The rate of FTS equals to the rate of hydrocarbon formation. The FTS reaction is polymeric including initiation, propagation and termination steps, so the rate of FTS is summation of above mentioned steps. Since termination step does not include CO consumption, the rate of FTS is equal to rate of CO consumption in the initiation and chain propagation steps [8]: −

=

=

+

(8)

Considering of Alkylidene-hydride-methylidyne mechanism (Based on section 2), the rate of initiator formation equals to the rate of CH+H incorporation to CH and the rate of propagation equals to the rate of CH+H incorporation to Alkylidene chain. It is assumed that the rate of CH+H incorporation is independent from chain length [62], so the rate of FTS equals to the rate of CH+H incorporation: −

=

As −

+

=

(9)

can be considered irreversible [8, 62], the rate of CH+H incorporation is

proportional to CH and H surface concentrations: =

.

.

(10)

12

Where M denotes active metal. It was concluded (Section 2) that CO dissociation is H-assisted. Also there are strong evidences that CO dissociation is aided by metal oxides [37, 59, 63- 67]. This effect has been nominated as SMSI (Strong Metal-Support Interaction). Mori et al. [59] proposed that metal oxide weakens CH-OH bond and facilitates its dissociation via CH-OH bond. Boffa et al. [67] found that the degree of CO dissociation is proportional to metal oxide Lewis acidity. They proposed that metal oxide Lewis acid sites are in the form of anionic vacancies (AV). After CHOH bound dissociation, hydroxide (OHAV) is formed in the AV site as shown in Fig. 2. Thus surface concentrations can be calculated from the following reactions:

and

+2 +

↔2

=

↔

+

↔

+

+

↔

+

.

+

(11)

.

=

.

.

.

=

.

.

+

↔

.

(12) .

=

.

=

.

(13) .

(14) .

(15)

CHM surface concentration can be calculated from summation of reaction 11 to 15:

+

+

+

.

.

.

⎯⎯⎯⎯⎯⎯⎯⎯

(16)

+

The AV sites should be regenerated to repeat FTS cycle. There are two candidates for OHAV removal, with aid of H2 or CO. As CO pool is much larger than H2 pool on FT metals, it can be concluded that OHAV removal with aid of adsorbed CO is more likely. The form of this reaction is close to Water Gas Shift (WGS) reaction via formate route. 13

Rethwisch and Dumesic studied WGS reaction over Fe3O4, ZnFe2O4, MgFe2O4, ZnO, MgO, SnO2, Al2O3, TiO2, Na-mordenite and SiO2 [68, 69]. They proposed following reaction scheme for formate formation: −

+

−

−

−

↔ +

− +

−

(17)

↔

−

−

+

+

(18)

This reaction scheme is shown in Fig. 3. On the other hand, Grenoble et al. [70] showed that in the presence of active metal, the rate of WGS increase several order of magnitudes that refer to higher CO adsorption on active metal compared to support. Thus the reaction mechanism can be modified as below (Fig. 4.): − −

+

−

−

↔ +

−

−

+

↔

(19) −

−

+

+

(20)

Thus:

+

=

↔

+

+

↔

+

.

.

(21)

+ (22)

.

.

=

.

.

.

For cycle repeating, The AV and M sites should regenerate via formate decomposition. Olympiou et al. [71] concluded that active metal can promote formate decomposition, so the following reactions can be proposed here for formate decomposition.

↔ +

→

+ +

14

.

=

=

.

.

(23) (24)

+

→

=

+

.

(25)

Overall formate formation is calculated from summation of reaction 21, 22 and 23: .

+

.

⎯⎯⎯⎯

(26)

+

Since OHAV, which is formed from CH-OH dissociation in reaction 15, reacts with COM to release AV for CH formation cycle repeating, so reactions 15 and 26 can explain direct relation between CO in gas phase and chain growth on metal surface (discussed in Section 2.1.3.). The

+

surface concentration is calculated from summation of reaction 12, 16 and 26:

+

+

.

+

.

.

.

.

.

.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

+

(27)

.

(28)

Thus: .

= .

=

. .

.

.

.

.

.

.

.

.

.

(29)

As C and O are in the form of CO in the feed, in steady state, C and O rate of removal should be equal. The rate of O removal is equal to the rate of formate decomposition (reaction 24 & 25). The rate of C removal is equal to the rate of CO2 and CH2 formation (reaction 10 & 25). So the rate of formate decomposition should be equal to rate of CO2 and CH2 formation: +

=

= =

(30) +

.

=

.

.

+

.

.

.

(31) (32)

15

=

.

.

.

.

.

=

.

.

. .

.

=(

.

=

+

).

.

.

.

.

(33) (34)

.

(35)

.

=

+

.

.

.

Substituting 35 in 29: .

=

.

. (36)

.

.

=

. .

.

.

(37)

. =

′

.

.

(38)

.

The rate of FTS is then:

−

=

=

−

=

.

. .

.

=

.

.

.

.

.

.

(39) (40)

.

Assuming that surface is mainly covered with CO [10], from site balance for M concentration:

1=

+

1=

+

=

(41) .

(42)

.

1 1+

(43) .

Substituting 43 in 40:

−

=

. (1 +

(44)

. .

)

16

−

= .

. (1 +

(45) )

.

The new Rate Equation based on the Generalized Kinetic (REGK) is then evaluated, in the following section. 3.2. STATISTICAL EVALUATION 3.2.1. KINETIC DATA GATHERING In first step, the kinetic data has been gathered from previous reported works in literature. For statistical evaluation, the values of experimental reaction rate and species partial pressure were required. Fortunately the species partial pressures were reported in the literature, but as it was not the case for the FTS reaction rate (r

). For the previous works that r

was not reported, it has

been calculated from the following formula [7]: r

=r

−r

(46)

For low conversion plug flow rectors (Fixed bed) the following equation was used to obtain the experimental reaction rate value [72, 73]:

r

Where the term

τ

τ

can be calculated by the following correlation [72, 73]:

X

= a. τ + b. τ 1 τ= GHSV The value of (X

) against 1/

and

(47)

(48) (49)

constants were obtained using data regression of CO conversion

at constant inlet partial pressures (y

17

) and temperature.

For CSTR reactors, the following equations were used to obtain the experimental reaction rate value [74]:

−r

= y

. 22.414 ∗

X (50)

τ

1 =φ τ

(51)

X

=1−

y

=

Where φ is the

y y

.φ .φ

(52)

P P

(53) .

After completion of data gathering, the whole data sets were sorted based on temperature (in supporting information Table S1, S2 & S3). 3.2.2. DATA REGRESSION For validity, investigation of REGK as compared with the previous ones, it is necessary to calculate constant parameters of REGK and the others for each data set. For this purpose, nonlinear regression techniques were applied. Thus experimental rate values were regressed against species partial pressures for each data set to obtain individual constant parameter values. 3.2.3. STATISTICAL EVALUATION PROCEDURE Statistical evaluation procedure includes following steps to check the accuracy and capability of REGK: A-

For each data set, the obtained constant parameters via regression technique were implemented in the REGK to calculate the reaction rate. Absolute Relative Residual (

) was calculated by: 18

−

=



(54)



B-

Calculated reaction rates were plotted versus reported experimental ones and the square of the coefficient of correlation function (R2) were calculated. In R2 calculation procedure, since

should be zero in the case of zero

, the following

equations were used: ∑ =

. (55)

=

∑

= . ∑ =

(56) . (57)

∑

R2 close to unity shows good regression. To show REGK ability for covering data sets

was calculated for all data points of

all data sets using the following formula:

=

100

−



(58)

Where subscript of adp referes to all data points. C-

For comparison, all aforementioned steps were repeated for each reported reaction rate equation in Table 1.

3.2.4. STATISTICAL EVALUATION OF REGK

19

Using kinetic data for iron and cobalt, Equations that have been proposed or used for wide range of operating conditions for cobalt and/or iron catalysts (Table 1) are compared with REGK. Since equations 1 and 5 contain water partial pressure in denominator, their results were calculated with iron kinetic data (Table S3). The results of MARR, R2, and P Table 3. P

% refers

%

are presented in

to the percentage of data that has ARR less than 25%. As Table 3 indicates,

REGK and equation 3 have lowest MAAR and highest R2 and they are the most accurate ones. Fig. 5. shows comparison between experimental and calculated FTS rates for REGK. As shown in the Figure, calculated rates are in a good agreement with the experimental data. For each data set and equation, constants and 95% confidence interval were reported in the supporting information. To compare the obtained constant values with the expected values, the value of min, max and average for adsorption parameters and number of negative ones, for REGK and equation 3 were reported in Table 4. As Table 4 indicates, kb values for Fe based catalysts are lower than Co based catalysts. Botes et al. [75] also reported this trend. As shown in the Table 4, equation 3 predicts negative adsorption parameter for 9 of 25 data sets that is not physically acceptable. Thus it can be concluded that REGK is the most reliable equation for iron as well as cobalt catalysts. To compare the value of calculated adsorption constants by the REGK equation as compared with expected one, using Botes et al. kinetic data (dataset No. 8, and 21 in supporting information), the effect of increasing CO partial pressure on the FTS reaction rate was presented in Fig. 6. In the figure, part b was constructed based on the same data as Botes et al. [75]. It should be noted that Fig. 6. Data is normalized to show the differences in the shapes of the curves for Co and Fe and is not suitable for directly comparing the activities of them. As shown in Fig. 6. for Fe based catalyst, increasing CO partial pressure has positive effect on FTS reaction

20

rate up to a partial pressure limit and then has negative effect on FTS reaction rate which was observed in literature [75]. For Co based catalysts increasing CO partial pressure has negative influence on FTS reaction rate that is consistent with literature too [75]. REGK equation not only can describe wide range of kinetic data for Co and Fe simultaneously, but also was derived based on the mechanism that consider major kinetic facts as follows: 1- It is consistent with the observed two paths in FTS. 2- The proposed generalized mechanism can explain CO dissociation rate enhancement via SMSI effect and is consistent with H-assisted CO dissociation. 3- Generalized mechanism can explain direct relation between CO in gas phase and chain growth on metal surface. 4- Generalized mechanism can predict alkanes as well as alkenes as primary products. 5- It predicts methyl branched hydrocarbons, consistent with experimental observations. 4. CONCLUSIONS Based on FTS mechanism investigation, a generalized mechanism was found that can be applied to FTS mechanism for both iron and cobalt based catalysts. It was shown that the proposed mechanism is consistent with major kinetic facts in FTS. Also a general rate equation was derived based on the proposed generalized mechanism that is capable to describe wide range of kinetic data for Co and Fe based catalysts simultaneously. 5. REFRENCES [1] R. L. Espinoza, Prepr. Pap. – Am. Chem. Soc., Div. Fuel Chem. 40 (1995) 172-176. 21

[2] R. B. Anderson, in: P.H. Emmett (Ed.), Catalysis, Vol. IV, Reinhold, New York, 1956, pp. 247–283. [3] M. E. Dry, Ind. Eng. Chem. Prod. Res. Dev. 15 (1976) 282-286. [4] I. C. Yates, C. N. Satterfield, Energy Fuels 5 (1991) 168–173. [5] M. E. Dry, J. Chem. Technol. Biotechnol. 77 (2001) 43-50. [6] F. G. Botes, B. van Dyk, C. McGregor, Ind. Eng. Chem. Res. 48 (2009) 10439–10447. [7] F. G. Botes, B. B. Breman, Ind. Eng. Chem. Res. 45 (2006) 7415-7426. [8] E. van Steen, H. Schulz, Appl. Catal. A Gen.186 (1999) 309–320. [9] M. Claeys, E. van Steen, in: Basic Studies. A.P. Steynberg and M.E. Dry (Eds), Studies in Surface Science and Catalysis, Vol. 152, Elsevier, Amsterdam, 2004, pp. 601-680 (chapter 8). [10] M. Ojeda, R. Nabar, A. U. Nilekar, A. Ishikawa, M. Mavrikakis, E. Iglesia, J. Catal. 272 (2010) 287-297. [11] M. A. Vannice, J. Catal. 37 (1975) 449-461. [12] R. C. Brady, R. Pettit, J. Am. Chem. Soc. 102 (1980) 6181-6182. [13] P. Biloen and W. M. H. Sachtler, in: Mechanism of Hydrocarbon Synthesis over FischerTropsch Catalysts. D. D. Eley, H. Pines, P. B. Weisz (Eds), Advances in Catalysis, Volume 30, Academic press INC, New York, 1981, pp. 165-216 (chapter 4). [14] M. E. Dry, Appl. Catal. A Gen. 138 (1996) 319–344. [15] B. W. Wojciechowski, Catal. Rev.-Sci. Eng. 30 (1988) 629-702. [16] A. Frennet, C. Hubert, J. Mol. Catal. A: Chem.163 (2000) 163–188. [17] B. H. Davis, Catal. Today 141 (2009) 25–33. [18] R. J. Kokes, W. K. Hall, P. H. Emmett, J. Am. Chem. Soc. 79 (1957) 2989-2996. [19] L.-M. Tau, H. A. Dabbagh, J. Halasz, B. H. Davis, J. Mol. Catal., 71 (1992) 37-55. [20] G. Blyholder, L. D. Neff, J. Phys. Chem. 70 (1966) 893-900. [21] G. Blyholder, W.V. Wyatt, J. Phys. Chem. 70 (1966) 1745-1750. [22] J. B. Benziger, R. J. Madix, J. Catal. 65 (1980) 36-48. [23] J. B. Benziger, R. J. Madix, J. Catal. 74 (1982) 55-66. [24] G. Odian, Principles of Polymerization, Fourth Edition, John Wiley & Sons, Inc., New Jersey, 2004. [25] H. Pichler and H. Schulz, Chem. Ing. Tech. 42 (1970) 1162–1174. [26] J. P. Hindermann, G. J. Hutchings, A. Kiennemann, Catal. Rev.-Sci. Eng. 35 (1993), 1127. 22

[27] H. Schulz, Catal.Today 214 (2013) 140-151. [28] J. Schweicher, A. Bundhoo, N. Kruse, J. Am. Chem. Soc. 134 (2012) 16135−16138. [29] J. Schweicher, Kinetic and Mechanistic Studies of CO Hydrogenation over Cobalt-based Catalysts, Ph.D. Thesis, Université libre de Bruxelles (U.L.B.), 2010. [30] J. Zieliński, Proc. 9th International Congress on Catalysis, Calgary, 1988, (M.J. Philips, M. Ternan, Eds.), Vol. 2, p. 751, The Chemical Institute of Canada, Ottawa, 1988. [31] P. M. Maitlis, J. Organomet. Chem. 689 (2004) 4366–4374. [32] W.A. A. van Barneveld, V. Ponec, J. Catal. 88, (1984) 382-387. [33] P. Biloen, J. N. Helle, W. M. H. Sachtler, J. Catal. 58, (1979) 95-107. [34] P. M. Maitlis, V. Zanotti, Chem. Commun. (2009) 1619–1634. [35] C. Jin, Deuterium Tracer Studies Of The Mechanism Of Cobalt Catalyzed FischerTropsch Synthesis, Master of Science Thesis, Eastern Kentucky University, 2012. [36] B. Shi, C. Jin, Appl. Catal. A Gen. 393 (2011) 178–183. [37] H. A. J. van Dijk, The Fischer-Tropsch synthesis: A mechanistic study using transient isotopic tracing, Ph.D. Thesis. Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 2001. [38] F. Fischer, H. Tropsch, Brennstoff-Chem. 7 (1926) 97-104. [39] V. Ponec, W. A. A. van Barneveld, Ind. Eng. Chem. Prod. Res. Dev. 18 (1979) 268-271. [40] W. A. A. van Barneveld, V. Ponec, J. Catal. 88 (1984) 382-387. [41] M. J. Overett, R. O. Hill, J. R. Moss, Coord. Chem. Rev. 206–207 (2000) 581–605. [42] L. -M. Tau, H. A. Dabbagh, B. H. Davis, Energy Fuels 5 (1991) 174-179. [43] I. M. Ciobicǎ, G. J. Kramer, Q. Ge, M. Neurock, R. A. van Santen, J. Catal. 212 (2002), 136-144. [44] M. Otarod, J. Happel, E. Walter, Appl. Catal. A Gen. 160 (1997) 3-11. [45] I. -G. Bajusz, J. G. Goodwin Jr., J. Catal 169 (1997) 157–165. [46] M. W. Balakos, S. S. C. Chuang, G. Srinivas, M. A. Brundage, J. Catal. 157 (1995) 5165. [47] J. Yang, Y. Qi, J. Zhu, Y. -A. Zhu, D. Chen, A. Holmen, J. Catal. 308 (2013) 37-49. [48] N. S. Govender, Mechanistic study of the High- Temperature Fischer-Tropsch Synthesis using transient kinetics, Ph.D. Thesis, Eindhoven University of Technology, 2010.

23

[49] N. S. Govender, F. G. Botes, M. H. J. M. de Croon, J. C. Schouten, J. Catal. 260 (2008) 254–261. [50] J. Gao, X. Mo, J. G. Goodwin, J. Catal. 275 (2010) 211-217. [51] V. Ponec, Catal. Rev.-Sci. Eng., 18 (1978) 151-171. [52] J. Gaube, H. -F. Klein, J. Mol. Catal. A: Chem. 283 (2008) 60–68. [53] J. Gaube, H. -F. Klein, Appl. Catal. A Gen. 374 (2010) 120–125. [54] J. Nakamura, I. Toyoshima, K. –I. Tanaka, Surf. Sci. 201 (1988) 185-194. [55] S. Storsæter, D. Chen, A. Holmen, Surf. Sci. 600 (2006) 2051–2063. [56] O. R. Inderwildi, S. J. Jenkins, D. A. King, J. Phys. Chem. C, 112, (2008) 1305-1307. [57] P. van Helden, J.-A. van den Berg, I. M. Ciobicǎ, Catal. Sci. Technol. 2 (2012) 491–494. [58] B. T. Loveless, C. Buda, M. Neurock, E. Iglesia, J. Am. Chem. Soc. 135 (2013) 6107−6121. [59] T. Mori, A. Miyamoto, N. Takahashi, M. Fukagaya, T. Hattori, Y. Murakami, J. Phys. Chem. 90 (1986) 5197-5201. [60] T. Herranz, X. Deng, A. Cabot, J. Guo, M. Salmeron, J. Phys. Chem. B 113 (2009) 10721–10727. [61] A. Tuxen, S. Carenco, M. Chintapalli, C. -H. Chuang, C. Escudero, E. Pach, P. Jiang, F. Borondics, B. Beberwyck, A. P. Alivisatos, G. Thornton, W. -F. Pong, J. Guo, R. Perez, F. Besenbacher, M. Salmeron, J. Am. Chem. Soc. 135 (2013) 2273−2278. [62] B. Todic, T. Bhatelia, G. F. Froment, W. Ma, G. Jacobs, B. H. Davis, D. B. Bukur, Ind. Eng. Chem. Res. 52 (2013) 669−679. [63] T. Komaya, A. T. Bell, Z. Weng-Sie, R. Gronsky, F. Engelke, T. S. King, M. Pruski, J. Catal, 150 (1994) 400-406. [64] S. Ali, B. Chen, J.G. Goodwin Jr., J. Catal. 157 (1995) 35-41. [65] A. L. Borer, C. Bronnimann, R. Prins, J. Catal. 145 (1994) 516-525. [66] W. M. H. Sachtler, M. Ichikawa, J. Phys. Chem. 90 (1986) 4752-4758. [67] A. Boffa, C. Lin, A. T. Bell, G. A. Somorjai, J. Catal. 149 (1994) 149-158. [68] D. G. Rethwisch, J. A. Dumesic, Appl. Catal., 21 (1986) 97-109. [69] G. Lozano-Blanco, J. W. Thybaut, K. Surla, P. Galtier, G. B. Marin, Ind. Eng. Chem. Res. 47 (2008) 5879–5891. [70] D. C. Grenoble, M. M. Estadt, D. F. Ollis, J. Catal. 67 (1981) 90-102.

24

[71] G. G. Olympiou, C. M. Kalamaras, C. D. Zeinalipour-Yazdi, A. M. Efstathiou, Catal. Today 127 (2007) 304–318. [72] T. K. Das, W. A. Conner, J. Li, G. Jacobs, M. E. Dry, B. H. Davis, Energy Fuels 19 (2005) 1430-1439. [73] T. K. Das, X. Zhan, J. Li, G. Jacobs, M. E. Dry, B. H. Davis, in: Fischer-Tropsch Synthesis: Kinetics and Effect of Water for a Co/Al2O3 Catalyst. B.H. Davis and M.L. Occelli (Eds), Studies in Surface Science and Catalysis, Vol. 163, Elsevier, Amsterdam, 2007, pp. 289314. [74] G. P. van der Laan, A. A. C. M. Beenackers, Appl. Catal. A Gen. 193 (2000) 39–53. [75] F. G. Botes, J. W. Niemantsverdriet, J. van de Loosdrecht ,Catal. Today 215 (2013) 112– 120. [76] B. Sarup, B. W. Wojciechowski, Can. J. Chem. Eng. 67 (1989) 62–74. [77] A. O. I. Rautavuoma, H. S. van der Baan, Appl. Catal. 1 (1981) 247–272. [78] J. Wang, Physical, chemical and catalytic properties of borided cobalt Fischer–Tropsch catalysts, Ph.D. Thesis, Brigham Young University, Provo, UT, 1987. [79] S. Ledakowicz, H. Nettelhoff, R. Kokuun, W. -D. Deckwer, Ind. Eng. Chem. Process Des. Dev. 24 (1985) 1043-1049. [80] P. J. van Berge, Fischer-Tropsch studies in the slurry phase favoring wax production, Ph.D. Thesis, Potchefstroomse Universiteit vir Christelike Hoer Onderwys, 1994. [81] G. A. Huff Jr., C. N. Satterfield, Ind. Eng. Chem. Process Des. Dev. 23 (1984) 696-705. [82] H. E. Atwood, C. O. Bennett, Ind. Eng. Chem. Process Des. Dev. 18 (1979) 163-170. [83] W. H. Zimmerman, D. B. Bukur, Can. J. Chem. Eng. 68 (1990) 292-301. [84] W. J. Shen, J. L. Zhou, B. J. Zhang, J. Nat. Gas Chem. 4 (1994) 385-400. [85] M. J. Keyser, R. C. Everson, R. L. Espinoza, Ind. Eng. Chem. Res. 39 (2000) 48-54. [86] C. Maretto, R. Krishna, Catal. Today 52 (1999) 279–289. [87] R. Krishna, S. T. Sie, Fuel Process. Technol. 64 (2000) 73–105. [88] R. M. de Deugd, R. B. Chougule, M. T. Kreutzer, F. M. Meeuse, J. Grievink, F. Kapteijn, J. A. Moulijn, Chem. Eng. Sci. 58 (2003) 583 – 591. [89] R. Philippe, M. Lacroix, L. Dreibine, C. Pham-Huu, D. Edouard, S. Savin, F. Luck, D. Schweich, Catal. Today 147S (2009) S305–S312. [90] A. Jess, C. Kern, Chem. Eng. Technol. 32 (2009) 1164–1175. [91] R. Zennaro, M. Tagliabue, C. H. Bartholomew, Catal. Today 58 (2000) 309–319. 25

[92] L. -P. Zhou, X. Hao, J. -H. Gao, Y. Yang, B. -S. Wu, J. Xu, Y. -Y. Xu, Y. -W. Li, Energy Fuels 25 (2011) 52–59. [93] C.G. Visconti, E. Troconi, L. Lietti, P. Forzatti, S. Rossini, R. Zennaro, Top. Catal. 54 (2011) 786-800.

Table 1: Reported rate equations that claim to cover a range of kinetic data

No

Study

Equation

Anderson-Dry (1956/1976) [2, 3]

−

= .

2

Yates & Satterfield (1991) [4]

−

= .

3

Botes et al (2009) [6]

−

= .

4

Botes & Breman (2006) [7]

−

= .

5

van Steen & Schulz (1999) [8]

−

= .

6

Ojeda et al. (2010) [10]

−

=

1

Catalyst

Previous Studies Covered/Compared

Fe

-

Co

[76,77,78]

Co

[4,77] & 13 other mechanistically derived equations

Fe

[2, 3,8,62,74,79,80]

Co & Fe

[81,77]

Co & Fe

[4]

. +

. .



(1 +

)

. .

.

.

1+

. .

.

(1 +

.

)

. .

1+ .

.

/ .

/

( . + ). (1 + . )

Experimental Conditions Covered Catalyst :Fe T(℃): P(bar): H2/CO: Catalyst :Co T(℃): 180-240 P(bar): 1-15 H 2/CO: 0.25-4 Catalyst :Co T(℃): 230 P(bar): 5.9-40.9 H 2/CO: 1-15.5 Catalyst :Fe T(℃): 220-260 P(bar): 4.5-32.7 H2/CO: 0.5-11.6 Catalyst :Co and Fe T(℃): 190-275 P_H 2 (bar): 1.0-30.2 P_CO(bar): 0.2-25.4 P_H 2O(bar): 0.2-5.6 Catalyst :Fe T(℃): 235 P_H 2 (bar): 2.5-10.0 P_CO(bar): 4.0-10.0

Further Studies

[82-85]

[86-91]

[75]

[75, 92]

-

[93]

Table 2: Monomer forms and formation chemistry in FTS.

Mechanism Enol

Monomer M-C-OH | H

Monomer formation Chemistry 2 + → 2( − ) + → − − + − → − + − + − → − +

Initiator

Initiator formation Chemistry -

2

CO insertion

Formate

M-CO

CO

+

→

−

M-CH3

-

M-OH

26

+ → 2( − ) + → − − + → − + − + − → − − + − → − − + − → − 2 + → 2( − ) + → − − + → − + − + − → −

− + + +

− +

2 Carbide

M-CH2

Alkyl

M-CH2

+ → 2( − ) + → − − + → − + − − + − → − + − + − → − + Same as Carbide monomer

Alkenyl

M-CH2

Same as Carbide monomer

Alkylidene Hydride methylidyne

2 M-CH+M-H

+ → 2( − ) + → − − + → − + − + − → −

-

-

M-CH3

M-CH=CH2

M=CH-CH2-M

− +

Same as CO insertion initiator 2 + → 2( − ) + → − − + → − + − − + − → − + − + − → − + − + − → − = 2 + → 2( − ) + → − − + → − + − − + − → − + − +( − + − )→ = − −

Table 3: Comparison between REGK and reported rate equations that claim to cover a range of kinetic data

No

1

2

Study

[2,3]

[4]

Catalyst

Fe

Co

Equation

−

−

= .

= .

. +

.

. (1 +

[6]

Co

−

= .

[7]

Fe

−

= .

1+

.

.

(1 +

6

[8]

[10]

Co & Fe

Co & Fe

−

−

= .

REGK

Co & Fe

−

)

.

/ .

= .

(1 +

. .

Co

-

-

-

Fe

16.4

0.966

83.1

Co & Fe

-

-

-

Co

10.4

0.975

93.3

Fe

8.3

0.984

91.6

Co & Fe

9.3

0.980

92.3

Co

9.2

0.982

95.8

Fe

8.3

0.989

97.4

Co & Fe

8.8

0.987

96.7

Co

11.7

0.978

85.8

Fe

8.7

0.989

95.5

Co & Fe

10.1

0.985

91.2

Co

-

-

-

Fe

19.7

0.948

72.1

Co & Fe

-

-

-

Co

11.8

0.948

91.7

Fe

8.8

0.985

93.2

Co & Fe

10.1

0.969

92.3

Co

10.0

0.982

94.2

Fe

6.9

0.991

98.1

Co & Fe

8.3

0.987

96.4

%

(%)

/

( ∙ + ) . = (1 + . )

.

-

.



1+ .

MARR (%)



.

.

5

.

.

.

4

)

.

.

3



Data

)

27

+

Table 4: Calculated adsorption parameters for REGK and eq.3

No.

Equation .

3

−

= .

1+ .

REGK

−

= .

(1 +

. . . .

.

Co

k Adsorption parameter Number of Min Max Mean negative k 0.144 2.15 1.01 4

Fe

0.026

0.377

0.159

5

Co Fe

0.011 0.008

1.923 0.484

0.428 0.165

0 0

Data

.

)

CO +S COS +H

3

1

+O 2 +S

CO2

C+O

COH +H

+H

CHOH

CH

+S CH+OH

Fig. 1. H-Assisted CO dissociation reaction scheme [10]

28

Fig. 2. OHAV formation on anionic vacancies after CH-OH bound dissociation

Fig. 3. Formate formation scheme as proposed by Rethwisch and Dumesic [68]

29

Fig. 4. Modified reaction scheme for formate formation

30

125

rcalc

100

+25%

75

-25%

50

25

0 0

25

50

75

100

125

rexp (normalized)

Fig. 5. Comparison between experimental and calculated FTS rates

b) FTS rate (a.u)

FTS rate (a.u)

a) Iron

Cobalt

0

5 10 CO partial Pressure (bar)

15

Iron

Cobalt

0

5 10 CO partial Pressure (bar)

15

Fig. 6. Typical effect of increasing CO partial pressure on the FTS reaction rate as predicted by REGK (a) and reference [75] (b).

31