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Ind. E n g . Chem. Res. 1989,28, 406-413
Cavalli, P.; Cavani, F.; Manenti, I.; Trifirb, F.; El-Sawi, M. Kinetic and Mechanistic Analysis of Toluene Ammoxidation to Benzonitrile on Vanadium-Titanium Oxides. Ind. Eng. Chem. Res. 1987,26, 804-810. Cavani, F.; Centi, G.; Manenti, I.; Trifirb, F. Catalytic Conversion of C4 Hydrocarbons of Vanadium-Phosphorus Oxides: Factors Influencing the Selectivity of 1-Butene Oxidation. Ind. Eng. Chem. Prod. Res. Deu. 1985a, 24, 221-226. Cavani, F.; Centi, G.; Trifirb, F. Structure Sensitivity of the Catalytic Oxidation of n-Butane to Maleic Anhydride. J. Chem. SOC., Chem. Commun. 1985b, 492-494. Centi, G.; Trifirb, F. Functionalization of Paraffinic Hydrocarbons by Heterogeneous Vapor-Phase Oxidation. 111. Conversion of the C,-C7 Alkane Series. Catal. Today 1988, 3, 151-162. Centi, G.; Burattini, M.; Trifirb, F. Oxi-Condensation of n-Pentane to Phthalic Anhydride. Appl. Catal. 1987, 32, 353-356. Centi, G.; Fornasari, G.; Trifirb, F. On the Mechanism of n-Butane Oxidation to Maleic Anhydride: Oxidation in Oxygen-Stoichiometry-Controlled Conditions. J. Catal. 1984, 89, 44-51. Centi, G.; Fornasari, G.; Trifirb, F. n-Butane Oxidation to Maleic Anhydride on Vanadium-Phosphorous Oxides: Kinetic Analysis with a Tubular Flow Stacked-Pellet Reactor. Ind. Eng. Chem. Prod. Res. Deu. 1985, 24, 32-37. Centi, G.; Trifirb, F.; Ebner, J. R.; Franchetti, V. M. Mechanistic Aspects of Maleic Anhydride Synthesis from C4 Hydrocarbons over Phosphorus Vanadium Oxide. Chem. Reu. 1988,88, 55-80. Chinchen, G.; Davies, P.; Sampson, R. J. The Historical Development of Catalytic Oxidation Processes. In Catalysis-Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Berlin, 1987; Vol. 8, pp 1-68. Donati, G.; Buzzi-Ferraris, G . Parameter Estimation for a HougenWatson Kinetic Model. Zng. Chim. It. 1970, 6, 139-149. Donati, G.; Buzzi Ferraris, G . Powerful Method for Hougen-Watson Model Parameter. Estimation with Integral Conversion Data. Chem. Eng. Sci. 1974,29, 1504-1509. Froment, G. F. Model Discrimination and Parameter Estimation in Heterogeneous Catalysis. AZChE J.,1975,21, 1041-1045. Froment, G . F.; Bishoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1976. Froment, G. F.; Hosten, L. H. Catalytic Kinetics: Modelling. In Catalysis-Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-verlag: Berlin, 1986 Vol. 2, Chapter 3, pp 97-170. Himmelblau, D. M. Process Analysis and Simulation: Deterministic Systems; Wiley: New York, 1968. Himmelblau, D. M. Process Analysis and Statistical Methods; Wiley: New York, 1970. Hodnett, B. K. Vanadium-Phosphorus Oxide Catalysts for Selective Oxidation of C4 Hydrocarbons to Maleic Anhydride. Catal. Reus-Sci.Eng. 1985, 27, 373-424.
Honicke, D.; Griesbaum, K.; Yang, Y. Heterogen Katalysierte Selektivoxidation von n-Pentenen und n-Pentan. Chem.-Ing. Technol. 1987a, 59, 222-223. Honicke, D.; Griesbaum, K.; Newrzella, A. Mixed Oxide Mo/V/Pcatalysts for the Partial Oxidation of Cyclopentene. In Abstracts of Papers, 194th National Meeting of the American Chemical Society, Div. of Colloid and Surface Chem., New Orleans, 198713. Hucknall, D. J. Selective Oxidation of Hydrocarbons; Academic Press: London, 1974. Johnson, J. W.; Johnston, D. C.; Jacobson, A. J.; Brody, J. F. Preparation and Characterization of VOHP04*0.5H20and Its Topotactic Transformation to (VO)2P20,. J. Am. Chem. SOC.1984,106, 8123-8128. Madon, R. J.; Boudart, M. Experimental Criterion for the Absence of Artifacts in the Measurement of Rates of Heterogeneous Catalytic Reactions. Ind. Eng. Chem. Fundam. 1982,21, 438-447. Mattson, G.; Sasser, D. The Vapour-Phase Oxidation of 1,3-Pentadiene. Oxid. Commun. 1984, 7, 333-345. Mears, D. E. Tests for Transport Limitations in Experimental Catalytic Reactors. Ind. Eng. Chem. Prod. Des. Deu. 1971, IO. 541-547. Schneider, P.; Emig, G.; Hofmann, H. Kinetic Investigation and Reactor Simulation for the Catalytic Gas-Phase Oxidation of nButane to Maleic Anhydride. Ind. Eng. Chem. Res. 1987. 26, 2236-2400. Seiyama, T.; Nita, K.; Maehara, T.; Yamazoe, N.; Takita, Y. Oxyhydrative Scission of Olefins. I. Oxidation of Lower Olefins. J . Catal. 1977, 49, 164-173. Torardi, C. C.; Calabrese, J. C. Ambient and Low-Temperature Crystal Structure of Vanadyl Hydrogen Phosphate (VO),H,P,09. Inorg. Chem. 1984,23, 1308-1310. Turner, J. C. R. An Introduction to the Theory of Catalytic Reactors. In Catalysis-Science and Technology; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: Berlin, 1984; Vol. 1, Chapter 2, pp 43-96. Villa, P. L.; Forzatti, P.; Buzzi-Ferraris, G.; Garone, G.; Pasquon, I. Synthesis of Alcohols from Carbon Oxides and Hydrogen. 1. Kinetics of the Low-Pressure Methanol Synthesis. Ind. Eng. Chem. Prod. Res. Deu., 1985, 24, 12-19. Volta, J. C.; Aguero, A.; Sneeden, R. P. A. Selective-Oxidation on Vanadyl Pyrophosphate Catalysts: oxidation of Linear and Branched Alkanes. In Heter. Catalysis and Fine Chemicals; Guisnet, M., Barrault, J., Bouchoule, C., Duprez, D., Montassier, C., Perot, G., Eds.; Elsevier Pub.: Amsterdam, 1988; pp 353-360. Weissermel, K.; Arpe, H.-J. Industrial Organic Chemistry; Verlag Chemie: Weinheim-New York, 1978. Receiued for reuiew J u n e 3, 1988 Accepted November 28, 1988
Effect of Particle Size on the Activity of a Fused Iron Fischer-Tropsch Cata1yst William H. Zimmerman, Joseph A. Rossin, and Dragomir B. Bukur* Kinetics, Catalysis, a n d Reaction Engineering Laboratory, Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843
T h e effect of particle size on the activity of a fused iron catalyst used for the Fischer-Tropsch synthesis has been studied. The significant resistance in our tests was found to be intraparticle mass transfer, which was caused by the low diffusivity of reactant in wax-filled catalyst pores. Particles of 30/60 and 60/ 100 mesh show strong mass-transport limitations with lower than expected activities and activation energies, while catalyst activity approaches its intrinsic value for 170/230-mesh particles. Catalyst effectiveness factors were calculated assuming first-order reaction kinetics and single reaction stoichiometry and were compared to those obtained by experiment. The calculated and experimental results were in good agreement, although the calculated values were consistently higher than the experimental values. The overprediction may be caused by basing the Thiele modulus on the diffusivity of H2 or by neglecting rate inhibition by water. Fixed bed reactors have often been employed in kinetics studies of the Fischer-Tropsch synthesis (FTS). Stirred
* Author t o whom correspondence should be addressed. 0888-5885/89/2628-0406$01.50/0
tank slurry reactors are better suited for detailed kinetic investigations since they are able to ensure uniform concentrations and temperature, but fixed beds are convenient for use in preliminary catalyst studies, as thev are inex1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 407 pensive and easy to operate and require relatively small amounts of catalyst. The disadvantages to studying the FTS in fixed beds are (1)the high heat of reaction makes it difficult to maintain an isothermal reactor, (2) the integral nature of the fixed bed complicates kinetic analysis, and (3) there is a trade-off between small particles with a high pressure drop or large particles with intraparticle concentration gradients. Careful design and proper operating procedures can minimize reactor temperature gradients, and reactor models can be utilized for kinetic analysis, but the potential for intraparticle mass-transfer limitations needs to be considered. Anderson et al. (1964) studied fused iron catalysts which had either been reduced or reduced and nitrided prior to use in fixed bed reactors, examining reaction kinetics and the effects of the extent of reduction and particle size on catalyst activity. Particle sizes ranged from 42/60 mesh (0.27-mm diameter) to 4/6 mesh (3-mm diameter). Catalyst activity increased with smaller particle sizes until the diameter reached about 0.3 mm for the most active catalysts tested. Catalyst particles were modeled as an active layer of catalyst surrounding an inert core, with the depth of the active layer governed by the reduction temperature. Their calculations allowed them to estimate the effective reactant diffusivity, and they were also able to quantify the depth of the active layer of catalyst. Variations in catalyst activity were attributed to the diffusion of reactant through a wax-filled pore and the depth of the active layer. Atwood and Bennett (1979) estimated the effectiveness factor for a catalyst with wax-filled pores using nonlinear reaction kinetics, which included inhibition by product water, to estimate the Thiele modulus. The effectiveness factor was then calculated from an expression derived from first-order kinetics and flat-plate geometry. They showed that the catalyst effectiveness factor was quite low for 2-6-mm particles but stated that 0.3-mm particles would be free of heat- and mass-transfer effects. Dixit and Tavlarides (1982) derived an integral expression for the catalyst effectiveness factor and applied it by using nonlinear FTS kinetics including the concentrations of both H2 and CO. Feimer et al. (1981) checked for intraparticle mass-transfer limitations experimentally using 60/ 100mesh precipitated iron catalyst in a fixed bed reactor by varying the total system pressure at constant reactant partial pressure. They did not see evidence of intraparticle diffusion resistance; however, as the authors noted, this technique is not reliable for wax-filled pores. Liquid concentrations at the pore openings are dependent only on species partial pressures, and the total system pressure in this case will have little subsequent effect on the reaction rate. The purpose of our investigation was to study the effect of catalyst particle size on FTS activity in a fixed bed reactor. Catalyst activity was determined in experiments conducted using fused magnetite ammonia synthesis catalyst at three different particle sizes (30/60, 60/100, 170/230 mesh) and two temperatures (235 and 250 "C). These experiments enabled us to determine apparent rate constants and activation energies as a function of particle size. We were also able to indirectly estimate catalyst effectiveness factors and Thiele moduli experimentally at each particle size. Calculated values of these quantities were determined considering a spherical catalyst particle with wax-filled pores, assuming first-order H2 kinetics and single-reaction stoichiometry. The effects of the extent of the water gas shift (WGS) reaction and average hydrocarbon product stoichiometry on catalyst effectiveness were also considered.
A , PURIFICATION TRAPS
x
HEATED
t
?
VENT
SOAP FILM
MASS FLOW CONTROLLER SAMPLE PORT
REACTOR SYNGAS CYLINDER
BACK PRESSURE REGULATOR
Figure 1. Schematic representation of fixed bed reactor system.
Experimental Section Fixed Bed Reactor System. A schematic representation of the fixed bed reactor system used during our investigation is shown in Figure 1. The reactor was constructed of 1.02-cm-i.d. tubing, with an effective bed length of approximately 30 cm (25-cm3bed volume). Five thermocouple wells, spaced axially at about 6-cm intervals, passed radially through the reactor wall to the center of the bed. The reactor was enclosed in an aluminum block to ensure even heating of the catalyst bed. The top onethird and bottom two-thirds of the block were heated by using separate temperature controllers to minimize axial temperature gradients, particularly in the entrance region of the reactor, and the catalyst was diluted with glass beads of the same mesh size range as the catalyst before loading the reactor. The dilution ratios employed ranged from about 4 to 10 parts glass beads per part catalyst, by volume. Premixed synthesis gas (Air Products and Chemicals or Matheson, >99.7% purity) with a molar H2/C0 ratio of approximately 1was used during all experiments in this study. The feed gas flow rate was adjusted by using a calibrated mass flow controller, and the gas passed through a series of 02-removal, alumina, and activated charcoal traps to remove trace impurities. The feed was preheated before entering the reactor and flowed downward through the vertical catalyst bed. Pressure drops across the bed were insignificant for the particle sizes and flow rates employed in this study. High molecular weight products were collected at system pressure in a heated trap located directly downstream of the reactor. After system pressure was released through a back-pressure regulator, any remaining condensables were collected in an ice trap operating a t ambient pressure. The flow rate of the exit gas leaving the ice trap was measured periodically by using a soap film flowmeter. Following any change in process conditions, the system was allowed to run undisturbed for 16-18 h to reach steady
408
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989
state. After the conclusion of this unsteady period, liquid samples were allowed to accumulate in the high-pressure and ice traps over a 6-h steady period. During the course of the steady period, several gas samples were collected and analyzed on a Carle AGC 400 gas chromatograph (GC) for H,, CO, C02, and Cl-C6 hydrocarbons. Two PerkinElmer GC's equipped with flame ionization detectors were used to quantify the C5-Clo hydrocarbons in the gas phase and also to analyze the aqueous and organic liquid samples collected in the ice trap. The product collected in the high-pressure trap was not routinely analyzed. The amount of water present in the aqueous liquid was determined by using Karl Fischer titration, and the water leaving the system in the gas phase was calculated assuming equilibrium between gas and liquid in the ice trap. The total mass balance closures obtained with the product collection and analytical system described were in the range 95-100%. Catalyst/Catalyst Reduction. All of the experiments in this investigation were conducted using a fused ironammonia synthesis catalyst (United Catalysts, Inc., designated (2-73-01). On an unreduced weight basis, the manufacturer's reported composition is 67-69% iron, 2-3% Al2O3,0.5-0.870KzO, 0.7-1.2% CaO, and less than 0.4% SiO,. Catalyst reduction was performed in situ using Hz at ambient outlet pressure and a space velocity of 20000 (volume of H2 (STP)/(volume of unreduced catalysthour)). At the start of the reduction, the bed temperature was increased from ambient to 150 "C over a 1-h period and held a t 150 "C for 2 h to remove moisture from the catalyst. The temperature was then increased at 2 "C/min until the bed reached 370 "C, which was maintained for 24 h. This was followed by two additional 24-h periods at 400 and 430 "C. After reduction, the catalyst was cooled to 200 "C, and the system was brought to operating pressure before exposure of the catalyst to synthesis gas. The temperature of the catalyst bed was then slowly increased to the desired operating value to avoid developing hot spots in the reactor.
Theoretical Section Reaction Stoichiometry. The FTS can be approximated as a single reaction that forms an average hydrocarbon product (C,H,) and water as its only products. Most iron catalysts used for the FTS also possess some WGS activity, which needs to be considered to account for COz production and Hz/CO usage. COz produced by the Boudouard reaction (2CO C(s) + C02) is neglected. The FTS and WGS reactions can be written as
-
CO
+ (1 + m/2n)Hz CO
+ HzO
r m
rwG.9
(l/n)C,H,
COZ
+ H2
+ HzO
(1)
(2)
It is convenient to combine eq 1 and 2 into a single reaction which forms hydrocarbons, water, and C02 as products. This simplification is possible when the ratio of reaction rates is known or can be calculated. Stern et al. (1985) have used this approach to treat the FTS/WGS system as a single reaction in models for slurry bubble columns. A new set of stoichiometric coefficients, dependent on the relative reaction rates, can then be defined which allow the two reactions to be added directly:
x = ~WGS/~.FTS (1 + x ) C O
-
-
-
rH,+CO = k 8 X 2
(5)
It is often possible to express the rate of the FTS for iron catalysts as first order with respect to H2. Anderson (1956) stated that the first-order dependence was applicable over iron catalysts up to a 60% conversion of reactants. Dry et al. (1972) studied FTS kinetics in a differential fixed bed reactor using a promoted, fused magnetite catalyst and found that the rate was first order in H2 over the range of conditions employed. With a differential reactor, reactant conversions are low and product inhibition is not a factor. Nettelhoff et al. (1985) also found that the first-order rate expression was valid for a precipitated catalyst at low conversions and a fused iron ammonia synthesis catalyst. A t high conversions, inhibition by product water becomes significant and more complex expressions are required (e.g., Anderson (1956), Dry (1976), and Huff and Satterfield (1984)), but a feature of these expressions is that they reduce to first order in H, at sufficiently low conversion levels. The rate of disappearance of H2, which determines its transport requirement, is related to the rate of H2 + CO disappearance through the stoichiometry of eq 4. The first-order dependence on Hz, with the simplifications yielding eq 4, allows a single diffusion/reaction equation to describe the intraparticle Hz concentration gradient:
(3)
+ (1 + m/2n - x)H, r m (l/n)C,H,
Limits can be placed on the values of x by considering the extremes of the WGS reaction. When the rate of the WGS is zero, x is zero and no COz is formed. The FTS and WGS reactions are in series with respect to water; thus, the rate of the WGS is limited by the rate at which water is produced via the FTS. In the case where all water produced reacts with CO to form COz, the rates of the two reactions must be equal and x is unity. It should be noted that x is not strictly a constant and can change with reaction conditions (e.g., temperature, concentration, and pressure) and position throughout the reactor or catalyst particle. When concentrations are not uniform in the reactor, the maximum of x = 1 may not be strictly true, since water produced locally may be transported before reacting with CO. In this case, x may exceed unity (Bukur and Brown, 1987). Limits may also be placed on the hydrogen to carbon ratio of the hydrocarbon product (mln). When n = 1, methane is the only hydrocarbon product formed; thus, m l n = 4. A t the other extreme, as n mT m/n 2. Effectiveness Calculations. The catalyst was taken to be a porous, spherical particle with an average diameter of dp. Volume average particle diameters were used in all calculations. High molecular weight products (waxes) are formed during the synthesis, and it was assumed that all pores are completely filled with this wax. It was also assumed that (1)steady conditions exist and the catalyst and reactor are isothermal and isobaric; (2) no interphase temperature or concentration gradients exist, such that surface conditions are the same as bulk; (3) the gas phase is in equilibrium with the wax at the mouth of the catalyst pores; and (4) the rate of the FTS is first order with respect to Hz:
+ (1 - x ) H 2 0 + xC02 (4)
where C*H2is the liquid-phase concentration of H2in equilibrium with the gas phase at the mouth of the pore on the surface of the catalyst, C *H2= (p,/HHJPH, and k,
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 409 Table I. Summary of Operating Conditions and Results of (2-73 Catalyst Tests (HJCO = 1) mesh size 30/60 (0.48 mm) 60/100 (0.21 mm)
run
T, O C
A- 1 A- 2 B-1
235 250 235 233 233 234 235 247 250
B-2 C-1 D-1 c-2 c-3 c-4
170/230 (0.078 mm)
P , MPa 1.48 1.48 1.54 0.79 0.79 0.83 1.48 0.79 1.48
s'
fw.+cn*
vb
Xb
740 670 720 1400 1400 1600 930 1200 1300
0.52 0.77 0.73 0.22 0.33 0.30 0.79 0.60 0.86
0.71 0.68 0.72 0.65 0.69 0.64 0.74 0.72 0.82
0.85 0.90
0.80 1.0 0.92 0.92 0.87 0.89 0.79
n 3.4 3.0 4.4 2.4 2.8 3.3 2.6 2.7 2.5
m/n 2.3 2.4 2.2 2.6 2.5 2.3 2.5 2.5 2.5
'Units are cm3 (STP){(g of catalyst-h). bValues measured at reactor exit.
is the first-order rate constant per unit catalyst volume. Diffusivities in liquids are much less than diffusivities in gases; thus, Knudsen diffusion was ignored, and the effective diffusivity in the catalyst pores was assumed to be De = ( ~ P / ~ ) D H ~ , W ~ * If it is assumed that m/n and x are independent of position in the catalyst particle, eq 6 and 6a may be integrated to yield the well-known expression for the catalyst effectiveness factor, 9,in terms of the Thiele modulus, 4 (e.g., Froment and Bischoff (1979)). x and the H2/C0 usage ratio U , which is commonly reported in FTS studies, are directly related through the single-reaction stoichiometry. Bukur and Brown (1987) have shown that U is relatively insensitive to conversion in the range 30-80% H2 + CO conversion. Deckwer et al. (1982a) found that the usage is only a weak function of temperature and the H2/C0 ratio. The result of the integration in terms of the catalyst effectiveness factor is 1 34 coth (34) - 1 (7) 17=4 34 where @ = -
dp k ,
(
-
6 De
1
+ m/2n - x 2 + m/2n
'I2
)
(8)
Kinetic Parameter Estimates. The rate constant appearing in eq 5 was estimated using data taken from catalyst tests in f=ed bed reactors, where it is assumed that (1)the reactor is at steady state, (2) the reactor conditions are isothermal and isobaric, and (3) the gas phase is in plug flow. Then, the differential H2 + CO balance is given by
fHz+COlr=O
(94
=0
In order to integrate eq 9 accurately, the partial pressure of H2 must be expressed in terms of fH2+C0,and the volume contraction of the gas phase during reaction must be accounted for. In a plug flow reactor, the gas velocity varies linearly with conversion such that nT =
fiTi(1
+ afH2+CO)
(10)
From the definitions of fractional conversion and the H2/C0 usage, U, the H2 partial pressure can be expressed as pH2
=
F/(1 + F ) +
u/(1 + u)fHz+CO fffH2+C0
P
(11)
where relations for U and a can be derived by examination of the stoichiometry of eq 4: 1 + m/2n - x 1 + m/2n - l / n U= a=(12) 1 + X 2 + m/2n
Equations 11 and 12 were used to integrate eq 9 over the length of the reactor to obtain an analytical expression for the rate constant in terms of measurable quantities, assuming that x and m/n are constant over the length of the catalyst bed:
This expression can be plotted as P/s versus the right-hand side to yield a straight line, and kOobcan be calculated from the slope of the best line through the origin.
Results and Discussion Three different catalyst particle size ranges were tested, 30/60, 60/lOO, and 170/230 mesh, which correspond to average particle diameters of approximately 0.48,0.21, and 0.078 mm, respectively. Results were obtained for each particle size a t 235 "C and for the 30/60- and 170/230mesh particles a t 250 "C, and the operating conditions employed are summarized in Table I. The majority of the data was taken using the 170/230-mesh particles where intraparticle mass transfer had the least effect. Although C-73 fused iron is a stable catalyst when used for the FTS, it is possible to experience deactivation during a long-term run. The rate of deactivation is accelerated by changing process conditions. In order to prevent errors in the results due to deactivation, only data taken in the early portions of the run were used for the 30/60- and 60/100-mesh catalysts (Table I). During the test of using 170/230-mesh catalyst, more sets of conditions were employed, and some of the data were taken a t longer times on stream. In this case, the last set of conditions used during the long-term run (designated as C-1 in Table I) was similar to the first set of conditions used in a previous run (D-1 in Table I) with 170/230-mesh catalyst. The results a t these conditions for the two runs were very similar, which confirms that deactivation did not occur during the test of the 170/230-mesh catalyst and also demonstrates the reproducibility of our results. The observed rate constants as a function of particle size and temperature are given in Table 11, which were obtained by using eq 13 at constant temperature and particle size, applying experimental values for U and m/n. The rate constants increase dramatically as the particle size decreases, which is indicative of the intraparticle concentration gradients present with larger particles. The activation energy with 30/60-mesh particles was 37 kJ/mol, roughly half the 81 kJ/mol obtained using the 170/230mesh particles. In the region of strong intraparticle dif/ ~ . activation energy fusion, 7 = 114 and kOob ( D J Z ~ ) ' The of the intrinsic reaction is much greater than the activation energy of diffusion; thus, when diffusional limitations are
410 Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 Table 11. Observed Rate Constants and ComDarison of ExDerimental and Calculated Effectiveness Factors experimental calculated ( x = 0 ) calculated ( x d,, mm knob 6 n 6 v 6 At 235 "C 0.48 0.025 1.95 0.43 3.67 0.25 2.71 0.21 0.035 0.85 0.73 1.61 0.49 1.19 0.078 0.053 0.32 0.95 0.60 0.84 0.44 0.48 0.21 0.078
0.036
2.38
At 250 "C 0.36
0.092
0.38
0.92
3.90 1.71 0.63
0.23 0.47 0.82
2.88 1.26 0.47
= 1) 1)
0.32 0.61 0.90 0.31 0.59 0.89
Units are mol/(g of catalyst (unreduced).h.MPa). Table 111. Physical Property Data Used for Transport Criteria and in Effectiveness Calculations (1.48 MPa, H .J C O = 1) at 235 O C at 250 "C DH*,co,cm2/h; Fuller et al. (Reid et al., 464 490 1977) 0.490 0.572 DH2,wax, cm2/h; Peter and Weinert (Kuo et al., 1983) 0.68 0.68 PI,g/cm3 (Deckwer et al., 1982b) 29.6 29.6 Cp,mr J / (mo1.K) (Reid et al., 1977) 2.63 X lo-* 2.67 X lo-* pm, cP; Wilkes approximation (Reid et al., 1977) A,, W/(cmK); Mason and Saxena 1.21 x 10-3 1.23 x 10-3 Reid et al., 1977) AHm, kJ/mol (Anderson, 1984) 360 360 Xp, W/(cm-K) (pure Fe) 0.680 0.598 Vp, cm3/g (measured) 0.25 0.25 cp (Anderson et al., 1964) 0.445 0.445 T (estd T = l / c p ) 2.25 2.25 ~
~
strong, E Ob = E/2. The reaction order is approximately first order, and in wax filled pores the diffusivity is independent of pressure. Under these conditions, a change of reaction order in the presence of strong diffusional limitations will not occur. We felt that it would be important to test for other transport limitations in our experiments, namely intraparticle and interphase concentration and temperature gradients. The criteria discussed by Mears (1971) were used for this purpose. The diffusivity of Hz in wax was obtained from the correlation reported by Kuo et al. (1983), and the heat of reaction was estimated assuming an average CzHBproduct, from Anderson (1984). The j-factor correlation of Petrovic and Thodos (1968),who established their correlation for j d in a packed bed of porous spheres a t low Reynold's number, was used to calculate masstransfer coefficients, and as an approximation, it was assumed that jh = j d . The remaining physical properties were estimated by using the techniques described by Reid et al. (1977). The physical properties used to evaluate the criteria are given in Table 111. The tests for intraparticle particle H2mass-transfer limitations failed for the 30/60and 60/100-mesh particles, while the test for the 170/ 230-mesh particles was close to the limits. This is in agreement with our experimental observations. The criteria indicate that interphase mass transport did not influence our results; thus, the lowered rates are due to intraparticle concentration gradients alone. Since the FTS is an exothermic reaction, heat-transfer limitations will cause catalyst temperatures to be higher than the bulk temperature, increasing the reaction rate. The criteria indicate that our system should have been free of any temperature gradients, interphase or intraparticle, during the catalyst tests. It is possible to estimate experimental values of the Thiele moduli and effectiveness factors when data for two
or more particle sizes are available. Assuming that the physical properties of the catalyst (i.e., cp and 7) are the same for the different size particles obtained by grinding and sieving a larger pellet, eq 8 shows that the Thiele modulus is proportional to the particle diameter:
41/41 = d P , l / d P , ,
(14)
The effectiveness factors for two different particle sizes are similarly related to the observed rate constants since ,.obs = kgnbsPH,= qk,,FH,: dll, =
ko,,obs/ko,Jnbs
(15)
Equations 14 and 15 with eq 7 give 2n unknowns ({#},{q}) and 3n - 2 equations, where n is the number of particle sizes for which data are available. When n = 2, a unique solution is obtained for the effectiveness factors at each particle size. For our results at 250 "C, data for only two particle sizes were available (30/60 and 170/230 mesh) and eq 7 , 14, and 15 were solved iteratively to obtain experimental values for the Thiele moduli and effectiveness factors, which are shown in Table 11. With the data at 235 " C , three particle sizes are available, giving rise to six unknowns in seven equations; thus, a unique set of effectiveness factors cannot be obtained. In this case, eq 15 was rearranged to form an objective function, Q:
Q
=
C(
k=2
~ k / ~- i ko,kobs/ko,i0bs)2
(16)
The best fit was obtained by adjusting (the index 1was arbitrarily selected to represent the 60/ 100-mesh catalyst) to minimize eq 16, and the effectiveness factors and remaining Thiele moduli at the minimum were calculated via eq 14 and 15. The results of these calculations are also shown in Table 11. The experimental values show that severe mass-transfer limitations occurred for the largest particle size (30/60 mesh), with an effectiveness factor of 0.36 at the worst case of 250 "C. The effectiveness factors decreased with temperature, which was expected as the rate constant, k,, increases more strongly with temperature than the diffusivity, leading to a larger Thiele modulus. A t the smallest particle size (170/230 mesh), the observed rate constants are higher and catalyst effectiveness approaches unity. Calculated values for the Thiele modulus and effectiveness factor can be obtained when the intrinsic rate constant and effective diffusivity are known by applying eq 7 and 8. Anderson et al. (1964) reported the porosity of their fused iron catalysts as a function of the extent of reduction ( f ) as ep = 0.445f, which we applied to our catalyst assuming 100% reduction. We further assumed that 7 l / t p = 2.25 and used the diffusivity of Hzin wax from the correlation reported by Kuo et al. (1983) (Table IIT) The intrinsic volumetric rate constants were esti2
Ind. Eng. Chem. Res., Vol. 28, No. 4, 1989 411 1
50
40 0.75
30 N X
E
8. 9
20
0.50 10
i
0.25 0.0
0 0.0
0.2
0.4
0.6
0.8
1.0
X
0.1
0.2
0.3
0.4
0.5
dp (mm)
Figure 2. Effect of x = r W G S / r mon the percent change in calculated Thiele modulus, Ab:.
Figure 3. Calculated effectiveness factors as a function of particle diameter and temperature and comparison with experimental values.
mated from the apparent rate constants and the experimental effectiveness factor estimates of the 170/230-mesh particles as
ment after reduction at 0.3 mm, while the average particle size prior to reduction was 0.48 mm. Anderson et al. (1964) also noticed a size decrease during catalyst reduction. The size decrease will cause the points appearing in Figure 3 to shift to the left, which leads to larger disagreements between experiment and calculations. Several factors may cause the experimental effectiveness factors to be lower than those expected from the calculations. It is optimistic to base the calculated Thiele modulus on the diffusivity of H2 since it is substantially higher than the diffusivity of CO. The lower CO diffusivity causes the intraparticle concentration gradient of CO to be more severe than that of H2. In the region of strong diffusional resistance, the gradient will reach the point that the assumption of first order in H2 kinetics is no longer valid inside portions of the catalyst. Although the bulk (external) conversion may be low, the local conversion inside the catalyst particle may be high. Rate inhibition by water will diminish reaction rates and also lowers the experimental effectiveness factors. The first-order kinetics used here do not account for water, although water concentrations will become significant at high conversions, particularly when the rate of the WGS is low. Water is also subject to mass-transport limitations, and a reverse gradient (negative first derivative) may form as water diffuses out of the catalyst, which will enhance product inhibition in the interior portions of the particle where reactant concentrations are low. The effects of CO concentration gradients and water inhibition would require non-first-order kinetics to be used as rate expressions. It is possible to calculate effectiveness factors in this situation by using integral methods. Dixit and Tavlarides (1982) used this technique for nonlinear FTS kinetics, which included the CO concentration dependence but did not account for water inhibition. Gonzo and Gottifredi (1983) summarize other techniques which use rational approximations to the effectiveness factor, which may be used for nonlinear reaction kinetics, including Langmuir-Hinshelwood rate forms with product inhibition. However, only in the case of first-order kinetics, such as that employed in this study, can one determine a single catalyst effectiveness factor for the entire catalyst bed. With other rate forms, the catalyst effectiveness factor in an integral fixed bed reactor will vary with axial position. Our results for the 170/230-mesh catalyst particles can be compared to other investigations using the same catalyst, shown in Table IV. Huff and Satterfield (1984) studied the C-73 fused iron catalyst in a slurry reactor, where size effects are unimportant since very fine (
