MoS

5246

Ind. Eng. Chem. Res. 1997, 36, 5246-5257

Kinetic Analysis of Mixed Alcohol Synthesis from Syngas over K/MoS2 Catalyst Tae Yun Park,† In-Sik Nam,* and Young Gul Kim Research Center for Catalytic Technology, Department of Chemical Engineering, School of Environmental Engineering, Pohang University of Science and Technology (POSTECH) and Research Institute of Industrial Science and Technology (RIST), P.O. Box 125, Pohang 790-600, Korea

A mechanistic kinetic model has been developed to describe the synthesis of mixed alcohol from syngas over 17 wt % K2CO3 promoted MoS2 catalyst. A rigorous kinetic network has been considered on the basis of a CO insertion mechanism for this reaction system. The kinetic model was derived by using LHHW formalism and steady-state approximation for reaction intermediates. The kinetic parameters were estimated by nonlinear regression of the experimental data using the method of reparameterization. The model successfully predicts the formation and distribution of the products within the range of experimental conditions. Mixed alcohol formation was maximized when the temperature was ∼320 °C independent of the pressure. With the higher pressure, the optimal reactor space time is longer, and the produced alcohols further react with syngas to form paraffins when the reaction temperature is higher than 320 °C and the space time exceeds its optimum. The H2/CO molar feed ratio affected the product composition of mixed alcohols and hydrocarbons, and their experimental and theoretical composition obeyed the Schulz-Flory distribution. The kinetic model developed in the present study has been simulated to examine the effect of operating conditions on the formation of mixed alcohols in the wider range of reaction conditions. Introduction Mixtures of methanol and higher alcohols (C2+OH) named mixed alcohols are well-known additives for automotive fuel blends. Other potential uses of higher alcohols are extensively discussed by Xiaoding et al. (1987). The development of catalysts for mixed alcohol synthesis from syngas has been studied by many investigators (Natta et al., 1957; Ichikawa, 1978; Courty et al., 1982; Quarderer, 1986; Nunan et al., 1989; Woo et al., 1991). Among the various catalysts, Mo-based catalysts can be considered promising due to their high activity and selectivity for alcohols and their active water-gas shift reaction. In particular, MoS2-based catalysts developed by Dow Chemical (Quarderer and Cochran, 1984; Woo et al., 1993b) exhibit high resistance to sulfur poisoning. Murchison et al. (1988) reported that the addition of cobalt to the alkali-promoted MoS2 enhances the selectivity of C2+OH. Supported molybdenum catalysts were also active for mixed alcohol synthesis (Tatsumi et al., 1984, 1987), and alcohol selectivity was strongly influenced by both alkali promoter and reactor pressure over MoS2 catalysts (Xie et al., 1986). Moreover, Woo et al. (1990, 1992a,b, 1993a,c, 1994) found that potassium was the best cation additive for alcohol selectivity among the various alkali promoters. The optimum K2CO3 loading on MoS2 catalyst was also reported as 17 wt %. As for the kinetic studies of mixed alcohol synthesis, a lumped kinetic model for higher alcohol synthesis over potassium-promoted zinc-chromium oxide catalyst (Tronconi et al., 1987, 1991; Beretta et al., 1996) and a mechanistic model for C2+ oxygenate products over Cs* To whom correspondence should be addressed. Tel.: 82562-279-2264. Fax: 82-562-279-8299. E-mail: isnam@ vision.postech.ac.kr. † Present address: Laboratorium voor Petrochemische Techniek, Rijksuniversiteit, B9000 Gent, Belgium. S0888-5885(96)00570-2 CCC: $14.00

promoted zinc-chromium oxide catalysts were investigated (Tronconi et al., 1991). A kinetic model for methanol and higher alcohol synthesis over a K2CO3promoted Cu/ZnO/Cr2O3 catalyst was also reported by Calverley and Smith (1992). Smith et al. (1990) also studied the kinetic model for higher alcohol synthesis over alkali-promoted Cu/ZnO and MoS2 catalysts. The reaction mechanism and kinetic model of Cu/Co (IFP) and Rh-based catalysts were also suggested by Xiaoding et al. (1987). From the recent studies of 13C NMR, a CO insertion mechanism for the alcohol chain growth was reported on alkali/Co/MoS2 catalysts by Santiesteban et al. (1988). It may be considered as one of the most probable reaction mechanisms with experimental verification for this complex reaction system. It should be noted that all kinetic models developed so far are simply based upon the experimental observations by chemical reaction. Although good predictability of the model by the reaction mechanism was observed, many ambiguities remained in the model developed in the literature for this reaction system, such as the following: (1) A rigorous mathematical model of the rate equations based upon the reaction network and mechanism was not presented. (2) Temperature dependencies of kinetic and equilibrium parameters were not correlated. (3) The water-gas shift reaction was not included for the kinetic study. Thus, a more analytic and systematic approach for the kinetic study of the synthesis of mixed alcohols over alkali/MoS2 catalysts is needed to describe the complex reaction system producing more than 20 products including oxygenates and hydrocarbons. In this study, the reaction system for mixed alcohol synthesis over 17 wt % K2CO3-promoted MoS2 catalyst is defined by identifying independent reactions and stoichiometric relationships with the limiting variable, i.e., CO conversions to each product. A mechanistic © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5247 Table 1. Properties of the MoS2-Based Catalyst particle size (Å) catalyst

BET surface area (m2/g)

composition

by XRDa

by BETb

65.1 44.6

MoS2.30

37 38

182 266

38

280

MoS2 prepared at 723 K 17 wt % K2CO3/MoS2 before reaction 17 wt % K2CO3/MoS2 after reaction

42.0

a D /λ(β cos θ): λ is the wavelength of Cu KR X-ray radiation; θ c is the Bragg angle; β is the half-width corrected for KR double separation and instrumental broadening. b Dp ) 6/FSg; F is the density; Sg is the specific surface area by BET.

kinetic model is derived from a rigorous kinetic network based upon a CO insertion mechanism. The effect of operating conditions, such as temperature, pressure, space time, and H2/CO molar feed ratio, and their optimal combination for mixed alcohol formation by simulation of the model are also discussed. Experimental Section Catalyst. Unsupported MoS2 was prepared by the thermal decomposition of (NH4)2MoS4 in a N2 atmosphere, as reported by Tauster et al. (1980). The (NH4)2MoS4 was obtained by adding a solution containing excess (NH4)2S with MoOCl3 at ambient temperature. MoOCl3 was manufactured by dissolving MoCl5 with methanol. For MoS2, (NH4)2MoS4 was heated for 2 h in a tube furnace with flowing nitrogen at 723 K. XRD patterns of the MoS2 catalyst prepared were identified by a Rigaku (Model DMax-B) diffractometer using Cu KR radiation. Elementary analysis of MoS2 was carried out using the combustion gas chromatographic method. The specific surface area was measured by the BET method on a Micromeritics Accusorb 2100E. Promoted MoS2 catalysts were prepared by impregnating K2CO3 on MoS2 and drying at 381 ( 1 K. The content of K2CO3 was 17 wt %. The catalysts were then ground to powder less than 200 mesh before use to avoid mass transport limitation. Indeed, the limitation was found to be negligible by the experiment for external diffusion and by the calculation method of Froment and Bischoff (1990). The characteristics of the catalyst are listed in Table 1. Experimental Procedure. The synthesis reaction was carried out in a tubular fixed-bed integral reactor made of stainless steel tube with 0.9 cm inside diameter, containing 1.0 g of catalyst. The following operating variables were explored: temperature, T ) 250-350 °C; total pressure, P ) 15-90 atm; space time, W/(FCO)0 or τ ) 4-22 g-cat‚h/mol; H2/CO molar feed ratio, ΘH2 ) 0.5-4. Premixed synthesis gas and N2 (3 vol % as an internal standard) were continuously fed to the reactor through a charcoal trap to eliminate carbonyl impurities. The steady-state activity and selectivity of the catalyst were observed after 6-20 h of reactor on-stream time. To confirm the steady state and catalyst deactivation of reaction, several data points were collected at the same reaction conditions used for reaction periods up to 50 h. Reactant and products were analyzed by a gas chromatograph (HP 5890). Concentrations of CO, CO2, CH4, and N2 in the product stream were determined by a thermal conductivity detector through a 4 m activated carbon-packed column. Compounds such as hydrocar-

Figure 1. Overall scheme for the modified CO insertion mechanism over K/MoS2 catalyst.

bons and oxygenates were separated on a 50 m PONA capillary column and analyzed by a flame ionization detector. Details have already been described elsewhere (Woo et al., 1991). Reaction Scheme The reaction system for linear mixed alcohols from syngas over a K/MoS2 catalyst is extremely complex and can be classified into the following reactions: alcohol synthesis, Fischer-Tropsch reactions for hydrocarbons, ester synthesis, and water-gas shift reaction (WGS). On the basis of the CO insertion mechanism (Santiesteban et al., 1988) and the reaction network developed by Smith et al. (1990), a detailed kinetic network was modified by consideration of all surface concentrations

5248 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997

involved in the reaction pathways. The overall scheme of the kinetic network is shown in Figure 1, and it can also be represented by

initiation

parallel reactions iCO + 2iH2 f CiH2i+1OH + (i - 1)H2O i ) 1, 2, 3, ..., n1 (14) iCO + (2i + 1)H2 f CiH2i+2 + iH2O i ) 1, 2, 3, ..., n2 (15)

CO + s T COs, KCO

(1)

H2 + 2s T 2Hs, KH

(2)

COs + Hs T CHOs + s, KCHO

(3)

i ) 1, 2, 3, ..., n3 (16)

CHOs + Hs T CH2Os + s, KCH2O

(4)

CH2Os + Hs T R1Os + s, KR1O

(5)

(i + 1)CO + 2iH2 f Ci-1H2i-1COOCH3 + (i - 1)H2O i ) 1, 2, 3, ..., n4 (17)

iCO + 2iH2 f CiH2i + iH2O

series reactions

chain growth RiOs + COs f RiCOOs + s, kie i ) 1, 2, 3, ..., n4 (6) RiOs + 2Hs f Ris + H2O +2s, kih i ) 1, 2, 3, ..., n2 (7) Ris + COs f RiCOs + s, kic i ) 1, 2, 3, ..., n3 (8) RiCOs + 2Hs f Ri+1Os + 2s, kiy i ) 1, 2, 3, ..., n1 (9) termination

(i - n)CO + CnH2n+1OH + 2(i - n)H2 f CiH2i+1OH + (i - n)H2O (18) n ) 1, 2, ..., i ) n + 1, n + 2, ..., n1 (i - n)CO + CnH2n+1OH + [2(i - n) + 1]H2 f CiH2i+2 + (i - n + 1)H2O (19) n ) 1, 2, ..., i ) n, n + 1, ..., n2 (i - n)CO + CnH2n+1OH + 2(i - n)H2 f CiH2i + (i - n + 1)H2O (20) n ) 1, 2, ..., i ) n, n + 1, ..., n3, i * 1

RiOs + Hs T RiOH + 2s, kta, k-ta i ) 1, 2, 3, ..., n1 (10)

(i - n + 1)CO + CnH2n+1OH + 2(i - n)H2 f Ci-1H2i-1COOCH3 + (i - n)H2O (21) n ) 1, 2, ..., i ) n, n + 1, ..., n4

RiCOOs + Hs f R1COORi-1 + 2s, kte i ) 1, 2, 3, ..., n4 (11)

water-gas shift reaction

Ris + Hs f CiH2i+2 + 2s, ktp, i ) 1, 2, 3, ..., n2 (12) Ris f CiH2i + Hs, kto i ) 1, 2, 3, ..., n3

(13)

K and k for reactions 1-13 denote an equilibrium constant and a rate constant, respectively. Reactions 1-5 are assumed to be in equilibrium. R indicates an alkyl group, i.e., Ri ) CiH2i+1, and R0 ) CH. Reactions 1 and 2 show associative adsorption for CO and dissociative adsorption for H2 on the catalytic active site, s, respectively. The methyl intermediate R1O is formed by repeated hydrogenation of adsorbed CO and H2 as described in reactions 3-5. The chain growth scheme (reactions 6-9) shows the formation of the various precursors, i.e., RiOs for alcohols, Ris for hydrocarbons, and RiCOOs for esters by CO insertion and hydrogenation. Alcohols and other products are formed by hydrogenation of their precursors, as shown in the termination step reactions 10-13. n1n4 are the maximum carbon numbers for the various products, and their values of experimental observation are n1 ) 5-6 for alcohols, n2 ) 7-8 for paraffins, n3 ) 4-5 for olefins, n4 ) 3-4 for esters. Mixed alcohols are assumed to be formed by a reversible step (reaction 10), which is also suggested by the previous studies (Santiesteban et al., 1988; Smith et al., 1990). For the reaction mechanism described by the elementary reaction network shown in Figure 1, the overall reaction schemes listed in reactions 1-13 can also be summarized into three categories of reactions:

CO + H2O T CO2 + H2

(22)

The parallel reactions 14-17 showed the formation of products directly from syngas, while the products synthesized from syngas with alcohols could be illustrated by the series reactions 18-21. It should be noted that alcohols are only reaction intermediates by their reversible reaction mechanism shown in the series reaction. The number of parallel and series reactions can be obtained by adding up the number of reactions involved in the overall reaction scheme as follows:

number of parallel reactions ) n1 + n2 + n3 + n4 (23) number of series reactions ) n1(n1 - 1) n2(n2 + 1) n3(n3 + 3) n4(n4 + 1) + + + 2 2 2 2 (24) If n1 ) n2 ) n3 ) n4 ) 10, the number of parallel and series reactions are 40 and 220, respectively. Therefore, the total number of overall reactions is 260. However, the number of kinetic equations relevantly describing the kinetic behavior of this reaction system should be same to the number of chemical species involved in the reactions 14-22, i.e., n1 + n2 + (n3 - 1) + n4 + 4. Note that 4 results from the number of the following chemical species, i.e., CO, H2, CO2, and H2O. In order to confirm the minimum number of reactions for the simplification of the complex reactions, the independence of reactions was examined.

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5249

By Gaussian elimination of the reaction matrix which comprises the stoichiometric coefficients of reactions 14-22, the number of independent reactions was found to be always identical to that of the parallel reactions (Park, 1992). Then, a set of kinetic equations can be derived for alcohols, hydrocarbons, esters, and CO2 representing the independent reactions that belong to a set of parallel reactions 14-17 and reaction 22. A criterion for checking the independence of multiple reaction system is developed. It states that the number of independent reactions for any multiple reaction system cannot be greater than that of chemical species involved in the reactions. In addition, it also makes the kinetic modeling of complex reaction system easier. The CO conversion into the various products is defined as

Xij ) (moles of CO consumed to produce i component group with carbon number j)/ (moles of CO fed to the reactor) (25) or

Xk )

FiE )

[

FCO ) (FCO)O(1 -

(i + 1)

Xei

i ) 1, 2, 3, ..., n4 n1

n3

∑ i)2

∑ i)1

( ) 2-

1 i

n2

Xpi ∑ i)1

Xai - 2

n4

Xoi -

(34)

∑ i)1

[

]]

(2i + 1) (i + 1)

Xei (35)

where Xai denotes the CO conversion into alcohols from reaction 14, and Xpi, Xoi, Xei, and XW represent the CO conversion into paraffins, olefins, esters, and CO2 from reactions 15-17 and reaction 22, respectively. Fi is the molar flow rate for species i, and Θi is the molar feed ratio for species i to CO. Kinetic Model From the elementary kinetic pathways represented by reactions 1-13, a mechanistic kinetic model can be derived by using the Langmuir-HinshelwoodHougen-Watson (LHHW) formalism. Assuming reactions 1-5 are in equilibrium,

By the substitution of eq 25 into reactions 14-17 and eq 26 into reaction 22, n2

(FCO)O

FT ) (FCO)O 1 + ΘH2 + ΘN2 - 2

moles of CO consumed by reaction k (26) moles of CO fed to the reactor

n1

[ ]

n3

Xai - ∑Xpi - ∑Xoi ∑ i)1 i)1 i)1

[COs] ) KCOPCO[s]

(36)

[Hs] ) (KHPH2)1/2[s]

(37)

1/2 [CHOs] ) K1PCOPH [s] 2

(38)

[CH2Os] ) K2PCOPH2[s]

(39)

3/2 [s] [R1Os] ) λ4PCOPH 2

(40)

n4

Xei - XW) ∑ i)1 n1

(27)

n2

Xai - ∑(2 + 1/i)XPi ∑ i)1 i)1

FH2 ) (FCO)O[ΘH2 - 2 n3

2

∑ i)2

n4

Xoi -

{2i/(i + 1)}Xei + Xw] ∑ i)1

FCO2 ) (FCO)oXw n1

n2

(28)

(29)

n3

where [ ] denotes surface concentrations of adsorbed components, Pi is the partial pressure of gaseous species i, and K and λ4 are equilibrium constants for each reaction steps. Note that the adsorption of CO2 and H2O was ignored on the catalyst surface for the simplification of the development of the kinetic model in the present study. However, the equilibrium reaction rate of the water-gas shift reaction is included in this work as in eq 61. From the steady-state approximation for the surface intermediates of alkyl groups,

[RiOs] )

(1 - 1/i)Xai + ∑Xpi + ∑Xoi + ∑ i)1 i)1 i)2

FH2O ) (FCO)O[

n4

{(i - 1)/(i + 1)}Xei - XW] ∑ i)1 1 FiOH ) (FCO)OXai i 1 Fi ) (FCO)OXpi i P

1 FiO ) (FCO)OXoi i

i ) 1, 2, 3, ..., n1

i ) 1, 2, 3, ..., n2

kiy[Ri-1COs][Hs]2 + k-taPiOH[s]2 kie[COs] + kih[Hs]2 + kta[Hs] i ) 2, 3, 4, ..., n1 (41)

(30) [RiCOOs] ) (31)

[Ris] )

i ) 2, 3, 4, ..., n4 (42)

ktp[Hs] + kic[COs] + kW

(32)

(33)

kie[Hs] kih[RiOs][Hs]2

[RiCOs] ) i ) 1, 2, 3, ..., n3

kie[RiOs][COs]

kic[Ris][COs] kiy[Hs]2

i ) 2, 3, 4, ..., n2

i ) 2, 3, 4, ..., n3

(43) (44)

The concentration of vacant site [s] can be determined from the site balance


[s]0 ) [s] + [COs] + [Hs] + [CHOs] + [CH2Os] + n1

[R1Os] +

n4

(riP), olefins (riO), and esters (riE) can be written

n2

[RiOs] + ∑[RiCOOs] + ∑[Ris] + ∑ i)2 i)1 i)1

1/2 θ λ2PH 2 RiO

OH

ri

Ads

)

n3

[RiCOs] ∑ i)1

(45) P

ri )

The last four terms of eq 45 are assumed to be negligible; then,

λ5PiOH -

1/2 θ λ7PH 2 Ri

E

ri )

i ) 1, 2, 3, ..., n2

Ads

riO ) ktoθRi

[s]0 ≈ [s] + [COs] + [Hs] + [CHOs] + [CH2Os] + [R1Os] (46)

i ) 1, 2, 3, ..., n1

Ads2

i ) 1, 2, 3, ..., n3

1/2 θ (λ1/λ6)PH 2 RiCOO

(57)

(58) (59)

i ) 1, 2, 3, ..., n4 (60)

The above assumption for [s]0 seems reasonable, since in a reaction scheme satisfying the Schulz-Flory distribution, the formation of the higher carbons (C2+) are decreased exponentially with respect to n (Sarup and Wojciechowski, 1989). Substituting eqs 36-39 into eq 46 and solving for [s],

First-order reversible kinetics is assumed for the formation of CO2 by water-gas shift reaction 22 (Newsome, 1980):

[s] ) [s]0/Ads

rWGS ) kPCO - (k/KP)PCO2

(47)

where Ads denotes the adsorption term, i.e.,

Ads ) 1 + KCOPCO + (KHPH2)

1/2

+

1/2 3/2 K1PCOPH + K2PCOPH2 + λ4PCOPH 2 2

Introducing surface coverage θi for surface species i using eq 47, eqs 36-40 become

θCO ) KCOPCO/Ads

(48)

θH ) (KHPH2)1/2/Ads

(49)

1/2 θCHO ) K1PCOPH /Ads 2

(50)

θCH2O ) K2PCOPH2/Ads

(51)

3/2 /Ads θR1O ) λ4PCOPH 2

(52)

The surface coverage for the intermediates can also be obtained by substituting eqs 47-52 and eqs 41-44:

θRiO )

(λ1PCO +

Reactor Model The mole balances of the tubular fixed-bed integral reactor employed in the present study are derived for the analysis of experimental kinetic data. Heat and mass transports across the catalyst loading were found to be fast compared to the reaction kinetics. Limitation due to pore diffusion was negligible and the reactor has been regarded as isothermal. Mole balances from eqs 57-61 and stoichiometric relationships from eqs 2735 yield OH

ri

dFiOH 1 dXai ) ) dW i dτ

i ) 1, 2, 3, ..., n1 (62)

dFiP 1 dXpi ) dW i dτ

i ) 1, 2, 3, ..., n2

(63)

dFiO 1 dXoi ) ) dW i dτ

i ) 2, 3, 4, ..., n3

(64)

riP )

+ λ3PH2

(61)

where KP ) exp[(4577.8/T) - 4.33]. The kinetic parameters, λ2 and λ5 in eq 57 relate to the production and consumption of alcohols, respectively, while λ7 and kto in eqs 58 and 59 relate to the formation of hydrocarbons. The partial pressure of CO, H2, and alcohols, as well as the surface coverage of RiOs, Ris, and RiCOOs, also affect the formation of products.

(λ8/λ9)θRi-1COPH2 + λ5PiOH 1/2 λ2PH )Ads 2

Ads

i ) 2, 3, 4, ..., n1 (53) θRiCOO )

θRi )

λ6PCOθRiO 1/2 PH 2

O

i ) 2, 3, 4, ..., n4

(54)

ri

riFT ) riP + riO

λ3θRiOPH2 1/2 (λ7PH + λ8PCO + ktoAds)Ads 2

i ) 2, 3, 4, ..., n2 (55) θRiCO )

λ9PCOAdsθR1 PH2

i ) 2, 3, 4, ..., n3

(56)

The λi (i ) 1, 2, ..., 9) is the kinetic parameter group defined by equilibrium and rate constants. From the termination reactions 10-13, the rate equation of the formation of alcohols (riOH), paraffins

riE )

dFiE 1 dXei ) dW i + 1 dτ rWGS )

i ) 1, 2, 3, ..., n4 (66)

dFCO2 dW

(65)

)

dXw dτ

(67)

where W is the catalyst loading and τ is the space time of CO in the reactor, i.e., W/(FCO)0. The rate of higher hydrocarbons formation, riFT is expressed by the summation of the rates of paraffins and olefins.

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5251 Table 2. Kinetic Parameters and the Fitness of the Model at T ) 270 °C

Table 3. Model Fitness from Nonlinear Regression at Five Different Reaction Temperatures 250 °C 270 °C 300 °C 320 °C

Parameter Values parameter

value

unit

KCO KH K1 K2 λ1 λ2 λ3 λ4 λ5 λ6 λ7 λ8 λ9 kto k

0.32661 × 10 0.14945 × 10 0.35913 × 10-1 0.61376 × 10-1 0.65146 × 10-1 0.24533 × 102 0.28730 × 102 0.59288 × 10-1 0.87843 × 103 0.30221 0.10849 × 103 0.86752 × 102 0.37502 × 10-1 0.16145 0.20823

MPa-1 MPa-1 MPa-3/2 MPa-2 mol‚kg-cat.-1‚h-1‚MPa-1 mol‚kg-cat.-1‚h-1‚MPa-1/2 mol‚kg-cat.-1‚h-1‚MPa-1 MPa-5/2 mol‚kg-cat.-1‚h-1‚MPa-1 MPa-1/2 mol‚kg-cat.-1‚h-1‚MPa-1/2 mol‚kg-cat.-1‚h-1‚MPa-1 dimensionless mol‚kg-cat.-1‚h-1 mol‚kg-cat.-1‚h-1‚MPa-1

m no. of residuals residual sum of squares mean percent errora std devb

20 800 0.536

19 760 3.074

15 600 3.840

350 °C

20 20 800 800 40.873 105.201

14.223 12.037 13.823 13.788 15.716 14.276 10.239 6.314 10.019 13.786

a The average of relative error between experimental and calculated values for CO conversion. b The standard deviation from mean percent error for CO conversion.

Fitness

∑X

ai

i

mean percent std devb

errora

14.69 12.02

∑X

∑X

pi

i

FT i

i

15.71 11.09

24.02 16.15

∑X

ei

i

32.58 47.02

XW 17.05 11.25

a The average of relative error between experimental and calculated values. b The standard deviation from mean percent error.

By substituting eqs 62-67 into eqs 57-61 and rearranging, 1/2 dXai iλ2PH2 θRiO iλ5PiOH ) dτ Ads Ads2 1/2 dXpi iλ7PH2 θRi ) dτ Ads

dXoi ) ktoθRi dτ

i ) 1, 2, 3, ..., n1 (68)

i ) 1, 2, 3, ..., n2 i ) 2, 3, 4, ..., n3

dXiFT dXpi dXoi ) + dτ dτ dτ 1/2 dXei (i + 1)(λ1/λ6)PH2 θRiCOO ) dτ Ads

(69)

Figure 2. Van’t Hoff plot for equilibrium constants: KH (4), KCO (0), λ4 (]), and K1 (O). Symbols by nonlinear regression at each temperature; lines by least-squares analysis of the symbols.

(70)

(71)

i ) 1, 2, 3, ..., n4 (72)

dXW ) kPCO - (k/Kp)PCO2 dτ Kp ) exp(4577.9/T - 4.33) (73) where Pi is the partial pressure of species i, which is also function of CO conversion for products, Xij by eqs 27-35. Since the sets of coupled nonlinear differential eqs 68-73 are only function of kinetic parameters, CO conversion into the various products, total pressure and H2/CO feed ratio, they can be numerically integrated in the task of parameter estimation. Parameter Estimation The 15 kinetic parameters (KCO, KH, K1, K2, λ1-λ9, kto, k) appearing in eqs 48-56 and eqs 68-73 have been estimated by nonlinear regression. By taking n1 ) n2

Figure 3. Temperature dependence of the kinetic parameter: λ1 (0), λ3 (4), λ5 (]), and λ6 (×). Symbols by nonlinear regression at each temperature; lines by least-squares analysis of the symbols.

) n3 ) n4 ) 10, 40 coupled nonlinear differential eqs 68-73 were solved by Gear’s method using IMSL subroutine DGEAR. Gear’s method is known to be applied to any degree of stiffness and allows appropriate accuracy of integration with moderate computer time.


Figure 4. Temperature dependence of the kinetic parameter: λ2 (9), λ7 (4), λ8 (×), λ9 (]), kto (0), and k (+). Symbols by nonlinear regression at each temperature; lines by least-squares analysis of the symbols.

Figure 5. Quality of fit for CO conversion at 250 (+), 270 (b), 300 (4), 320 (0), and 350 °C (O).

Table 4. Kinetic Constants Estimated by Reparameterizationa Parameter Group of Equilibrium Constants KH

K1

K2

λ4

1.70768 × 10-2 -0.98938 × 103

-0.33730 × 101 -0.86282 × 105

-0.34122 × 101 -0.10118 × 105

-0.31825 × 101 -0.10863 × 104

KCO Ri

-0.90489

βi

-0.40600 × 104

Parameter Group of Rate Constants λ1 Ri

-0.89267

βi

0.75336 × 104

Ri βi a

λ2

λ3

λ5

λ6

0.40903 × 101 0.53719 × 104

0.45309 × 101 0.64180 × 104

0.64758 × 101 0.62206 × 104

-0.11496 × 101 0.23281 × 104

λ7

λ8

λ9

kto

0.48380 × 101 0.26929 × 105

0.35305 × 101 0.24013 × 105

-0.17750 × 101 0.14626 × 105

0.23007 × 101 0.68914 × 104

k -0.24454 0.11401 × 105

Ri and βi are the parameters in eq 76.

The parameter estimates have been obtained by minimizing the following residual sum of squares at five different reaction temperatures: m 10 4

min

∑ ∑∑

[Xexp ij (%)

-

2 Xcal ij (%)]k

(74)

k)1j)1 i)1

where m is the number of different experimental conditions for total pressure and space time at a given temperature, and Xijexp and Xijcal are the experimental and calculated CO conversions for products, respectively. The Levenverg-Marquardt technique in IMSL subroutine ZXSSQ has been employed to perform the multiresponse nonlinear regression. To make sure that the minima were not local, more than 1300 different initial values were tried. Calculated values of the kinetic parameters and the fitness for the kinetic model

Figure 6. Formation of alcohol with respect to reaction temperatures for 15 (+), 30 ([), 50 (4), 70 (0), and 90 atm (O) at ΘH2 ) 1.01 and τ ) 17.1 g-cat‚h/mol. Symbols experimental; lines simulated.

at 270 °C are illustrated in Table 2 as an example. The mean percent error, which is the average of relative error between experimental and calculated values for various components, shows that the degree of the agreement of the model with experimental data is fairly good except for the components, ∑iXei and ∑iXFT i . The values of mean percent error for ∑iXei and ∑iXFT were i somewhat large, for two reasons: (i) their values are very small (average ∑iXei ) 0.03, ∑iXFT ) 0.15%) i compared to other values, so that the amount of their residuals in eq 74 is too small to be minimized during the regression procedure; (ii) small detection errors of gas chromatograph can be significant in that low conversion region. Standard deviation from the mean percent error reveals the well-distributed experimental -calculated CO conversions for products.


Figure 7. Conversion of CO with respect to reaction temperatures (XCO, O), to CO2 formation (XW, 4), to mixed alcohol formation (∑iX1i, ×) and to paraffin formation (∑iXpi, +) at 320 °C, 90 atm, τ ) 17.1 g-cat‚h/mol, and ΘH2 ) 1.01. Symbols experimental; lines simulated.

Figure 8. Effect of pressure on CO conversion (XCO, O) and CO2 formation (XW, ×) at ΘH2 ) 1.01 and τ ) 17.1 g-cat‚h/mol. Symbols experimental; lines simulated.

Table 3 shows the overall degree of model fitness resulting from nonlinear regression at five different reaction temperatures. The number of residuals were given in eq 74 as 4 × 10 × m. In this case, the mean percent error and standard deviation were determined for the total CO conversion (XCO),

XCO )

∑i Xai + ∑i Xpi + ∑i Xoi + ∑i Xei + XW

(75)

The increase of the residual sum of squares as reaction temperature increases is simply because the magnitude of the experimental and calculated CO conversion for each products becomes larger at higher reaction temperature. It does not mean a poorer agree-

Figure 9. Effect of pressure on mixed alcohol formation (∑iXai, O) and paraffin formation (∑iXpi, ×) at ΘH2 ) 1.01 and τ ) 17.1 g-cat‚h/mol. Symbols experimental; lines simulated.

Figure 10. Effect of space time on CO conversion (XCO, O), CO2 formation (XW, 0), and formation of mixed alcohols (∑iXai, 4) and paraffins (∑iXpi, ]) at 320 °C, 90 atm, and ΘH2 ) 1.01. Symbols experimental; lines simulated.

ment of calculated conversion with experimental observation as temperature increases. The Van’t Hoff relationships for equilibrium constant group are shown in Figure 2 while the Arrhenius plots for the rate constant group are also illustrated in Figures 3 and 4. Their good linearity reflects the theoretical feature of the kinetic model derived in the present study. In order to establish the kinetic parameters as a function of temperature, the reparameterization procedure proposed by Kittrell (1970) has been performed using the experimental data observed in the range of reaction temperatures from 250 to 350 °C, simultaneously:

Ki or ki ) exp[Ri - βi(1/T - 1/T h )]

i ) 1, 2, ..., 15 (76)


Figure 12. Effect of H2/CO molar feed ratio on CO conversion (XCO, O), CO2 formation (XW, 4), mixed alcohol formation (∑iXai, 0), and paraffin formation (∑iXpi, ]) at 320 °C, 90 atm, and τ ) 12.5 g-cat‚h/mol. Symbols experimental; lines simulated.

Figure 13. Effect of H2/CO molar feed ratio on the formation of methanol (9), ethanol (4), propanol (O), and butanol (]) at 320 °C, 90 atm, and τ ) 12.5 g-cat‚h/mol. Symbols experimental; lines simulated.

Figure 11. Effect of space time on the formation of alcohols at 320 (a) and 350 °C (b) and on that of paraffins at 350 °C (c) for C1 product (i ) 1, O), C2 product (i ) 2, ]), C3 product (i ) 3, 4), and C4 product (i ) 4, ×) when p ) 90 atm and ΘH2 ) 1.01. Symbols experimental; lines simulated.

where T h is the average reaction temperature. The sum of squares of residuals was 0.17642 × 103, and the kinetic parameter values calculated by eq 76 did not significantly differ from the parameter estimates determined by nonlinear regression at each reaction temperature. Computer time required for the entire procedure was 4.96 h on a Sparc Workstation (Model SDT-200) from TriGem Co. The result of the final parameter estimates is listed in Table 4. It should be noted that the validity of rate and adsorption constants estimated in the present study has been also confirmed by the criteria of Boudart et al. (1967).


Figure 14. Effect of H2/CO molar feed ratio on the selectivity of mixed alcohols (O), methanol (0), ethanol (4), propanol (]), and butanol (×) at 320 °C, 90 atm, and τ ) 12.5 g-cat‚h/mol. Symbols experimental; lines simulated.

Results and Discussion Simulating the reactor model based upon eqs 68-73 with the parameter estimates in Table 4 permits the accuracy of the model to be tested by experimental observation. The comparison between observed and predicted responses at all reaction temperatures covered in the present study for CO conversion shown in Figure 5, indicates that the agreement is very satisfactory. Effect of Operating Conditions. Figure 6 shows the temperature dependence of mixed alcohol formation (∑iXai) with respect to the total pressures of the reactor. The alcohol formation exhibits the maximum at the reaction temperature of 320 °C. It does not significantly vary as the pressure increases. When the pressure is lower than 30 atm, the amount of alcohol formation is very small and does not increase significantly, even when the temperature is increased. However, CO conversion (XCO), CO2 formation (XW), and formation of paraffins (∑iXpi) exponentially increase at higher reaction temperature as shown in Figure 7. It suggests

that the produced alcohols are consumed to form the paraffins with syngas at temperatures above 320 °C. The effect of pressure on the catalytic activity for this reaction network at T ) 320 °C, τ ) 17.1 g-cat.‚h/mol and ΘH2 ) 1.01 was shown in Figures 8 and 9. As the pressure increased, both CO conversion and CO2 formation increased. In addition, the amount of alcohol formation becomes larger as the pressure increases, while that of paraffin formation does not increase any more when the pressure is higher than 86 atm (Figure 9). Moreover, in the region where pressure is above 86 atm, ∑iXai becomes greater than ∑iXpi based upon the simulation results. It suggests that the formation of mixed alcohols is dominant in this region of reaction conditions. Thus, it can be concluded that, at the higher the pressure, more alcohol forms during the course of the reaction. The dependence of ∑iXai, ∑iXpi, XCO, and XW on the reactor space time (τ) at 320 °C, 90 atm, and ΘH2 ) 1.01 is also examined in Figure 10. The increasing rate of mixed alcohol formation is fast until τ is ∼10 g-cat.‚h/ mol and then it almost keeps constant at the longer τ, while other components are continuously increased. The results for individual alcohols at the same reaction conditions were similar to those of mixed alcohols shown in Figure 11a. At 350 °C, however, it was evident that alcohols, particularly methanol, were consumed when τ was longer than ∼10 g-cat.‚h/mol, while all paraffins increased for every value of τ examined in the present study (Figure 11b,c). From Figures 10 and 11, the optimal space time (τopt) of this reaction system can be obtained for mixed alcohol formation and it is slightly affected by the change of the reaction temperature. Moreover, as discussed in Figures 6 and 7, alcohols further react with syngas to produce paraffins when the temperature is higher than 320 °C and the space time exceeds τopt. It is also found that an increase of pressure also increases τopt. Figures 12-14 show the influence of the H2/CO molar feed ratio (ΘH2) on the formation of mixed alcohols and other products. Note that there was good agreement of the simulated results with the experimental observations even if the experimental data points shown in Figures 12-14 were not employed for the estimation of parameters. As shown in Figure 12, ∑iXai and ∑iXpi increase as ΘH2 increases even though XCO almost remains constant and XW exponentially decreases. The various responses of mixed alcohol formation (Figure

Figure 15. Schulz-Flory distributions for alcohols (a) and paraffins (b) at 300 °C, 50 atm, and τ ) 21.4 g-cat‚h/mol. Symbols experimental; lines simulated. RSF is the chain growth probability for the Schultz-Flory distribution.


Figure 16. Effect of reaction temperature and pressure on alcohol formation at τ ) 15.0 g-cat‚h/mol and ΘH2 ) 1.01.

13) show that the amount of methanol formed increases, while the conversion into the higher alcohols (XA2+) reveals its maximum at specific ΘH2. Although ∑iXai increases with respect to ΘH2, the selectivity of mixed alcohols is almost unchanged, while the selectivity of methanol increases up to ΘH2 ) 2 and then that of higher alcohols decreases as ΘH2 increases (Figure 14). Similar results are also observed for hydrocarbons. Consequently, a high ΘH2 is favorable for C1 products, i.e., methane or methanol, but unfavorable for higher alcohols and hydrocarbons. It can be observed from the CO insertion mechanism (see Figure 1), that the decrease of ΘH2 will increase the partial pressure of CO and result in more CO insertion and C-C chain growth, leading to the increase in the formation of higher alcohols and hydrocarbons, while the opposite favors the production of lower alcohols and hydrocarbons. Due to the decrease of higher alcohol and hydrocarbon production at high ΘH2, the formation of water should be small, as expected in reactions 14-17. Thus, it is not surprising that XW decreases as ΘH2 increases. Product Distribution. The experimental observations and the calculated results for alcohols (CiOH) and hydrocarbons (CiHC) show that the formation of alcohols and hydrocarbons exponentially decreases as their carbon number increases, typical for a Schulz-Flory distribution. Figure 15 exhibits the distribution for both experimental and calculated ln(mol %) for alcohols (a) and hydrocarbons (b). To illustrate the formation of mixed alcohols with respect to the reaction conditions, the temperature and pressure dependences of ∑iXai are examined in Figure 16. It reveals that there is an optimal reaction temperature around 320 °C, regardless of the reaction pressure, as already observed and discussed in Figures 6 and 7.

parameterization has been made for the estimation of the kinetic parameters as a function of reaction temperature. The model successfully predicted the product formation and the distribution of the formation of alcohols within the range of experiment covered in this study. The formation of the mixed alcohol exhibits a maximum when the temperature is at 320 °C, which is almost independent of the reactor pressure. In this study, reaction temperature seems to be a more important operating variable than any other ones. The higher the pressure the more favorable for the formation of mixed alcohols. When the pressure was lower than 30 atm, however, the amount of alcohol formation did not significantly increase even though the reaction temperature increases. The optimal reactor space time depends on the pressure; that is, the higher pressure permits the longer τopt. Alcohols are also consumed by the further reaction with syngas to produce paraffins at a temperature higher than 320 °C and at a space time longer than τopt. H2/CO molar feed ratio affects the composition of mixed alcohols and hydrocarbons formed during the course of reaction. Product distribution of alcohols and hydrocarbons obeys Schulz-Flory distribution. Finally, it is hoped that the model developed in this study will provide a basis for the simulation and the design of a commercial reactor for the formation of mixed alcohols over K/MoS2 catalyst. Notation Ads: adsorption term defined in eq 47 Fi: molar flow rate of species i, mol/h (Fi)0: molar flow rate for species i fed to the reactor, mol/h Ki: equilibrium constants for ith reaction K1 ) KCHOKCOKH1/2, MPa-3/2 K2 ) KCH2OKCHOKCOKH, MPa-2 ki: rate constant for ith reaction, kg-cat‚mol-1‚h-1 kto: rate constant for olefin formation, h-1 [i]: surface concentration for species i, mol/kg-cat. m: number of different experimental condition at a temperature ni: maximum carbon number of the product group i Pi: partial pressure of species i, MPa P: total pressure in the reactor, MPa Ri: alkyl group with carbon number i () CiH2i+1) s: active site of catalyst W: catalyst loading, g Xij: CO conversion for component group i with carbon number j defined in eq 25 Xi: CO conversion for reaction i defined in eq 26 Greek Letters

Conclusion A rigorous reaction scheme has been developed on the basis of the CO insertion mechanism which well describes the kinetic behavior of mixed alcohol formation from syngas. Overall and independent reactions from the reaction network are identified to establish the stoichiometric relationship for all components involved in the reaction system. Based upon these reactions, a set of LHHW kinetic model was derived with the steadystate approximation for reaction intermediates. Re-

λi: parameter group, i ) 1, 2, ..., 9 λ1 ) kieKCO[s]2o , mol‚kg-cat.-1‚h-1‚MPa-1 λ2 ) ktaKH1/2[s]2o , mol‚kg-cat.-1‚h-1‚MPa-1/2 λ3 ) kihKH[s]3o , mol‚kg-cat.-1‚h-1‚MPa-1 λ4 ) KR1OKCH2OKCHOKCOKH3/2, MPa-5/2 λ5 ) kta[s]o2, mol‚kg-cat.-1‚h-1‚MPa-1 λ6 ) (kieKCO)/(kteKH), MPa-1/2 λ7 ) ktpKH1/2[s]o2, mol‚kg-cat.-1‚h-1‚MPa-1/2 λ8 ) kicKCO[s]o2, mol‚kg-cat.-1‚h-1‚MPa-1 λ9 ) (kicKCO)/(kiyKH[s]o), dimensionless

Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5257 Θi: molar feed ratio of species i to CO [) (Fi)0/(FCO)0] θi: surface coverage of species i τ: space time [) W/(FCO)0], kg-cat.‚h/mol Superscripts E: ester family FT: Fischer-Tropsch reaction for hydrocarbons O: olefin family OH: alcohol family P: paraffin family Subscripts a: alcohol family p: paraffin family o: olefin family e: ester family W, WGS: water-gas shift reaction

Acknowledgment The authors thank the Korean Science and Engineering Foundation (KOSEF) and the Research Institute of Industrial Science and Technology (RIST) for the partial financial support. We also express our appreciation to Mr. C. M. Chung, Y. I. Song, S. H. Kim, and K. D. Kim for their experimentation. Literature Cited Beretta, A.; Tronconi, E.; Forzatti, P.; Pasquon, I.; Micheli, E.; Tagliabue, L.; Antonelli, G. B. Development of a Mechanistic Kinetic Model of the Higher Alcohol Synthesis over a Cs-doped Zn/Cr/O Catalyst. 1. Model Derivation and Data Fitting. Ind. Eng. Chem. Res. 1996, 35, 2144-2153. Boudart, M.; Mears, D.; Vannice, M. A. Ind. Chim. Belg. 1967, 32, 281. Calverley, E. M.; Smith, K. J. Kinetic model for alcohol synthesis over a promoted Cu/ZnO/Cr2O3 catalyst. Ind. Eng. Chem. Res. 1992, 31, 792-803. Courty, Ph.; Duraud, D.; Freund, E.; Sugier, A. C1-C6 alcohols from synthesis gas on copper-cobalt catalysis. J. Mol. Catal. 1982, 17, 241-254. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; Wiley: New York, 1990. Ichikawa, M., Catalysis by supported metal crystallines from carbonyl clusters. Bull. Chem. Soc. Jpn. 1978, 51, 22682272. Kittrell, J. R. Mathematical Modelling of Chemical Reactions; Academic Press: New York, 1970; Vol. 8, p 97. Lee, J. S.; Kim, S. H.; Nam, I.-S.; Chung, J. S.; Kim, Y. G.; Woo, H. C. Role of Alkali Promoters in K/MoS2 Catalysts for CO-H2 Reaction. Appl. Catal. A: General 1994, 110, 11-25. Murchison, C. B.; Conway, M. M.; Stevens, R. R.; Quarderer, G. J. Mixed alcohols from syngas over moly catalysts. Proc. 9th Int. Congr. Catal. 1988, 2, 626-633. Natta, G.; Colombo, U.; Pasquon, I. Catalysis; Reinhold Publ. Co.: New York, 1957; Vol. V, Chapter 3. Newsome, D. S. The water-gas shift reaction. Catal. Rev.-Sci. Eng. 1980, 21(2), 275-318. Nunan, J. G.; Herman, R. G.; Klier, K. Higher alcohol and oxygenate synthesis over Cs/Cu/ZnO/M2O3 (M ) Al, Cr) catalysts. J. Catal. 1989, 116, 222-229. Park, T. Y. A Kinetic Study on the Synthesis of Linear Mixed Alcohols over K/MoS2 Catalyst. M.S. Thesis, Pohang Institute of Science and Technology, 1992. Quarderer, G. J. Mixed alcohols: a high value product natural gas. AIChE Spring National Meeting, 1986; paper 25a. Quarderer, G. J.; Cochran, G. A. Catalytic process for producing mixed alcohols from H2/CO. Eur. Patent App. 0119609, 1984. Santiesteban, J. G.; Bogdan, C. E.; Herman, R. G.; Klier, K. Mechanism of C1-C4 alcohol synthesis over alkali/MoS2 and alkali/Co/MoS2 catalysts. Proc. 9th Int. Congr. Catal. 1988, 2, 561-568.

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Received for review September 16, 1996 Revised manuscript received May 31, 1997 Accepted August 12, 1997X IE9605701

Abstract published in Advance ACS Abstracts, November 1, 1997. X

MoS

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