Kinetic Model of FischerâTropsch Synthesis in a ... - ACS Publications

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Kinetic Model of Fischer−Tropsch Synthesis in a Slurry Reactor on Co−Re/Al2O3 Catalyst Branislav Todic,† Tejas Bhatelia,† Gilbert F. Froment,§ Wenping Ma,‡ Gary Jacobs,‡ Burtron H. Davis,‡ and Dragomir B. Bukur*,†,§ †

Chemical Engineering Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar Center for Applied Energy Research, 2540 Research Park Drive, Lexington, Kentucky 40511, United States § Texas A&M University, 3122 TAMU, College Station, Texas 77843, United States ‡

S Supporting Information *

ABSTRACT: A kinetic model for Fischer−Tropsch synthesis is derived using a Langmuir−Hinshelwood−Hougen−Watson approach. Experiments were conducted over 25% Co/0.48% Re/Al2O3 catalyst in a 1 L slurry reactor over a range of operating conditions (T = 478, 493, 503 K; P = 1.5, 2.5 MPa; H2/CO = 1.4, 2.1; WHSV = 1.0−22.5 NL/(gcat·h)). Rate equations were based on the elementary reactions corresponding to a form of well-known carbide mechanism. The 1-olefin desorption rate constant was assumed to be a function of carbon number due to the effect of weak interaction of the hydrocarbon chain with the catalyst surface. Values of estimated activation energies are in good agreement with those reported previously in the literature. The kinetic model was able to correctly predict all of the major product distribution characteristics, including the increase in chain growth probability and decrease in olefin-to-paraffin ratio with carbon number, as well as formation rates of methane and ethylene.

1. INTRODUCTION Fischer−Tropsch synthesis (FTS) is a heterogeneously catalyzed reaction in which a mixture of CO and H2 is converted into a wide range of hydrocarbon products. Because the main products of the reaction are n-paraffins and 1-olefins, FTS is the key process in gas-to-liquid (GTL) technology for the conversion of natural gas into liquid fuels and waxes. In recent years, there has been an increase in GTL production capacities, including the construction of the largest plants to date (i.e., Pearl GTL, a joint development by Qatar Petroleum and Shell, and Oryx GTL owned by Qatar Petroleum and Sasol, both located in Qatar). In today’s competitive world market, advanced design and optimization of such large scale plants requires a more detailed knowledge of reaction chemistry, heat and mass transport, fluid mechanics, etc. Therefore, kinetic models used for this application need to be robust, physically reasonable, and based on fundamental principles.1 It is generally accepted that FTS is a polymerization reaction involving stepwise chain growth. The product distribution is typically described by the Anderson−Schulz−Flory (ASF) distribution, where chain growth is governed by a growth probability factor (α) that is independent of the number of carbon atoms in the product molecule.2 However, deviations from ASF over all of the commercially relevant catalyst types (Co, Fe, Ru) are well-known in the literature, and include the following: higher than expected yield of methane, low yield of C2 (particularly ethylene) and decreasing slopes in the ASF diagram (i.e., increasing chain growth probabilities) with increasing carbon number.3−6 Another important characteristic of FTS product distributions for all catalyst types is an exponential decrease in the olefin-to-paraffin ratio (OPR) with increasing carbon number. In the past 20 years, the main effort has been on development of © 2012 American Chemical Society

detailed FTS kinetic models which account for non-ASF product distribution and olefin-to-paraffin ratio variation with carbon number. Different explanations for the observed product distribution have been proposed: accumulation of heavy products in the reactor,5,7,8 two parallel FTS mechanisms,9,10 two types of active sites or growth monomers,11,12 and most notably secondary reactions of 1-olefin.6,13−20 In the latter theory, it is assumed that desorbed 1-olefins can readsorb on FT active sites and that this adsorbed species can either be hydrogenated to form n-paraffin or participate in chain growth. This concept (1-olefin readsorption) has been used in hydrocarbon selectivity models, coupled with enhancement of 1-olefin readsorption with increasing carbon number due to: intraparticle diffusion effects,6,18 solubility effect in FT wax,14−16,19 and/or physisorption.17,20,21 Most of these models had in common an exponential dependency of olefin chain length ec×n, deduced in one way or another. However, several experimental studies recently questioned the importance of 1-olefin readsorption on product distribution.22−24 Botes25 argued that the observed product distribution can be caused by increasing interactions of adsorbed surface intermediate with the catalyst surface, which also leads to an exponential dependency of carbon number in the rate equation for olefin formation. His chain-length-dependent olefin desorption (selectivity) model could explain the same deviation as some of the previous models, but with a smaller number of parameters and a simpler form of model equations. Received: Revised: Accepted: Published: 669

October 16, 2012 December 17, 2012 December 17, 2012 December 17, 2012 dx.doi.org/10.1021/ie3028312 | Ind. Eng. Chem. Res. 2013, 52, 669−679

Industrial & Engineering Chemistry Research

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After in situ reduction, the reactor was cooled to 453 K for pressurizing the reactor to a desired reaction pressure (i.e., 1.5 MPa) using syngas. The FTS reaction was already taking place as the reaction temperature was slowly increased to 493 K. The feed gases, including purified CO, H2, and N2, were controlled separately by three mass flow controllers, and were premixed and directed into the reactor. After leaving the reactor, the exit gas passed through warm (373 K) and cold (273 K) traps to condense out the liquid products. Higher molecular weight hydrocarbons (i.e., wax at room temperature) were withdrawn from the STSR through a porous 2 μm sintered metal filter during routine daily sampling. Inlet and outlet gases were analyzed online by a Micro GC equipped with four packed columns. The liquid organic and aqueous products were analyzed using a HP 5890 GC with capillary column DB-5 and a HP 5790 GC with Porapak Q packed column, respectively. Reactor wax samples were analyzed by a high temperature HP 5890 GC employing an alumina-clad column. 2.3. Kinetic Experiment Design and Data. Kinetic experiments were carried out using a fractional factorial design with two-three levels of four different factors (temperature, pressure, feed ratio, and gas space velocity). Three temperatures (478, 493, and 503 K), two pressures (1.5 and 2.5 MPa), two H2/CO ratios (1.4 and 2.1), and three levels of space velocities (from 1 to 22.5 NL/(g-cat·h)) were chosen in order to study the effect of each factor on response values and provide a sufficiently wide range of experimental data needed for kinetic modeling. In order to minimize physical transport resistances, catalyst particles with a diameter of 44−90 μm were used and the STSR was well-mixed. Three separate experimental runs were performed on the Re−Co catalyst corresponding to three temperature levels of experimental data (run 1 493 K, run 2 478 K, run 3 503 K). To achieve stable and reproducible catalyst activity, an initial stabilization period of 120−170 h was required. Initial conditions were the same for all three runs (T = 493 K, P = 1.5 MPa, H2/CO = 2.1, SV = 8 NL/(g-cat·h)). Figure 1 shows that the catalyst activity during the initial period was reproducible.

Even though some selectivity models can describe product distributions very well, their shortcoming is failing to provide a deeper understanding of FTS reaction kinetics. A distinct advantage of detailed kinetic models over hydrocarbon selectivity models is that the detailed kinetic model has a more realistic interpretation of the FTS reaction mechanism, and product formation rate equations contain the true intrinsic kinetic parameters. Lox and Froment26,27 developed a detailed model of FTS kinetics based on a strict Langmuir−Hinshelwood− Hougen−Watson (LHHW) methodology for a promoted iron catalyst but without utilizing the concept of 1-olefin readsorption. Wang et al.28 expanded this approach by including readsorption of 1-olefins, but the proposed model was not able to account for changes in growth probability and olefin-to-paraffin ratio (OPR) with carbon number. This was followed by a series of studies on promoted iron catalysts by Li and co-workers, that coupled the LHHW mechanistic approach with the inclusion of secondary reactions,29 physisorption effect,30 different active sites for olefin hydrogenation,31 or different types of monomer.12 Recently, greater emphasis has been placed on developing detailed kinetic models for cobalt catalyzed FTS.32−36 In this work, we show that coupling of the mechanistic approach based on carbide mechanism with Botes25 assumption of chain-length-dependent olefin desorption yields a kinetic model capable of describing experimentally obtained product distributions, including previously described evolution with carbon number.

2. EXPERIMENTAL SECTION 2.1. Catalyst Preparation. The catalyst support used was Sasol Catalox-150 γ-Al2O3. To achieve 25% Co loading, a slurry impregnation method was used.37 In this method, the ratio of the volume of loading solution used to the weight of alumina was 1:1, such that approximately 2.5 times the pore volume of solution was used to prepare the catalyst. Two impregnation steps of cobalt nitrate were used, each to load 12.5% of Co by weight. This was due to the solubility limit of cobalt nitrate. Between each step, the catalyst was dried under vacuum in a rotary evaporator at 353 K and the temperature was slowly increased to 373 K. After the cobalt nitrate was added and dried, Re promoter was added by aqueous incipient wetness impregnation of dissolved Re2O7 precursor to achieve 0.48% by weight Re. After a final drying step, the catalyst was calcined at 623 K under flowing air for 4 h. The weight percentages of Re and Co reflect elemental metal content in the calcined catalyst. 2.2. Slurry Reactor Operation and Product Analysis. The 25% Co/Al2O3 catalyst with 0.48% Re was ground to 170− 325 mesh. A 1 L stirred tank slurry reactor (STSR) was charged with ∼315 g of startup solvent, Polywax 3000, which was melted by holding the furnace at 413 K. The reactor was sealed and then purged by flowing inert gas (e.g., N2) at 30 NL/h for 3−4 h before transferring the ex-situ activated Co catalyst (∼16.0 g) from a fixed bed catalyst activation reactor to the STSR. Ex-situ reduction of the Co catalyst was conducted at 623 K at 1 bar for 15 h using a H2/He (1:3) gas mixture at a flow rate of 60 NL/h in a fixed-bed reactor with an i.d. of 2.5 cm. The reduced catalyst was transferred to the STSR in an inert atmosphere. The reactor temperature was then ramped to 503 K at a rate of 1 K/min under flowing N2. At this temperature, the N2 flow was cut off and H2 flow at 30 NL/h was introduced; the reactor was held for 10 h in H2 flow to ensure that the catalyst remained in a reduced state. The impeller speed was set to 750 rpm during catalyst in situ reduction and FTS reaction.

Figure 1. Evolution of CO conversion with time during the initial period (493 K, 1.5 MPa, H2/CO = 2.1, 8 NL/(g-cat·h)).

Following this initial period, the process conditions (pressure, H2/CO ratio and space velocity) were varied at a constant 670

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CO insertion,41 enolic,42 and alkenyl mechanisms.43 However no conclusive evidence has as of yet been provided to establish one of them as the definitive FTS mechanism, and the consensus has not been reached. Out of the proposed mechanisms, the carbide mechanism is the one most often used in kinetic modeling. The main characteristic of this mechanism is that the hydrocarbons are formed by successive addition of a building unit with one carbon atom and no oxygen into the growing chain.26 In our work, we adopted this approach. Ten different interpretations of the carbide mechanism were taken from the literature26,29 and coupled with the chain-length-dependent olefin desorption concept to derive kinetic models (designated FTS-I to FTS-X). All of the reaction pathways used in the model derivation can be found in the Supporting Information (Table S2 for FTS-I and Table S3 for FTS-II to FTS-X). 3.2. Chain-Length-Dependent Olefin Desorption. As stated earlier, Botes25 proposed a hydrocarbon selectivity model based on a chain-length-dependent olefin desorption effect. His model had three basic elementary reactions: chain growth, chain desorption (forming olefins), and chain hydrogenation (forming paraffins). The main assumption of this model is that rates of chain growth and chain hydrogenation to paraffin are independent of chain length, while chain desorption to olefin is a function of carbon number. This carbon number dependence is caused by the interaction of the chain with the catalyst surface, resulting in a longer residence time of high molecular weight hydrocarbons. This approach has some fundamental basis as explained below. There are several experimental and modeling studies which show that the strength of olefin adsorption at the surface increases linearly with increasing carbon number.44−49 This dependency is usually ascribed to a weak Van der Waal’s interaction of the chain with the surface50 and can be expressed as follows:

temperature. The baseline conditions were repeated in order to assess the catalyst deactivation. Cumulative degree of deactivation at time t on stream is calculated from experimental values of CO conversion as CD =

XCO(t0) − XCO(t ) × 100% XCO(t0)

(1)

where XCO is the CO conversion, t0 is time on stream (TOS) at the end of the initial period, and t is TOS when the baseline conditions were repeated. Tests were terminated when catalyst deactivation exceeded 20%, and no data with cumulative deactivation above this limit were used for kinetic modeling. Summary of the process conditions achieved during the three experimental runs, which were used in the kinetic modeling, can be found in the Supporting Information (Table S1). In total, 24 usable mass balances were collected. Process conditions were maintained for about 24 h, and steady state samples were usually collected during the last 8 h. Total mass balance and atomic closures were typically better than 100 ± 5%. The catalyst activity slowly decreased with time in all three runs. Figure 2 shows that the rate of deactivation was fairly similar

n ΔHads,o = a0 + a1n

(2)

where ΔHnads,o is the heat of adsorption of an olefin molecule with n C atoms and a0 and a1 are constants. If one recalls the Evans− Polanyi relation,51 it is reasonable to assume that the activation energy of the desorption step will also be linearly dependent on carbon number, i.e.:

Figure 2. Evolution of CO conversion with time for the baseline conditions (493 K, 1.5 MPa, H2/CO = 2.1, 8 NL/(g-cat·h)).

n 0 Ed,o = Ed,o + ΔEn

(3)

where End,o is

the activation energy of the desorption step of 1-olefin molecule with n C atoms, E0d,o is the part of the desorption energy that is independent of chain length, and ΔE is a contribution in the increase of desorption energy per every CH2 group. Applying this in the Arrhenius equation for the 1-olefin desorption rate constant (kd,n) results in the following expression:

for all the runs. The average deactivation rate, in terms of cumulative deactivation per hour, was 0.077, 0.112, and 0.097%/h for runs 1, 2, and 3, respectively. Shi and Davis8 showed that the product accumulation is an issue in the FTS reactors and that the products collected at a given time represent a mixture of freshly produced products and those that had accumulated in the reactor. A recent study by Masuku et al.38 showed that this effect is dominant for hydrocarbons higher than C17. Therefore our kinetic analysis focused only on hydrocarbons in C1−C15 range. Changes in product distribution with time are shown in Figure 3. It can be seen that hydrocarbon product distribution did not change significantly with time in spite of deactivation and/or product accumulation.

n

kd, n = Ad e−Ed,o / RT 0

= Ad e−(Ed,o +ΔEn)/ RT 0

= Ad e−Ed,o / RT e−ΔEn / RT

(4)

Grouping terms of this equation leads to the following: 0

3. COMPREHENSIVE KINETIC MODEL DEVELOPMENT 3.1. Mechanism of FTS. Several possible reaction pathways for FTS have been proposed in the past and include the following: carbide (also known as alkyl or CH2 insertion),39,40

kd,0 = Ad e−Ed,o / RT = f (T ) ≠ f ′(n)

(5)

e−ΔEn / RT = ecn

(6)

c=− 671

ΔE RT

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Figure 3. Reproducibility of hydrocarbon product distribution at replicated conditions during the kinetic period: (a) run 1 (493 K, 1.5 MPa, H2/CO = 2.1, 8 NL/(g-cat·h)); (b) run 2 (478 K, 1.5 MPa, H2/CO = 2.1, 3.7 NL/(g-cat·h)); (c) run 3 (503 K, 1.5 MPa, H2/CO = 2.1, 11.3 NL/(g-cat·h)).

Then the final form of the equation for the olefin desorption rate constant is the following: kd, n = kd,0ecn

(8)

3.3. Derivation of Rate Equations. The derivation starts with a form of carbide mechanism and uses the LHHW approach to relate the rate of hydrocarbon formation with the partial pressures of reacting gases and intrinsic kinetic (rate and equilibrium) constants of elementary reactions. The methodology applied has been well-established by authors who developed detailed kinetic models of FTS in the past, mainly Lox and Froment26 and Li and co-workers.28−31,52,53 The derivation makes use of the following assumptions: • Only one type of FTS active site is present on the Co catalyst surface. • The total number of active sites on the catalyst surface is constant. • The concentrations of surface intermediates and vacant sites are at steady state. • Methane and ethylene have different formation rate constants than other n-paraffins and 1-olefins, respectively. • Rate constants of chain propagation and hydrogenation to n-paraffin are independent of carbon number (Figure 4). • The rate constant of chain desorption to form 1-olefin is exponentially dependent on carbon number (eq 8). • Elementary steps for the formation of n-paraffins and 1-olefins are rate-determining steps (RDS), as is one of the elementary steps involved in chain propagation or monomer formation. All other elementary steps are considered to be quasi-equilibrated. An example of the detailed LHHW derivation procedure (model FTS-I) can be found in the Supporting Information.

Figure 4. Scheme of chain propagation (kp), hydrogenation to n-paraffin (kh), and desorption to 1-olefin (kd,n).

Here we will only show the important starting definitions and the final equations of model FTS-I. It is assumed that elementary steps 1, 5, and 6 are rate-determining steps, while the other steps are considered to be sufficiently rapid to be pseudoequilibrated. Rates of formation of n-paraffin and 1-olefin with carbon-number n can be written as: R CnH2n+2 = k5[CnH 2n + 1−S]PH2 cn

R CnH2n = k6,0e [CnH 2n + 1−S]PH2

n≥2 n≥3

(9) (10)

where [CnH2n+1−S] is the surface fraction of adsorbed species CnH2n+1−S. Methane and ethylene are assumed to have different formation rate constants: R CH4 = k5M[CH3−S]PH2

(11)

R C2H4 = k6E,0e 2c[C2H5−S]

(12)

Surface fractions of various growing chain intermediates [CnH2n+1−S] can be connected through the growth probability 672



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where i is the product species (i = CH4, C2H4, C2H6, ...), Rexp i is the experimental reaction rate of i, Fi is the molar flowrate of product species i at the reactor outlet, and W is the catalyst mass. Species used in our modeling are C1−C15 n-paraffins and C2−C15 1-olefins. Minor FTS products, like 2-olefins and oxygenates, are not considered. 4.2. Optimization Methodology. Optimal values of different rival model parameters were estimated by minimizing a multiresponse objective function:54

factor to intrinsic kinetic constants, partial pressures of CO, H2, and H2O and fraction of vacant sites [S]. The chain growth probability factor for a molecule having n carbon atoms (αn) is defined as follows: αn =

[CnH 2n + 1−S] k1PCO = [Cn − 1H 2n − 1−S] k1PCO + k5PH2 + k6,0ecn

n≥3

(13)

where αn depends on n through the exponential term in the denominator. Because methane and ethylene have different termination rate constants, growth probabilities for n = 1 and n = 2 should be defined separately: α1 =

[CH3−S] k1PCO = [H−S] k1PCO + k5MPH2

(14)

α2 =

[C2H5−S] k1PCO = [CH3−S] k1PCO + k5PH2 + k6Ee 2c

(15)

⎛ R exp − R cal ⎞2 i,j i,j ⎟ Fobj = ∑ ∑ ⎜⎜ exp ⎟ R i,j ⎠ i=1 j=1 ⎝ Nresp Nexp

where Nresp is the number of responses (n-paraffin and 1-olefin species, Nresp = 29) and Nexp is the number of experimental cal balances (conditions, Nexp = 24). Rexp i,j and Ri,j are experimental and calculated formation rates of species i in a balance j, respectively. Weighting factors were not used in the objective function, because of lack of availability of sufficient number of replicate balances, needed to calculate them. To avoid getting trapped in a local minimum, the genetic algorithm (GA) is used as a global optimization tool, followed by the Levenberg−Marquardt (LM) method for refined local optimization.29,55 Another advantage of using this approach is that the GA does not require any initial guesses for the parameters. The local optimization with LM utilizes parameters estimated by the GA as initial guesses. The algorithm of the MATLAB program used for kinetic parameter estimation can be found in the Supporting Information (Figure S1). The parameter estimation was first performed with isothermal data at 478, 493, and 503 K for all 10 models. Various models were discriminated based on the results of isothermal estimations. The best models at isothermal conditions were selected and nonisothermal estimation was performed on them. On the basis of the statistical and physicochemical tests, a final model was selected.26 4.3. Statistical and Physicochemical Tests. Different models were compared and discriminated based on various statistical tests and the physicochemical significance of estimated kinetic parameters. The accuracy of the model fit relative to the experimental data was obtained by statistical analysis using the mean absolute relative residual (MARR):19,29

The calculation of the fraction of vacant sites S requires relating it to partial pressures and kinetic constants through a site balance. The assumption made here is that the deactivation is negligible (i.e., the total number of active catalytic sites does not decrease over time). Therefore, the fraction of vacant sites can be calculated as follows: ⎧ ⎪ [S] = 1/⎨1 + ⎪ ⎩ +

K 7PH2 +

⎛ 1 1 K 7PH2 ⎜⎜1 + + K K K 4 3 4PH 2 ⎝

n i ⎫ PH2O ⎞ ⎪ 1 ⎟(α1 + α1α2 + α1α2 ∑ ∏ αj)⎬ ⎪ K 2K3K4 PH2 2 ⎟⎠ i=3 j=3 ⎭

(16)

Reaction rate equations for methane, ethylene, n-paraffin, and 1-olefin are the following: R CH4 = k5MK 7 0.5PH21.5α1[S]

(17)

R C2H4 = k6E,0e 2c K 7PH2 α1α2[S]

(18)

n

R CnH2n+2 = k5K 7 0.5PH21.5α1α2 ∏ αi[S]

n≥2 (19)

i=3

Nresp Nexp

n

R CnH2n = k6,0ecn K 7PH2 α1α2 ∏ αi[S] i=3

(22)

MARR =

n≥3

∑∑ i=1 j=1

(20)

cal R iexp ,j − R i,j

R iexp ,j

×

1 × 100% NrespNexp (23)

Equations 16−20 coupled with the equations for chain growth probabilities 13−15 represent model FTS-I equations. They allow for the explicit calculation of product formation rates.

The significances of the overall regression and estimated kinetic parameters were evaluated by the F and t tests, respectively. The error covariance needed for these tests was calculated from replicate baseline conditions at 493 K. All model parameters are intrinsic kinetic constants. Therefore, in addition to providing a good fit of the experimental data, the model parameters must satisfy physicochemical laws. Physicochemical constraints that have to be satisfied are the following:54,56,57 • Kinetic rate constants ki have to obey the Arrhenius temperature dependency, with activation energy:

4. PARAMETER ESTIMATION AND MODEL DISCRIMINATION 4.1. Reactor Model. Experiments were conducted in a reactor that can be idealized as a continuously stirred tank reactor (CSTR), with catalyst particles of sufficiently small diameter so that the physical transport resistances can be neglected. Rate of product formation can be calculated as follows: F R iexp = i (21) W

Ea, i > 0 673

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• Adsorption is an exothermic process so that the adsorption enthalpy has to satisfy: −ΔHa,0i > 0

• The adsorption entropy has to satisfy two conditions:

(25) 58

0 < −ΔSa,0i < Sg,0 i

(26)

41.8 < −ΔSa,0i < 51.4 + 1.4 × 10−3ΔHa,0i

(27)

where is the standard entropy of a gaseous species i, ΔS0a,i is the standard adsorption entropy, and ΔH0a,i is the heat of adsorption. 4.4. Isothermal Parameter Estimation and Initial Model Discrimination. The kinetic model parameters (reaction rate constants ki, the equilibrium and adsorption constants Ki, and parameter c) were first estimated at isothermal conditions (478, 493, and 503 K) for 10 rival models (FTS-I to FTS-X). The searching interval in the GA for kinetic parameters ki (rate and equilibrium constants) was set to 10−20 < ki < 1020, which is considered to be a very wide range in accordance with transition state theory.55 The parameter c was constrained between −1 and 0. The initial model discrimination was based on the overall fit of isothermal data based on MARR values (eq 23). The best models were FTS-III, FTS-X, and FTS-I, with MARR of 21.2, 22.5, and 25.5%, respectively. These models were then used in parameter estimation and discrimination using the data at all temperatures simultaneously. 4.5. Nonisothermal Parameter Estimation and Final Model Selection. The parameters are activation energies Ea,i, reaction and adsorption enthalpies ΔHi, preexponential factors Ai and a weak interaction contribution to 1-olefin desorption energy ΔE. The total number of points used simultaneously in nonisothermal estimation was 696 (24 mass balances with 29 responses). In this estimation, the Arrhenius law was directly introduced, as well as the expression for the equilibrium constant:26 S0g,i

⎛ Ea, i ⎞ ki(T ) = Ai exp⎜ − ⎟ ⎝ RT ⎠

(28)

⎛ ΔHi ⎞ ⎟ K i(T ) = Ai exp⎜ − ⎝ RT ⎠

(29)

Figure 5. Comparison between experimental and calculated rates of (a) methane, C2−4 and C5+ formation. (b) CO and H2 consumption.

In order to obtain realistic values of activation energies and heats of adsorption, the estimation of these parameters were constrained to a range of literature values. Carbon monoxide and hydrogen adsorption enthalpy bounds were −50 to −200 and −10 to −100 kJ/mol,59,60 respectively. Activation energies of chain propagation (and/or initiation), n-paraffin hydrogenation, and 1-olefin desorption were kept within the ranges 50−150, 70−120, and 80−150 kJ/mol, respectively.12,26,28,29,61,62 Values of Ai were searched in a wide range of 10−20−1020. Considering the values reported for weak van der Waals interactions on metallic surfaces,47,49,63 the parameter ΔE was kept in a physically reasonable range of 0−10 kJ/(mol·CH2). Nonisothermal parameter estimation was followed by statistical and physicochemical tests for the evaluations of models FTS-I, FTS-III, and FTS-X. Although models FTS-III and FTS-X produced a good fit of the data, both returned parameters that did not satisfy physicochemical constraints for the adsorption entropy (eq 27) and, as such, were discarded. Model FTS-I was consistent with physical laws and produced a good fit to the experimental data. It was chosen to be the best among the models tested.

5. RESULTS AND DISCUSSION 5.1. Estimated Model Parameters. Estimated parameter values of the model FTS-I are given in the Supporting Information (Table S4). The MARR value was 26.6%, and the F test showed that the model fit is statistically meaningful. Moreover, the t test showed that all parameters are statistically different from zero.54 The heat of hydrogen adsorption (ΔH7) was −25 kJ/mol and is similar to the reported value of −15 kJ/mol for Co-catalysts.64 The activation energy for CO activation step (E1), or the overall FTS energy barrier, was estimated to be 100.4 kJ/mol, which is in the middle of reported values (80−120 kJ/mol) for cobalt-based catalysts.60 Because experimental and modeling studies have thus far not reported activation energies for termination steps on Co-catalysts, we will base our comparison to existing values for the Fe-catalysts. The paraffin formation activation energy, E5 = 72 kJ/mol, is comparable, but slightly lower than the reported values of 80−90 kJ/mol by Dictor and Bell,61 94 kJ/mol by 674



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Figure 6. Comparison between experimental and calculated product distributions for (a−c) T = 478 K, P = 1.5 MPa, H2/CO = 2.1, WHSV = 3.7, NL/ (g-cat·h), XCO = 37%; (d−f) T = 493 K, P = 2.5 MPa, H2/CO = 2.1, WHSV = 6.1 NL/(g-cat·h), XCO = 57%; (g−i) T = 503 K, P = 2.5 MPa, H2/CO = 2.1, WHSV = 11.5 NL/(g-cat·h), XCO = 52%.

Lox and Froment,26 87 kJ/mol by Wang et al.,28 and 74 kJ/mol by Chang et al.31 In the present study, methane was assigned a separate rate constant because of its well-known higher formation rate. One of the explanations for this is that methane has a lower energy barrier for formation compared to other paraffins. Our results also corroborate this, since the value for E5M was found to be 63 kJ/mol. Because of the lower activation energy for this step methane formation from CH3−S is more favored over chain growth, compared to higher surface chains (i.e., CnH2n+1−S with n ≥ 2).65 In contrast, ethylene is known to have a lower formation rate and was therefore also provided with a separate rate constant parameter in the model. By analogy this can likely be attributed to a higher activation energy for ethylene formation compared to other 1-olefins, caused by the higher binding strength of ethylene as discussed by Goda et al.50 Our results tend to confirm this view, as activation energies for ethylene and 1-olefin desorption steps (E06E and E06) of 108 and 97 kJ/mol, respectively, were obtained from fitting of the data by the model. It is also worth noting that the olefin formation activation energies estimates are consistent with reported values in the 100−130 kJ/mol range.26,29,61 5.2. Chain-Length Dependency of 1-Olefin Desorption. Recognizing that the model incorporates chain-length dependency for 1-olefin desorption, note that the activation energy E06 is only a part of the activation energy of 1-olefin desorption that is independent of chain length. The actual activation energy of 1-olefin desorption is a linear function of carbon number and is different for each molecule (eq 3), increasing by a value of ΔE per every CH2 group: kJ ⎞ n ⎛ ⎜ ⎟ = 97.2 + 1.12n Ed,o ⎝ mol ⎠

The postulated cause for this change is a weak Van der Waal’s type interactions of the 1-olefin chain with the catalyst surface.50 Recently, De Moor et al.44 and Nguyen et al.45 used statistical thermodynamics and computational chemistry methods to study 1-olefin adsorption on zeolites and demonstrated that including weak van der Waals interactions with the surface indeed causes a linear increase in adsorption strength. The contribution of these forces to the strength of adsorption has been estimated to be as high as 6−8 kJ/(mol·C atom) for Co-catalysts.47 Therefore, even though weak compared to the energy of a chemical bond between an olefin chain and the active site, the cumulative effect of these forces with increasing chain length cannot be neglected. Weitkamp et al.66 hypothesized that this could affect chain growth probability. Cheng et al.46,47 showed that inclusion of these interactions leads to an exponentially decreasing olefin-to-paraffin ratio and increasing chain growth probability with carbon number. Our model is in agreement with these results and shows that the change in the activation energy for the 1-olefin desorption step, caused by weak van der Waals forces, is ΔE = 1.1 kJ/(mol·C atom). This leads to a constant c = −0.26 to −0.28 (eq 7) which matches the values reported previously.6,14,15,20 5.3. Mechanism and Surface Species. Model FTS-I is based on a form of carbide FTS mechanism proposed by Lox and Froment.26 Wang et al.28 and Kim et al.62 also used this mechanism in modeling of FTS kinetics. It is different than most commonly used forms of carbide mechanism and includes several Eley−Rideal type steps (steps 1, 2, 3, and 5). It postulates that chain initiation proceeds by adsorption of CO on an active site with adsorbed hydrogen (H−S) (step 1), which is considered to be a slow step and has some similarities with the H-assisted CO dissociation concept.64 H−S−CO is subsequently

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models of FTS kinetics. Wang et al.28 and Yang et al.29 included the olefin readsorption concept into their models for Fe catalysts and expressed the olefin concentration in terms of partial pressures but the models were unable to account for experimental deviations from the ASF distribution and trends in OPR with increase in carbon number. A model developed by Anfray et al.32 included solubility enhanced olefin readsorption by using liquid phase concentrations of reactants and readsorbing olefin species, but the agreement between the model predictions and experimental data for olefins was not good (Co FTS catalyst). Botes25 found that the olefin formation rate is directly proportional to ecn and only models which included this term could adequately describe the observed product distributions. Guo et al.30 used a model based on olefin readsorption and included an olefin formation rate constant dependence on chain length kole,n = kole,0e−(E+an)/RT, where the constant a accounts for a nonintrinsic physisorption effect. No theoretical justification for

hydrogenated with molecular hydrogen to H−S−CH2 (steps 2 and 3) and transformed to chain starter CH3−S (step 4). Chain propagation occurs by adsorption of CO on the active site that already contains a coverage of CnH2n+1−S (n = 1, 2, ...) to form CnH2n+1−S−CO,67 followed by subsequent hydrogenation to CnH2n+1−S−CH2 and transformation to Cn+1H2n+3−S. These steps have some similarity with the chain propagation steps in the COinsertion mechanism, because CO directly reacts with the adsorbed chain.65 However the difference is that CO is first hydrogenated to CH2 and only then inserted into the chain, which is consistent with the carbide mechanism. Hydrogenation of CnH2n+1−S to n-paraffin and desorption to 1-olefin are rate-determining steps.68,69 A mechanistic LHHW kinetic model provides relevant information about species that exist on the catalyst surface. Therefore, this model provides calculated surface coverage for all species considered to be involved in the FTS carbide mechanism. Calculated coverage of adsorbed species which contain CO from our model varies between 10 and 45% depending upon the process conditions. This can be related to experimental and modeling studies which show that under FTS reaction conditions the most dominant surface species is adsorbed CO, with reported coverage in the 20−65% range.65,68,70 The reported experimental hydrogen coverage is lower than the CO coverage (less than 10%)71,72 whereas in our model it is around 4%. 5.4. Model Predictions of the Experimental Rates. Figure 5a shows a comparison between experimental and calculated rates of methane, of C2−C4 and C5−C15 hydrocarbon formation. The majority of the data points are within a reasonable range of error, and the calculated C5−C15 rates are in a good agreement with the experimental data. The rates of carbon-monoxide and hydrogen consumption were calculated for given conditions by summing up calculated rates of hydrocarbon formations in accordance with reaction stoichiometry: 15

R CO =

∑ n(R C H n

2n + 2

+ R CnH2n)

n=1

(31)

15

R H2 =

∑ [(2n + 1)R C H n

n=1

2n + 2

+ 2nR CnH2n]

(32)

The comparison between calculated and experimental rates for CO and H2 consumption is shown in Figure 5b. Higher errors for these two species are due to the fact that they were not used in the objective function, and they were more affected by catalyst deactivation than the hydrocarbon species, as well as the fact that eqs 31 and 32 do not include formation rates of minor products (e.g., oxygenates) and heavy hydrocarbon products (>C15). However, in spite of this, the estimates are still within a reasonable error range. The model provides a good prediction of the main products (n-paraffin and 1-olefin) over a wide range of conditions used. In addition to providing a good fit of n-paraffin and 1-olefin formation (Figure 6a, d, and g), the model is also able to account for other features observed in the experiments. For example, higher methane and lower ethylene formation are also predicted. Consistent with the literature14,73 calculated chain-growth probabilities αn increased from 0.8 to 0.95 for C3 to C15 hydrocarbons (Figure 6b, e, and h). An exponential decrease in the 1-olefins to n-paraffins ratio (OPR) for C3+ hydrocarbons is also predicted by the proposed model (Figure 6c, f, and i). 5.5. Importance of the Exponential Chain-Length Dependence. Accounting for typical experimental deviations from ASF and variations of OPR with carbon number has been a challenging issue in the development of mechanistic LHHW

Figure 7. Comparison between model FTS-I (containing the exponential tem) and FTS-I without the exponential term (T = 478 K, P = 1.5 MPa, H2/CO = 2.1, WHSV = 3.7 NL/(g-cat·h), XCO = 37%): (a) product distribution; (b) 1-olefin/n-paraffin ratio. 676



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this type of rate equation was provided. Guo’s model provided a good fit of the data, including deviations from the ASF distribution and OPR variation with carbon number. The estimated olefin readsorption rate constant was 2 orders of magnitude lower than the corresponding forward reaction constant, and it is likely that the addition of a rate constant dependent on chain length had a far more significant effect on the model predictions than the inclusion of 1-olefin readsorption term. Teng et al.52,53 proposed two models based on the same reaction mechanism. The first model52 included the 1-olefin readsorption term and the model predictions followed a classical ASF distribution. In the subsequent model Teng et al.53 replaced the mechanistically derived readsorption rate equation with an equation containing ecn, in the forward reaction rate for olefin formation. The reversible reaction was not considered in the model derivation. This model was also able to account for non-ASF behavior and the experimental OPR. The models by Guo et al.30 and Teng et al.53 as well as the model used in this study show that addition of an exponential term ecn directly into the olefin formation rate law is essential in order to obtain good agreement with experimental results. This exponential dependency enables us to predict the increase in alpha with carbon number (eq 13). When model FTS-I parameters are estimated without the ecn term in the 1-olefin rate equation, predictions show a constant alpha value in the C3−C15 range (Figure 7a). The OPR in the FTS-I model is exponentially decreasing with carbon number, whereas without the exponential term it is a constant (Figure 7b). Our model shows how this exponential dependency can be related to increasing adsorption strength with increase in molecular weight of 1-olefins. However, additional studies are needed to investigate the exact nature of weak interactions of the adsorbed surface intermediate with the surface of the catalyst and to quantify them.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +974-4423-0134. Fax: +974-4423-0065. E-mail: dragomir. [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication was made possible by NPRP grant 08-173-2050 from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors. B.T. would like to thank Dr. Nikola Nikacevic, from the University of Belgrade, for his support and helpful discussion.

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REFERENCES

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6. CONCLUSIONS Kinetic experiments were performed on a rhenium-promoted Co/Al2O3 catalyst over a range of process conditions. Several LHHW models were derived based on the different forms of carbide FTS mechanism. The model FTS-I was shown to be the best considering physicochemical and statistical tests. This model provided a good fit of the n-paraffin and 1-olefin formation rates, as well as a reasonable prediction of the reactant consumption rates, for the studied conditions. Adding an exponential dependency of carbon number, related to the chain-lengthdependent olefin desorption concept, was shown to be the key for prediction of both increasing chain-growth probability in the ASF distribution and decreasing olefin-to-paraffin ratio with carbon number. To our knowledge, this is the first LHHW model of FTS over promoted Co catalyst that is able to predict these experimental observations. Strict mechanistic methodology allowed for intrinsic kinetic parameters to be estimated over industrially relevant process conditions. The kinetic model presented here, coupled with appropriate mass and energy balance equations, can therefore be used as the basis for advanced design, scale-up, and optimization of all FTS reactor types.

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ASSOCIATED CONTENT

S Supporting Information *

Tables S1−S4, Figure S1, and derivation of model FTS-I. This material is available free of charge via the Internet at http://pubs. acs.org. 677



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