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CO oxidation in a fixed bed reactor with high frequency cycling of the feed
Chemical Engineering Science 54 (1999) 4459}4468
CO oxidation in a "xed bed reactor with high frequency cycling of the feed J.H.B.J. Hoebink*, A.J.L. Nievergeld, G.B. Marin Eindhoven University of Technology, Laboratorium voor Chemische Technologie, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract An experimental set-up is presented, which allows cycling of the feed for transient operation of "xed bed microreactors at frequencies up to 10 Hz. The set-up was applied for the transient oxidation of CO by O over Pt/c-Al O . The results gave clear evidence that CO may adsorb on oxygen covered sites under simultaneous production of CO . O does, however, not adsorb on CO covered sites, which causes a delay in the transient of the CO production. A kinetic model including rate parameters was presented, which gives an adequate description of the experimental data and provides much more detailed information than could be obtained from steady-state experiments. A simulation study is performed, with CO oxidation as an example, to explore how feed composition cycling is a!ected by di!usion inside catalyst pellets. If the time scale of di!usion inside the catalyst is much smaller than the time scale of the applied oscillation, intrinsic kinetics might be obtained from experiments with cycling of the feed. This statement supposes that di!usion limitation would be absent in the corresponding steady-state without composition cycling, and that the reaction kinetics is in the dynamic regime. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Transient kinetics; CO oxidation; Catalytic "xed bed; Feed composition cycling; High frequency; Di!usion limitation
1. Introduction The operation of chemical reactors under transient conditions, when compared to the traditional steadystate operation, is well known for its potential to increase the reactor performance, e.g. conversion, selectivity, energy saving. An overview was presented recently (Matros et al., 1997). One way of achieving better performance is periodic perturbation of the reactor feed composition, as demonstrated for instance in catalytic benzene oxidation (Fiolitakis et al., 1983). This type of operation was reviewed by Silveston et al. (1995) for catalytic reactors. A typical example is cycling of the feed in catalytic converters for automobile exhaust gas (Silveston, 1995), although perturbations in this case are not intentional but induced by the lambda sensor based control system.
*Corresponding author. Tel.: 00 31 40 2472850; fax: 00 31 40 2446653. E-mail address: [email protected] (J.H.B.J. Hoebink). Current address: AspenTech Europe BV, P.O. Box 258, 5680 AG Best, the Netherlands. Current address: Universiteit Gent, Laboratorium voor Petrochemische Techniek, Krijgslaan 281, B-9000 Gent, Belgium.
Improved reactor performance is due to non-linear reaction kinetics (Lie et al., 1993), in particular when perturbations are applied at a timescale which is comparable to the timescale of the reaction. In case of multiple reactions, however, various timescales of reaction may prevail and the e!ect of cycling at a "xed frequency could be positive for one reaction, but negative for another (Nievergeld et al., 1997). A detailed knowledge of the kinetics on the level of elementary steps is a prerequisite for the successful design of a dynamically operated reactor (Matros et al., 1997), as each step in a kinetic model has its own distinct timescale. In general, this could be achieved through transient kinetic studies, which provide much extra mechanistic and kinetic information when compared to classical steady-state kinetics, leading to a wider applicability of a kinetic model. For periodic operation a mechanistic analysis of wave fronts was presented by Fiolitakis et al. (1983). The current paper describes a laboratory micro-reactor set-up for such purpose, developed at Eindhoven University, which allows feed composition cycling at frequencies up to 10 Hz. This enables to cover the range
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 1 0 3 - 7
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of typical frequencies around 1 Hz, met in automotive exhaust gas converters, where current technology for laboratory reactors usually applies frequencies of 0.01}0.1 Hz. Experimental results were obtained with this set-up on CO oxidation over a commercial Pt/Rh/CeO /c-Al O catalyst (Nibbelke et al., 1998; Nievergeld, 1998). In a kinetic study one wants to avoid transport limitation in order to obtain intrinsic kinetics. The criteria for such an approach are well-developed only for steadystate reactors. For transient reactors an onset has been made only for stepwise (Dekker, 1995) and pulsewise (Huinink et al., 1996) operation. Since high frequency perturbations may cause reactor operation in the sliding regime (Matros, 1984), the e!ects of di!usion limitation inside catalyst pellets during cycling of the feed are discussed with emphasis on determination of the maximum applicable frequency that still allows to obtain intrinsic kinetic data.
The continuity equation for component i, with i"O , CO, CO , in the gas phase is
2. Simulation model
*h G"R G *t
A simulation study was performed for the case of an in"nitely large, #at porous plate of catalytic material with thickness 2r . Both open sides are in contact with an N ideally mixed gas phase, #own through with a diluted CO/O mixture which reacts in the catalyst. Catalyst and gas phase have equal volumes in order to approach the situation in a "xed bed reactor. External mass transfer resistance is neglected. The kinetics for CO oxidation were taken from Herz and Marin (1980) who proposed the following elementary steps, based on steady-state experiments: k
? !&& CO*, CO#* && k B !-
*C e < E G"F (C !C )!N A @ T D G E G G *t with N the di!usive #ux through the gas phase/catalyst G interface. The initial condition corresponds with the assumed steady state at t"0, so C "CQQ . The #ux N is E G E G G obtained from the continuity equation for component i in the gas phase inside the catalyst: *C *C N G"D N G!a ¸ R e N *t *x R G with the steady state pro"les as initial condition, so C (x, 0)"C (x)QQ for 0(x(2r . The boundary conN G N G N dition at x"0 connects the pellet concentration to the gas phase concentration, so C "C . At the centre of N G E G the catalyst, e.g. x"r , all #uxes are zero because of N symmetry. Species coverages on the catalyst surface obey the continuity equation:
with initial coverages given by the steady state coverages, so h (x, 0)"h (x)QQ for 0(x(2r . G G N The partial di!erential equations were transformed into ordinary ones by application of collocation along the catalyst coordinate x. The complete set of di!erential equations was solved with routine D02NHF from the NAG Fortran library. The steady state was obtained by setting all time derivatives equal to zero, and solving the resulting set of ordinary di!erential equations and algebraic equations with routines D02EBF and C05NBF from the NAG library. Parameter values are summarized in Table 1. The corresponding gas phase residence time amounts to 0.01 s.
I? - 2O*, O#2* && IA CO . CO*#O* & This model predicts a "rst order reaction in oxygen and inhibition by CO in the steady-state. Rate parameters were used as adapted by Lie et al. (1993) and evaluated at 600 K. At time t"0 it is assumed that the reactor is in the steady state. For t'0 the CO and O feed concentrations oscillate in counterphase: C (t)"C (1#B sin(2n ft)), t*0, D !D !C (t)"C (1#B sin(2n ft#n)), t*0, D - D - where the superscript 0 denotes the time-average value of the corresponding feed concentration.
3. Simulated possible e4ects of internal di4usion limitation All calculations were performed at a temperature of 600 K. As the calculations started from a steady state before cycling, the results may show some transient behaviour prior to stable harmonic oscillations. The discussion focuses on the latter. If the oscillation frequency value approaches the reciprocal gas phase residence time, a comparison of inlet and outlet signals shows some signal damping and phase shift, which is not in#uenced by the reaction. For a proper understanding of the various phenomena the timescale of the applied oscillation, expressed by the oscillation period, t , should be compared with the timescale of di!usion and of the various reaction steps.
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Table 1 Parameter values and other conditions, used in the simulation model Parameter
Value
a A r N F T D < C D !-
1.4;10 1.3;10\ 1.25;10\ 7;10\ 10\, 10\ 1.3;10\ 0.18
m m\ . m m\ 0 m m s\ m m s\ m mol m\
The former can be estimated from: r t " N . D As the present calculations apply e!ective di!usivities of 10\ or 10\ m s\, the corresponding di!usion timescale is typically either 0.01 or 0.1 s. The timescale of adsorption of a component A follows from (Huinink et al., 1996): e C e @ " @ " , !R k hL ¸ a T ? * R where n stands for the order in vacant sites, which is 1 for CO and 2 for oxygen according to the kinetic model. When evaluated for oxygen, the order of magnitude of the timescale is 1 s at 600 K, taking the data of Lie et al. (1993) and a value h "0.01, which seems realistic on * basis of the current simulation "ndings. The timescale of CO adsorption is 2;10\ s, while for CO desorption a timescale of 3;10\ s is found in an analogous way if C "0.18 mol m\ and h "0.8. For the surface reac!!tion a timescale of 3;10\ s is found similarly when assuming C "0.12 mol m\ and h "0.2. Oxygen ad- sorption, having the largest timescale, is therefore rate controlling, as is known from the literature, and CO adsorption/desorption can be considered as in equilibrium. Lie et al. (1993) studied a monolith reactor with cycling of the feed, using the same kinetic model for CO oxidation, but without consideration of di!usion limitation in the catalytic washcoat. They noticed with increasing axial distance in the reactor an increase of the amplitude of the CO gas phase concentration, whereas for oxygen the amplitude decreased and even inversed. So, out of phase oscillation of CO and O at the reactor inlet turned into in phase oscillation at the outlet. This can be explained as follows. When the CO concentration decreases periodically, free sites become available for oxygen adsorption and the CO production rate increases accord ingly due to a better balance of adsorbed CO and O adatoms with respect to the stoichiometry of the surface reaction. The fact that a CO decrease is accomt
Parameter
Value
¸ R e N C D B F = /= e @
2.48;10\ 0.45 0.12 0.15 0.1, 1, 5, 10 10 0.45
mol m\ . . m m\ mol m\ * Hz kg kg\ m m\ 0
panied by an oxygen increase, due to counterphase oscillation in the feed, causes an extra enhancement of the CO production rate. This positive feedback mechanism causes an increase of the oscillation amplitude of the CO gas concentration with increasing axial distance. For the oxygen oscillation the feedback is negative, which causes attenuation of the amplitude and even inversion with increasing axial distance. Lie et al. (1993) reported a positive e!ect of cycling on the time average rate of CO production, since the periodic rate enhancements largely overcompensate the periodic decreases, which arise during the half period of high CO concentrations. The e!ects observed are due to non-linear kinetics. The current results will be discussed "rst at an oscillation frequency of 0.1 Hz, which means that di!usion and kinetics will show dynamic behaviour (Matros, 1984). When D "10\ m s\ or larger, model simulations show that the concentrations of CO and O in the cata lyst are spatially rather uniform, as are the surface coverages of adsorbed CO and O adatoms. Therefore the CO production rate, expressed as turnover frequency, is more or less uniform in space as well, as shown in Fig. 1, where it is plotted vs. time for both the gas/catalyst interface and the centre of the catalyst. The rate oscillates in phase with the oxygen gas phase concentration and with the O adatom surface coverage. The time average CO production, which is controlled by kinetics, is higher under cycling conditions, when compared to the steady state, in accordance with the work of Lie et al. (1993). For D "10\ m s\ and the same frequency of 0.1 Hz, the concentrations of CO and O decrease con siderably with increasing distance from the outer surface of the catalyst due to low di!usion rates. For this reason the surface coverage of CO decreases in the same direction, but the surface coverage of O adatoms increases because of less CO inhibition. By consequence, the CO production rate is higher at larger distance from the outer surface, as also could be expected in a steady state without cycling of the feed. Fig. 2 shows the di!erent oscillatory behaviour in time at three distinct positions inside the catalyst. At the outer surface, x"0 mm, the oscillation is still harmonic. At x"0.0625 mm, the amplitude of the oscillation has considerably grown and the
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Fig. 1. Oscillation of the CO turnover frequency in time at the outer surface and in the centre of the catalyst, showing rather uniform rates with respect to position. Conditions: 0.1 Hz, D "10\ m s\.
Fig. 2. Oscillation of the CO turnover frequency for low cycling frequency and low di!usivity at di!erent positions inside the catalyst. The behaviour is controlled by kinetics and di!usion. Conditions: 0.1 Hz, D "10\ m s\.
maxima are rather #at. In the centre, x"0.125 mm, a double peak arises periodically, because the oxygen surface coverage approaches the maximum value of 0.5 twice during a period. At the outer surface, CO and O concentrations oscillate in counterphase, as in the feed, but in the centre of the catalyst both oscillations have become in phase. This behaviour is as reported by Lie et al. (1993), but in the present situation, the periodic enhancements are much smaller. Surface sites that become available during the low CO concentration part of a cycle are not completely "lled with O adatoms because of a restricted supply of reactants, notably oxygen, by di!usion. Therefore the rate enhancements, that could potentially result from a more stoichiometric balance between adsorbed CO and O adatoms, produce vacant surface sites as well. The fraction of vacant sites increases typically to 0.17 in the centre of the catalyst at the times the rate is enhanced, while it is around 0.01 anywhere in the catalyst at all other times. When compared to a steady state, cycling promotes on a time average basis the kinetically controlled rate of
Fig. 3. Oscillation of the CO turnover frequency for high cycling frequency and low di!usivity at di!erent positions inside the catalyst. The behaviour is controlled by di!usion. Conditions: 10 Hz, D "10\ m s\.
CO production, see the case of D "10\ m s\ dis cussed above, by providing a periodically better CO*/O* ratio in the whole catalyst. Di!usion limitation promotes the rate in the steady state by providing a better CO*/O* ratio with increasing distance from the outer surface. The combination of cycling and limited di!usion, however, has hardly any, if not a negative e!ect on the time average production rate, as discussed above for the case of D "10\ m s\. At a cycling frequency of 10 Hz and D "10\ m s\ the results are comparable to the case of 0.1 Hz cycling and the same di!usivity, meaning that the spatial distribution of concentrations, surface coverages and CO production rate is rather uniform. The major di!erence at 10 Hz is that all oscillations, when compared at increasing distance from the outer surface, show a small increase in phase shift, since the timescale of cycling is nearer to the timescale of di!usion. For the same reason all oscillations are damped in comparison to the 0.1 Hz situation. The time average CO production at 10 Hz is about the same as at 0.1 Hz. When cycling at 10 Hz with a di!usivity D " 10\ m s\ a di!erent situation arises. The time scales of cycling and di!usion have the same value, which causes serious damping of all oscillations and phase shifts as well. The e!ects become more pronounced at larger distances from the outer surface. An example is shown in Fig. 3 for the CO production rate versus time at three di!erent positions inside the catalyst. The CO and O concentrations inside the catalyst decrease with larger distance from the outer surface. The CO surface coverage decreases as well, while the O coverage increases. Therefore the production rate increases with larger distance from the outer surface, but contrary to the 0.1 Hz case the amplitudes do not rise but #atten. This is recognised at the external surface in the bulk #ow, where at 0.1 Hz the CO bulk gas concentration oscillates non-harmonically with an amplitude of circa 40% around the value of
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4;10\ mol m\, while it is rather constant at the same value for 10 Hz. It means that the time average CO production is not really a!ected by the cycling frequency in case of signi"cant di!usion limitation. The case of an e!ective pellet di!usivity of 10\ m s\ and a pellet radius of 0.125 mm is quite typical for kinetic experiments in a micro "xed bed reactor. The simulation results suggest that cycling does not a!ect the intrinsicity of experimental data, if the time scale of the applied oscillation is much larger than the time scale of di!usion. It seems not relevant for this case to perform cycling experiments at frequencies above 10 Hz, since damping and phase shift of the oscillation would occur inside the catalyst.
4. Experimental set-up The complete experimental set-up has been described in detail by Campman (1996) and Nievergeld (1998). Its feed section consists of two sets of mass #ow controllers, which allow the generation of two feeds with di!erent composition. The reactor section is shown in Fig. 4. Four magnetic valves (switching time 3}5 ms) are used to generate square wave concentration cycles. By opening the valves two by two one feed is passed to the reactor, while the other one is directed to the ventilation. Switching is synchronized by two timers using 1 ms increments, permitting either symmetrical or asymmetrical cycling between 0.05 and 20 Hz. Pressure changes in the reactor
Fig. 4. Schematic view of the experimental set-up with four switching valves, allowing to direct either of the feeds to the preheater/reactor or to the vent. Real time analysis with mass spectrometry, time-averaged analysis with gaschromatography.
Fig. 5. Detailed view, drawn to scale, of the reactor in Fig. 4. The inner diameter of the catalyst bed is 13 mm.
due to switching the valves are minimized by carefully adjusting the pressure controllers downstream of the reactor and in the ventilation line. Downstream of the magnetic valves two separate feed lines, one for each feed, pass a preheater and end inside the reactor, just above the catalyst bed. This arrangement was chosen since the valves could operate at upmost 343 K, while much higher reactor temperatures were desired. Moreover mixing between the two feeds should be minimized. The reactor itself, made of stainless steel, is shown in Fig. 5. It is contained in a cylindrical oven. The two feed lines end in precision-machined chambers in the top of the reactor. Sapphire beads, one for each chamber and located downstream of the reactor inlet, act as one-way valves. Although Fig. 5 shows only two beads and chambers for simplicity, six of them are present actually, distributing each feed over three parallel channels equally divided over the cross-section of the reactor. If not pressurized by a magnetic valve, each sapphire bead is lifted by a #exible metal spring thus closing the corresponding feed line. The strength of the metal spring was adjusted in such a way that the pressurized feed line is open, while the other one remains closed. A sintered quartz plate enhances a radial distribution of the inlet feed stream over the reactor cross-section. A thermocouple in a well is used to measure the axial temperature pro"le in the catalyst bed. A back-pressure controller maintains the desired reactor
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pressure. The catalyst bed itself is 10 mm high with a diameter of 13 mm. Immediately upstream and downstream of the catalyst bed capillaries (length 1.8 m, internal diameter 0.3 mm) are inserted for continuous sampling of the gas #ow. Switching between the sample lines occurs manually with a zero volume three way valve. The residence time of the two sampling chambers is very small compared to the period of the applied oscillations under the experimental conditions. The #ow in the capillaries, although laminar, can be approached as plug #ow because of the small capillary diameter (Taylor, 1953). Real time analysis of either feed or e%uent is performed with a quadrupole mass spectrometer (VG Sensor Lab 200D). A fast analysis was performed by VG Medical Software, as applied in breath analysis in a medical environment, running on a dedicated personal computer. This arrange-
ment allows a sample frequency of 120/n Hz, where n denotes the number of atomic mass units to be measured.
5. Experimental results The catalyst bed consisted of 1.1 g Pt/c-Al O pellets with diameters in the range 0.1-0.15 mm and 1.5 g inert a-Al O with diameters between 0.15 and 0.21 mm. The catalyst was provided by Degussa A.G. Fig. 6 presents reactor outlet responses when switching between two helium feed #ows with di!erent argon content. At low frequency, e.g. 2 Hz in Fig. 6A, square wave signals are recorded. Operation is apparently in the quasi-steadystate regime, as de"ned by Matros (1984), since the horizontal concentration levels, coinciding with the
Fig. 6. Responses at the reactor outlet when switching between inert feeds with 0.5 and 0.1 mol% Ar in He. Frequency 2 Hz (Fig. 6A) and 10 Hz (Fig. 6B). Bed content: 1.0 g Pt/c-Al O catalyst and 1.46 g a-Al O inert. Total #ow 5.5;10\ mol s\. Temperature 393 K.
J.H.B.J. Hoebink et al. /Chemical Engineering Science 54 (1999) 4459}4468
steady-state concentrations, are reached very soon after switching. The rise time is typically 0.1 s, depending on the total #ow through the catalyst bed. The rise time has a notable in#uence on the response at high frequency, as shown for 10 Hz in Fig. 6B. This frequency is about the maximum that can be reached with the set-up from the analytical point of vue, as for faster cycling the sampling rate of the mass spectrometer will become too slow to observe su$cient data points in the ascents and descents of the signal. For faster oscillations the maximum and minimum signal values do not correspond anymore with the steady-state concentrations, as to be expected in the dynamic regime (Matros, 1984). For not too high frequencies, i.e. below 10 Hz for inert gases, the reactor inlet and outlet responses coincide perfectly, when the o!-set due to the residence time in the bed is taken into account. It indicates that ideal plug #ow exists in the catalyst bed. It also means that di!usion inside the catalyst is either too fast or too slow to be observed. For a similar catalyst bed Fig. 7 shows an example of reactor inlet responses when switching between feeds with 0.5 mol% O in He and 0.5 mol% CO in He. The concentration of the reactant, #owing through the reactor, increases a little just before switching. This artifact is
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Fig. 7. Responses at the reactor inlet when switching between feeds with 0.5 mol% CO in He and 0.5 mol% O in He. Frequency 0.1 Hz, 393 K. For other conditions, see Fig. 6.
also observed in most outlet responses, which are presented in Fig. 8. Symbols in the "gure indicate measurements, while lines show model predictions which will be discussed later. Results obtained at 0.1 Hz and 373 K are shown in Fig. 8A. At the onset of the oxygen half-cycle an immediate breakthrough followed by a dip in the
Fig. 8. Responses at the reactor outlet when switching between feeds with 0.5 mol % CO in He and 0.5 mol % O in He. Symbols refer to measurements, curves to model predictions. Fig. 8A: 0.1 Hz, 373 K. Fig. 8B: 0.1 Hz, 433 K. Fig 8C: 0.25 Hz, 433 K. For other conditions, see Fig. 6.
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O concentration is observed, indicating that oxygen can not adsorb on a CO covered surface. Once the CO production has started, vacant sites become available, which cause a temporary decrease of the O signal before relaxing to the steady-state value. After switching to CO a lag time in the CO signal is observed with simultaneous production of CO , which indicates that CO can adsorb on a surface covered with O adatoms. Fig. 8B shows the behaviour at 0.1 Hz and 433 K. Due to the higher temperature CO desorption occurs at a higher rate and vacant sites become available rather soon after switching from CO to O . Therefore, in comparison with Fig. 8A, the oxygen signal shows a sharp peak at the onset of the oxygen half-cycle before the CO production starts. The amount of CO produced is equal during the oxygen half-cycle and during the CO half-cycle. Fig. 8C shows the results at 433 K and a frequency of 0.25 Hz. The behaviour is similar to Fig. 8B, but the time-average CO production is much larger due to faster cycling. The CO concentration does not reach the steady-state value anymore at the end of the CO half-cycle, which becomes more pronounced at frequencies above 0.25 Hz, and also at lower temperatures. The complete set of experiments covered the range 373}433 K and frequencies 0.1}0.5 Hz. Fixed conditions were a total pressure of 110 kPa, 1.1 g catalyst and a total #ow, including the diluent helium, of 5.6;10\ mol s\. During the oxygen part of the period the oxygen partial pressure was 0.55 kPa, while the same pressure was applied for CO during the other half of the cycle. The bed temperature was uniform during the experiments. 6. Interpretation of the experimental results The experimental results were interpreted as intrinsic kinetics, as the simulation results indicated that the intrinsicity is not a!ected by cycling for low enough cycling rate and high enough di!usivity. The e!ective di!usivity inside the catalyst pellets used was estimated as 10\ m s\, based upon a pellet porosity of 0.45 and a tortuosity of 5. The kinetic model used is shown in Table 2 (Nievergeld, 1998). A much more detailed set of steps than proposed by Herz and Marin (1980) was required to describe the transient data, which illustrates the power of transient kinetic methods. Features of the model are reversible adsorption of CO and molecular adsorption of O , followed by instantaneous dissociation (Campman, 1996). One reaction path, step 4, contains the Langmuir-Hinshelwood reaction between adsorbed CO and O adatoms. The product CO is allowed to adsorb reversibly on the support, step 7. The kinetic parameters of CO adsorption/desorption were determined from in dependent experiments and were hardly depending on temperature. To account for the observed adsorption of CO on sites covered with oxygen and the subsequent production of CO , a second reaction path was included,
Table 2 Elementary steps and reaction paths Elementary reaction k
CO#* 8 CO* k
N1
N2
Step number
2
0
1
1
1
2
1
1
3
2
0
4
0
2
5
0
2
6
0
0
7
\
k
O #* P O * k
O *#* P 2O* k
CO*#O* P CO #2* k
CO#O* 8 OCO* k
\
k
OCO* P CO #* k
CO #) 8 CO ) k \ 2CO#O P2CO
Note: (*) Site on Pt and ()) Site on c-/Al O .
see steps 5 and 6, where gas phase CO is reversibly adsorbed as an OCO* species that might produce CO (Nievergeld, 1998). The same interpretation was used by Nibbelke et al. (1998) to quantify the CO oxidation over a commercial Pt/Rh/CeO /c-Al O catalyst. It is in line with suggestions by Barshad et al. (1985), who observed new peaks in time-average IR spectra during periodic operation, when compared to the steady-state. They concluded that CO adsorbs both on oxygen covered sites and on platinum oxides. The latter can be excluded in the present study. Platinum oxides are formed at a timescale of minutes (Turner and Maple, 1984), where the timescale of the applied oscillations is in the order of seconds. Consequently, the amount of oxides, if present, should be constant in time as the oxide formation is in the sliding regime (Matros, 1984). Since no adsorption of oxygen on oxides takes place and the reduction of the oxides also proceeds at a timescale of minutes, the oxygen adsorption capacity would be smaller than the CO adsorption capacity. It was observed, however, that equal amounts of CO were produced during each of the half-cycles of an oscillation period. All rates were expressed in accordance with the law of mass action. The rate coe$cient for the chemisorption of CO and O is obtained from collision theory:
R¹ 1 k" s , G ¸ 2nM G R G where s refers to the sticking probability on a clean G surface. Because of asssumed instantaneous dissociation
J.H.B.J. Hoebink et al. /Chemical Engineering Science 54 (1999) 4459}4468 Table 3 Final kinetic parameters estimates with corresponding 95% con"dence intervals obtained from regression of experimental data at 4 temperatures with the kinetic model of Table 2 Parameter
Unit
Value
s !A B !E B !b B !s - A *& E *& b *& k k \ k k k \
* s\ kJ mol\ kJ mol\ * s\ kJ mol\ kJ mol\ m mol\ s\ s\ s\ m mol\ s\ s\
0.186$0.002 6;10$1;10 119.7$0.7 14.6$0.1 5.26;10\$0.05;10\ 3.7;10$0.5;10 43.9$0.6 9.35$0.05 219$4 0.040$0.001 1.75$0.04 0.864$0.009 0.809$0.006
of oxygen, the rate constant k is set to in"nity, which makes the chemisorption of O "rst order in the vacant sites (Oh et al., 1986) and causes an overall steady-state rate proportional to p /p (Campman, 1996). - !The desorption coe$cient of CO is obtained from
E !b h B !- !- , k "A exp ! B !\ B !R¹ which accounts for surface non-uniformity or interaction of adsorbed CO molecules. The coe$cient of the surface reaction between CO* and O* is described in an analogous way:
E !b h *& !- . k "A exp ! *& *& R¹ All other parameters were considered as independent of temperature. Final kinetic parameter estimates with their 95% con"dence intervals, obtained via multiresponse nonlinear regression of the experimental data with the kinetic model, are shown in Table 3. Fig. 8A}C show a comparison of experimental data and model predictions. The agreement in general is satisfactory. All parameter estimates are well in the range calculated from the transition state theory (Zhdanov, 1988) and close to values reported in the literature. The sticking probability of CO on a clean surface, s , is lower than !the value reported by Herz and Marin (1980) but much higher than the value reported by Graham (1993). The activation energy and the pre-exponential factor of the CO desorption are in good agreement with literature data (Herz and Marin, 1980; Campman 1996). The estimated value of b which accounts for the dependency B !of the activation energy on the degree of coverage, is only half the value reported by Zhdanov and Kasemo (1994) and Oh et al. (1986) for the CO oxidation over Rh/Al O .
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The sticking probability of O on a clean surface is smaller than the value obtained by Herz and Marin (1980). They assumed, however, a second order oxygen adsorption in their kinetic model and this leads to a higher value of s . The activation energy of the surface - reaction is lower than the value of Herz and Marin (1980) but is close to the result of Graham (1993). The value of the pre-exponential factor of the surface reaction is in good agreement with the value of Herz and Marin (1980) but smaller than the value reported by Graham (1993). The value of b agrees well with the value of Zhdanov *& and Kasemo (1994). Graham (1993) mentioned much higher values for the rate coe$cients of CO adsorption on and desorption from the support. Their values suggest that the sorption takes place on a time-scale of less than 0.1 s. However, the values of the estimates shown in Table 3 are in agreement with transient experiments conducted with a feed containing CO only which showed that the time-scale of adsorption and desorption is approximately 1 s. In the literature no values of the parameters of steps 5 and 6 are reported. The estimates are in line with the observations of Barshad et al. (1985). They suggested a rather low value of h and a poten-!tially fast reaction of OCO* to CO , indicating a relative ly low value of the equilibrium constant and a high value for the rate coe$cient for the desorption of OCO*, k . 7. Conclusions A simulation study was performed, with CO oxidation as an example, to explore how feed composition cycling can be a!ected by di!usion inside catalyst pellets. For a typical case as met when performing kinetic experiments in micro "xed bed reactors, intrinsic kinetics might be obtained from composition cycling experiments. A prerequisite is that the time scale of cycling is much larger than the time scale of di!usion inside the catalyst, provided the elementary reaction steps are in the dynamic regime. Cycling frequencies above 10 Hz seem not relevant as damping and phase shift of the imposed oscillations would occur inside the catalyst. An experimental set-up was presented, which allows cycling of the feed for transient operation of "xed bed microreactors at frequencies up to 10 Hz. This maximum frequency was bound by instrumental analysis, e.g. the sampling frequency of the applied mass spectrometer. Application, however, of higher frequencies seems not useful in view of the timescale of di!usion that is usually met in laboratory catalytic "xed bed reactors. The transient oxidation of CO by O over Pt/c-Al O was studied with this set-up. The results gave evidence that CO may adsorb on oxygen covered sites under simultaneous production of CO . O does, however, not adsorb on CO covered sites, which causes a delay in the transient of the CO production. A kinetic model
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including rate parameters was presented, which gives an adequate description of the experimental data and provides much more detailed information than could be obtained from steady-state experiments.
Acknowledgement The authors gratefully acknowledge the major e!orts of M.A.J. Campman for the development and design of the reactor and its set-up. They are grateful to the Dutch Technology Foundation STW for the "nancial support. Dr E.S. Lox from Degussa A.G. is acknowledged for providing the catalyst samples.
Notation
A B A *& A a B C E G C N G D E B E *& F T f k ? k G k \ k ¸ R M G N G R t t t t < x
preexponential factor for CO desorption, s\ preexponential factor for surface reaction, s\ external surface of the catalyst, m speci"c surface area of the catalyst, m m\ amplitude of imposed oscillation, dimensionless gas phase concentration of component i, mol m\ concentration of component i inside pellet pores, mol m\ e!ective di!usivity, m m s\ activation energy for CO desorption, kJ mol\ activation energy for surface reaction, kJ mol\ volumetric #ow rate, m s\ cycling frequency, s\ adsorption rate coe$cient, m mol\ s\ adsorption rate coe$cient of CO or O , m mol\ s\ desorption rate coe$cient of CO, s\ rate coe$cient of the surface reaction, s\ active sites per unit speci"c surface area, mol m\ molecular weight of component i, kg mol\ di!usive #ux of component i through gas phase/catalyst interface, mol m\ s\ gas constant, J mol\ K\ time, s timescale of the oscillation, s timescale of di!usion, s timescale of adsorption of component A, s reactor volume, m pellet coordinate, m
Greek letters b
coe$cient, accounting for surface non-uniformity or interaction of CO molecules, dimensionles
e @ e N h G *
interpellet void fraction, m m\ intrapellet void fraction, m m\ degree of surface coverage of species i vacant site dimensionless
References Campman, M.A.J. (1996). Kinetics of carbon monoxide oxidation over supported platinum catalysts. Ph.D. thesis, Eindhoven University of Technology, Eindhoven. Dekker, F.H.M. (1995). Transient kinetics in heterogeneous catalysis. Ph.D. thesis, University of Amsterdam, Amsterdam. Fiolitakis, E., Schmid, M., Hofmann, H., & Silveston, P.L. (1983). Investigation of the catalytic oxidation of benzene to maleic anhydride by wave front analysis with respect to the application of periodic operation. Canadian Journal of Chemical Engineering, 61, 703}709. Graham, W.R.C. (1993). Oxidation of carbon monoxide on platinum catalyst: kinetic model discrimination using experimental steadystate multiplicity and feed composition cycling. Ph.D. thesis, University of Alberta. Huinink, J.P., Hoebink, J.H.B.J., & Marin, G.B. (1996). Pulse experiments over catalyst beds: a window of measurable reaction rate coe$cients. Canadian Journal of Chemical Engineering, 74, 580}585. Lie, A.B.K., Hoebink, J.H.B.J., & Marin, G.B. (1993). The e!ects of oscillatory feeding of CO and O on the performance of a mono lithic catalytic converter of automobile exhaust gas: a modeling study. ¹he Chemical Engineering Journal, 53, 47}54. Matros, Y.Sh. (1984). Unsteady processes in catalytic reactors. Studies in Surface Science and Catalysis, 22. Matros, Y.Sh., Bunimovich, G.A., & Strots, V.O. (1997). Reaction kinetics as a basis for optimal transient operation of catalytic reactors. Studies in Surface Science and Catalysis, 109, 141}155. Nibbelke, R.H., Nievergeld, A.J.L., Hoebink, J.H.B.J., & Marin, G.B. (1998). Development of a transient kinetic model for the CO oxidation by O over a Pt/Rh/CeO /c-Al O three-way catalyst. Applied Catalysis, Series B, 19, 245}259. Nievergeld, A.J.L. (1998). Automotive exhaust gas conversion: reaction kinetics, reactor modelling and control. Thesis, Eindhoven University of Technology, Eindhoven. Nievergeld, A.J.L, van Selow, E.R., Hoebink, J.H.B.J., & Marin, G.B. (1997). Simulation of a catalytic converter of automotive exhaust gas under dynamic conditions. Studies in Surface Science and Catalysis, 109, 449}458. Oh, S.H., Fisher, G.B., Carpenter, J.E., & Goodman, D.W. (1986). Comparative kinetic studies of CO}O and CO}NO reactions over single crystal and supported rhodium catalysts. Journal of Catalysis, 100, 360}376. Silveston, P.L. (1995). Automotive exhaust catalysis under periodic operation. Catalysis ¹oday, 25, 175}195. Silveston, P., Hudgins, R.R., & Renken, A. (1995). Periodic operation of catalytic reactors*introduction and overview. Catalysis ¹oday, 25, 91}112. Taylor, G.I. (1953). Dispersion of soluble matter in solvent #owing slowly through a tube. Proceedings of Royal Society of ¸ondon, Series A, 219, 186. Turner, J.E., & Maple, M.B. (1984). Oxide formation and reduction over Pt, Pd and Ir: A driving mechanism for oscillations in the CO oxidation reaction. Surface Sciences, 147. Zhdanov, V.P., & Kasemo, B. (1994). Steady-state kinetics of CO oxidation on Pt: Extrapolation from 10\ to 1 bar. Applied Surface Sciences, 74, 147}164. Zhdanov, V.P., Pavlicek, J., & Knor, Z. (1988). Preexponential factors for elementary surface processes. Catalytic Reviews2Science and Engineering, 30, 501}517.
CO oxidation in a "xed bed reactor with high frequency cycling of the feed J.H.B.J. Hoebink*, A.J.L. Nievergeld, G.B. Marin Eindhoven University of Technology, Laboratorium voor Chemische Technologie, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Abstract An experimental set-up is presented, which allows cycling of the feed for transient operation of "xed bed microreactors at frequencies up to 10 Hz. The set-up was applied for the transient oxidation of CO by O over Pt/c-Al O . The results gave clear evidence that CO may adsorb on oxygen covered sites under simultaneous production of CO . O does, however, not adsorb on CO covered sites, which causes a delay in the transient of the CO production. A kinetic model including rate parameters was presented, which gives an adequate description of the experimental data and provides much more detailed information than could be obtained from steady-state experiments. A simulation study is performed, with CO oxidation as an example, to explore how feed composition cycling is a!ected by di!usion inside catalyst pellets. If the time scale of di!usion inside the catalyst is much smaller than the time scale of the applied oscillation, intrinsic kinetics might be obtained from experiments with cycling of the feed. This statement supposes that di!usion limitation would be absent in the corresponding steady-state without composition cycling, and that the reaction kinetics is in the dynamic regime. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Transient kinetics; CO oxidation; Catalytic "xed bed; Feed composition cycling; High frequency; Di!usion limitation
1. Introduction The operation of chemical reactors under transient conditions, when compared to the traditional steadystate operation, is well known for its potential to increase the reactor performance, e.g. conversion, selectivity, energy saving. An overview was presented recently (Matros et al., 1997). One way of achieving better performance is periodic perturbation of the reactor feed composition, as demonstrated for instance in catalytic benzene oxidation (Fiolitakis et al., 1983). This type of operation was reviewed by Silveston et al. (1995) for catalytic reactors. A typical example is cycling of the feed in catalytic converters for automobile exhaust gas (Silveston, 1995), although perturbations in this case are not intentional but induced by the lambda sensor based control system.
*Corresponding author. Tel.: 00 31 40 2472850; fax: 00 31 40 2446653. E-mail address: [email protected] (J.H.B.J. Hoebink). Current address: AspenTech Europe BV, P.O. Box 258, 5680 AG Best, the Netherlands. Current address: Universiteit Gent, Laboratorium voor Petrochemische Techniek, Krijgslaan 281, B-9000 Gent, Belgium.
Improved reactor performance is due to non-linear reaction kinetics (Lie et al., 1993), in particular when perturbations are applied at a timescale which is comparable to the timescale of the reaction. In case of multiple reactions, however, various timescales of reaction may prevail and the e!ect of cycling at a "xed frequency could be positive for one reaction, but negative for another (Nievergeld et al., 1997). A detailed knowledge of the kinetics on the level of elementary steps is a prerequisite for the successful design of a dynamically operated reactor (Matros et al., 1997), as each step in a kinetic model has its own distinct timescale. In general, this could be achieved through transient kinetic studies, which provide much extra mechanistic and kinetic information when compared to classical steady-state kinetics, leading to a wider applicability of a kinetic model. For periodic operation a mechanistic analysis of wave fronts was presented by Fiolitakis et al. (1983). The current paper describes a laboratory micro-reactor set-up for such purpose, developed at Eindhoven University, which allows feed composition cycling at frequencies up to 10 Hz. This enables to cover the range
0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 1 0 3 - 7
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of typical frequencies around 1 Hz, met in automotive exhaust gas converters, where current technology for laboratory reactors usually applies frequencies of 0.01}0.1 Hz. Experimental results were obtained with this set-up on CO oxidation over a commercial Pt/Rh/CeO /c-Al O catalyst (Nibbelke et al., 1998; Nievergeld, 1998). In a kinetic study one wants to avoid transport limitation in order to obtain intrinsic kinetics. The criteria for such an approach are well-developed only for steadystate reactors. For transient reactors an onset has been made only for stepwise (Dekker, 1995) and pulsewise (Huinink et al., 1996) operation. Since high frequency perturbations may cause reactor operation in the sliding regime (Matros, 1984), the e!ects of di!usion limitation inside catalyst pellets during cycling of the feed are discussed with emphasis on determination of the maximum applicable frequency that still allows to obtain intrinsic kinetic data.
The continuity equation for component i, with i"O , CO, CO , in the gas phase is
2. Simulation model
*h G"R G *t
A simulation study was performed for the case of an in"nitely large, #at porous plate of catalytic material with thickness 2r . Both open sides are in contact with an N ideally mixed gas phase, #own through with a diluted CO/O mixture which reacts in the catalyst. Catalyst and gas phase have equal volumes in order to approach the situation in a "xed bed reactor. External mass transfer resistance is neglected. The kinetics for CO oxidation were taken from Herz and Marin (1980) who proposed the following elementary steps, based on steady-state experiments: k
? !&& CO*, CO#* && k B !-
*C e < E G"F (C !C )!N A @ T D G E G G *t with N the di!usive #ux through the gas phase/catalyst G interface. The initial condition corresponds with the assumed steady state at t"0, so C "CQQ . The #ux N is E G E G G obtained from the continuity equation for component i in the gas phase inside the catalyst: *C *C N G"D N G!a ¸ R e N *t *x R G with the steady state pro"les as initial condition, so C (x, 0)"C (x)QQ for 0(x(2r . The boundary conN G N G N dition at x"0 connects the pellet concentration to the gas phase concentration, so C "C . At the centre of N G E G the catalyst, e.g. x"r , all #uxes are zero because of N symmetry. Species coverages on the catalyst surface obey the continuity equation:
with initial coverages given by the steady state coverages, so h (x, 0)"h (x)QQ for 0(x(2r . G G N The partial di!erential equations were transformed into ordinary ones by application of collocation along the catalyst coordinate x. The complete set of di!erential equations was solved with routine D02NHF from the NAG Fortran library. The steady state was obtained by setting all time derivatives equal to zero, and solving the resulting set of ordinary di!erential equations and algebraic equations with routines D02EBF and C05NBF from the NAG library. Parameter values are summarized in Table 1. The corresponding gas phase residence time amounts to 0.01 s.
I? - 2O*, O#2* && IA CO . CO*#O* & This model predicts a "rst order reaction in oxygen and inhibition by CO in the steady-state. Rate parameters were used as adapted by Lie et al. (1993) and evaluated at 600 K. At time t"0 it is assumed that the reactor is in the steady state. For t'0 the CO and O feed concentrations oscillate in counterphase: C (t)"C (1#B sin(2n ft)), t*0, D !D !C (t)"C (1#B sin(2n ft#n)), t*0, D - D - where the superscript 0 denotes the time-average value of the corresponding feed concentration.
3. Simulated possible e4ects of internal di4usion limitation All calculations were performed at a temperature of 600 K. As the calculations started from a steady state before cycling, the results may show some transient behaviour prior to stable harmonic oscillations. The discussion focuses on the latter. If the oscillation frequency value approaches the reciprocal gas phase residence time, a comparison of inlet and outlet signals shows some signal damping and phase shift, which is not in#uenced by the reaction. For a proper understanding of the various phenomena the timescale of the applied oscillation, expressed by the oscillation period, t , should be compared with the timescale of di!usion and of the various reaction steps.
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Table 1 Parameter values and other conditions, used in the simulation model Parameter
Value
a A r N F T D < C D !-
1.4;10 1.3;10\ 1.25;10\ 7;10\ 10\, 10\ 1.3;10\ 0.18
m m\ . m m\ 0 m m s\ m m s\ m mol m\
The former can be estimated from: r t " N . D As the present calculations apply e!ective di!usivities of 10\ or 10\ m s\, the corresponding di!usion timescale is typically either 0.01 or 0.1 s. The timescale of adsorption of a component A follows from (Huinink et al., 1996): e C e @ " @ " , !R k hL ¸ a T ? * R where n stands for the order in vacant sites, which is 1 for CO and 2 for oxygen according to the kinetic model. When evaluated for oxygen, the order of magnitude of the timescale is 1 s at 600 K, taking the data of Lie et al. (1993) and a value h "0.01, which seems realistic on * basis of the current simulation "ndings. The timescale of CO adsorption is 2;10\ s, while for CO desorption a timescale of 3;10\ s is found in an analogous way if C "0.18 mol m\ and h "0.8. For the surface reac!!tion a timescale of 3;10\ s is found similarly when assuming C "0.12 mol m\ and h "0.2. Oxygen ad- sorption, having the largest timescale, is therefore rate controlling, as is known from the literature, and CO adsorption/desorption can be considered as in equilibrium. Lie et al. (1993) studied a monolith reactor with cycling of the feed, using the same kinetic model for CO oxidation, but without consideration of di!usion limitation in the catalytic washcoat. They noticed with increasing axial distance in the reactor an increase of the amplitude of the CO gas phase concentration, whereas for oxygen the amplitude decreased and even inversed. So, out of phase oscillation of CO and O at the reactor inlet turned into in phase oscillation at the outlet. This can be explained as follows. When the CO concentration decreases periodically, free sites become available for oxygen adsorption and the CO production rate increases accord ingly due to a better balance of adsorbed CO and O adatoms with respect to the stoichiometry of the surface reaction. The fact that a CO decrease is accomt
Parameter
Value
¸ R e N C D B F = /= e @
2.48;10\ 0.45 0.12 0.15 0.1, 1, 5, 10 10 0.45
mol m\ . . m m\ mol m\ * Hz kg kg\ m m\ 0
panied by an oxygen increase, due to counterphase oscillation in the feed, causes an extra enhancement of the CO production rate. This positive feedback mechanism causes an increase of the oscillation amplitude of the CO gas concentration with increasing axial distance. For the oxygen oscillation the feedback is negative, which causes attenuation of the amplitude and even inversion with increasing axial distance. Lie et al. (1993) reported a positive e!ect of cycling on the time average rate of CO production, since the periodic rate enhancements largely overcompensate the periodic decreases, which arise during the half period of high CO concentrations. The e!ects observed are due to non-linear kinetics. The current results will be discussed "rst at an oscillation frequency of 0.1 Hz, which means that di!usion and kinetics will show dynamic behaviour (Matros, 1984). When D "10\ m s\ or larger, model simulations show that the concentrations of CO and O in the cata lyst are spatially rather uniform, as are the surface coverages of adsorbed CO and O adatoms. Therefore the CO production rate, expressed as turnover frequency, is more or less uniform in space as well, as shown in Fig. 1, where it is plotted vs. time for both the gas/catalyst interface and the centre of the catalyst. The rate oscillates in phase with the oxygen gas phase concentration and with the O adatom surface coverage. The time average CO production, which is controlled by kinetics, is higher under cycling conditions, when compared to the steady state, in accordance with the work of Lie et al. (1993). For D "10\ m s\ and the same frequency of 0.1 Hz, the concentrations of CO and O decrease con siderably with increasing distance from the outer surface of the catalyst due to low di!usion rates. For this reason the surface coverage of CO decreases in the same direction, but the surface coverage of O adatoms increases because of less CO inhibition. By consequence, the CO production rate is higher at larger distance from the outer surface, as also could be expected in a steady state without cycling of the feed. Fig. 2 shows the di!erent oscillatory behaviour in time at three distinct positions inside the catalyst. At the outer surface, x"0 mm, the oscillation is still harmonic. At x"0.0625 mm, the amplitude of the oscillation has considerably grown and the
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Fig. 1. Oscillation of the CO turnover frequency in time at the outer surface and in the centre of the catalyst, showing rather uniform rates with respect to position. Conditions: 0.1 Hz, D "10\ m s\.
Fig. 2. Oscillation of the CO turnover frequency for low cycling frequency and low di!usivity at di!erent positions inside the catalyst. The behaviour is controlled by kinetics and di!usion. Conditions: 0.1 Hz, D "10\ m s\.
maxima are rather #at. In the centre, x"0.125 mm, a double peak arises periodically, because the oxygen surface coverage approaches the maximum value of 0.5 twice during a period. At the outer surface, CO and O concentrations oscillate in counterphase, as in the feed, but in the centre of the catalyst both oscillations have become in phase. This behaviour is as reported by Lie et al. (1993), but in the present situation, the periodic enhancements are much smaller. Surface sites that become available during the low CO concentration part of a cycle are not completely "lled with O adatoms because of a restricted supply of reactants, notably oxygen, by di!usion. Therefore the rate enhancements, that could potentially result from a more stoichiometric balance between adsorbed CO and O adatoms, produce vacant surface sites as well. The fraction of vacant sites increases typically to 0.17 in the centre of the catalyst at the times the rate is enhanced, while it is around 0.01 anywhere in the catalyst at all other times. When compared to a steady state, cycling promotes on a time average basis the kinetically controlled rate of
Fig. 3. Oscillation of the CO turnover frequency for high cycling frequency and low di!usivity at di!erent positions inside the catalyst. The behaviour is controlled by di!usion. Conditions: 10 Hz, D "10\ m s\.
CO production, see the case of D "10\ m s\ dis cussed above, by providing a periodically better CO*/O* ratio in the whole catalyst. Di!usion limitation promotes the rate in the steady state by providing a better CO*/O* ratio with increasing distance from the outer surface. The combination of cycling and limited di!usion, however, has hardly any, if not a negative e!ect on the time average production rate, as discussed above for the case of D "10\ m s\. At a cycling frequency of 10 Hz and D "10\ m s\ the results are comparable to the case of 0.1 Hz cycling and the same di!usivity, meaning that the spatial distribution of concentrations, surface coverages and CO production rate is rather uniform. The major di!erence at 10 Hz is that all oscillations, when compared at increasing distance from the outer surface, show a small increase in phase shift, since the timescale of cycling is nearer to the timescale of di!usion. For the same reason all oscillations are damped in comparison to the 0.1 Hz situation. The time average CO production at 10 Hz is about the same as at 0.1 Hz. When cycling at 10 Hz with a di!usivity D " 10\ m s\ a di!erent situation arises. The time scales of cycling and di!usion have the same value, which causes serious damping of all oscillations and phase shifts as well. The e!ects become more pronounced at larger distances from the outer surface. An example is shown in Fig. 3 for the CO production rate versus time at three di!erent positions inside the catalyst. The CO and O concentrations inside the catalyst decrease with larger distance from the outer surface. The CO surface coverage decreases as well, while the O coverage increases. Therefore the production rate increases with larger distance from the outer surface, but contrary to the 0.1 Hz case the amplitudes do not rise but #atten. This is recognised at the external surface in the bulk #ow, where at 0.1 Hz the CO bulk gas concentration oscillates non-harmonically with an amplitude of circa 40% around the value of
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4;10\ mol m\, while it is rather constant at the same value for 10 Hz. It means that the time average CO production is not really a!ected by the cycling frequency in case of signi"cant di!usion limitation. The case of an e!ective pellet di!usivity of 10\ m s\ and a pellet radius of 0.125 mm is quite typical for kinetic experiments in a micro "xed bed reactor. The simulation results suggest that cycling does not a!ect the intrinsicity of experimental data, if the time scale of the applied oscillation is much larger than the time scale of di!usion. It seems not relevant for this case to perform cycling experiments at frequencies above 10 Hz, since damping and phase shift of the oscillation would occur inside the catalyst.
4. Experimental set-up The complete experimental set-up has been described in detail by Campman (1996) and Nievergeld (1998). Its feed section consists of two sets of mass #ow controllers, which allow the generation of two feeds with di!erent composition. The reactor section is shown in Fig. 4. Four magnetic valves (switching time 3}5 ms) are used to generate square wave concentration cycles. By opening the valves two by two one feed is passed to the reactor, while the other one is directed to the ventilation. Switching is synchronized by two timers using 1 ms increments, permitting either symmetrical or asymmetrical cycling between 0.05 and 20 Hz. Pressure changes in the reactor
Fig. 4. Schematic view of the experimental set-up with four switching valves, allowing to direct either of the feeds to the preheater/reactor or to the vent. Real time analysis with mass spectrometry, time-averaged analysis with gaschromatography.
Fig. 5. Detailed view, drawn to scale, of the reactor in Fig. 4. The inner diameter of the catalyst bed is 13 mm.
due to switching the valves are minimized by carefully adjusting the pressure controllers downstream of the reactor and in the ventilation line. Downstream of the magnetic valves two separate feed lines, one for each feed, pass a preheater and end inside the reactor, just above the catalyst bed. This arrangement was chosen since the valves could operate at upmost 343 K, while much higher reactor temperatures were desired. Moreover mixing between the two feeds should be minimized. The reactor itself, made of stainless steel, is shown in Fig. 5. It is contained in a cylindrical oven. The two feed lines end in precision-machined chambers in the top of the reactor. Sapphire beads, one for each chamber and located downstream of the reactor inlet, act as one-way valves. Although Fig. 5 shows only two beads and chambers for simplicity, six of them are present actually, distributing each feed over three parallel channels equally divided over the cross-section of the reactor. If not pressurized by a magnetic valve, each sapphire bead is lifted by a #exible metal spring thus closing the corresponding feed line. The strength of the metal spring was adjusted in such a way that the pressurized feed line is open, while the other one remains closed. A sintered quartz plate enhances a radial distribution of the inlet feed stream over the reactor cross-section. A thermocouple in a well is used to measure the axial temperature pro"le in the catalyst bed. A back-pressure controller maintains the desired reactor
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pressure. The catalyst bed itself is 10 mm high with a diameter of 13 mm. Immediately upstream and downstream of the catalyst bed capillaries (length 1.8 m, internal diameter 0.3 mm) are inserted for continuous sampling of the gas #ow. Switching between the sample lines occurs manually with a zero volume three way valve. The residence time of the two sampling chambers is very small compared to the period of the applied oscillations under the experimental conditions. The #ow in the capillaries, although laminar, can be approached as plug #ow because of the small capillary diameter (Taylor, 1953). Real time analysis of either feed or e%uent is performed with a quadrupole mass spectrometer (VG Sensor Lab 200D). A fast analysis was performed by VG Medical Software, as applied in breath analysis in a medical environment, running on a dedicated personal computer. This arrange-
ment allows a sample frequency of 120/n Hz, where n denotes the number of atomic mass units to be measured.
5. Experimental results The catalyst bed consisted of 1.1 g Pt/c-Al O pellets with diameters in the range 0.1-0.15 mm and 1.5 g inert a-Al O with diameters between 0.15 and 0.21 mm. The catalyst was provided by Degussa A.G. Fig. 6 presents reactor outlet responses when switching between two helium feed #ows with di!erent argon content. At low frequency, e.g. 2 Hz in Fig. 6A, square wave signals are recorded. Operation is apparently in the quasi-steadystate regime, as de"ned by Matros (1984), since the horizontal concentration levels, coinciding with the
Fig. 6. Responses at the reactor outlet when switching between inert feeds with 0.5 and 0.1 mol% Ar in He. Frequency 2 Hz (Fig. 6A) and 10 Hz (Fig. 6B). Bed content: 1.0 g Pt/c-Al O catalyst and 1.46 g a-Al O inert. Total #ow 5.5;10\ mol s\. Temperature 393 K.
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steady-state concentrations, are reached very soon after switching. The rise time is typically 0.1 s, depending on the total #ow through the catalyst bed. The rise time has a notable in#uence on the response at high frequency, as shown for 10 Hz in Fig. 6B. This frequency is about the maximum that can be reached with the set-up from the analytical point of vue, as for faster cycling the sampling rate of the mass spectrometer will become too slow to observe su$cient data points in the ascents and descents of the signal. For faster oscillations the maximum and minimum signal values do not correspond anymore with the steady-state concentrations, as to be expected in the dynamic regime (Matros, 1984). For not too high frequencies, i.e. below 10 Hz for inert gases, the reactor inlet and outlet responses coincide perfectly, when the o!-set due to the residence time in the bed is taken into account. It indicates that ideal plug #ow exists in the catalyst bed. It also means that di!usion inside the catalyst is either too fast or too slow to be observed. For a similar catalyst bed Fig. 7 shows an example of reactor inlet responses when switching between feeds with 0.5 mol% O in He and 0.5 mol% CO in He. The concentration of the reactant, #owing through the reactor, increases a little just before switching. This artifact is
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Fig. 7. Responses at the reactor inlet when switching between feeds with 0.5 mol% CO in He and 0.5 mol% O in He. Frequency 0.1 Hz, 393 K. For other conditions, see Fig. 6.
also observed in most outlet responses, which are presented in Fig. 8. Symbols in the "gure indicate measurements, while lines show model predictions which will be discussed later. Results obtained at 0.1 Hz and 373 K are shown in Fig. 8A. At the onset of the oxygen half-cycle an immediate breakthrough followed by a dip in the
Fig. 8. Responses at the reactor outlet when switching between feeds with 0.5 mol % CO in He and 0.5 mol % O in He. Symbols refer to measurements, curves to model predictions. Fig. 8A: 0.1 Hz, 373 K. Fig. 8B: 0.1 Hz, 433 K. Fig 8C: 0.25 Hz, 433 K. For other conditions, see Fig. 6.
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O concentration is observed, indicating that oxygen can not adsorb on a CO covered surface. Once the CO production has started, vacant sites become available, which cause a temporary decrease of the O signal before relaxing to the steady-state value. After switching to CO a lag time in the CO signal is observed with simultaneous production of CO , which indicates that CO can adsorb on a surface covered with O adatoms. Fig. 8B shows the behaviour at 0.1 Hz and 433 K. Due to the higher temperature CO desorption occurs at a higher rate and vacant sites become available rather soon after switching from CO to O . Therefore, in comparison with Fig. 8A, the oxygen signal shows a sharp peak at the onset of the oxygen half-cycle before the CO production starts. The amount of CO produced is equal during the oxygen half-cycle and during the CO half-cycle. Fig. 8C shows the results at 433 K and a frequency of 0.25 Hz. The behaviour is similar to Fig. 8B, but the time-average CO production is much larger due to faster cycling. The CO concentration does not reach the steady-state value anymore at the end of the CO half-cycle, which becomes more pronounced at frequencies above 0.25 Hz, and also at lower temperatures. The complete set of experiments covered the range 373}433 K and frequencies 0.1}0.5 Hz. Fixed conditions were a total pressure of 110 kPa, 1.1 g catalyst and a total #ow, including the diluent helium, of 5.6;10\ mol s\. During the oxygen part of the period the oxygen partial pressure was 0.55 kPa, while the same pressure was applied for CO during the other half of the cycle. The bed temperature was uniform during the experiments. 6. Interpretation of the experimental results The experimental results were interpreted as intrinsic kinetics, as the simulation results indicated that the intrinsicity is not a!ected by cycling for low enough cycling rate and high enough di!usivity. The e!ective di!usivity inside the catalyst pellets used was estimated as 10\ m s\, based upon a pellet porosity of 0.45 and a tortuosity of 5. The kinetic model used is shown in Table 2 (Nievergeld, 1998). A much more detailed set of steps than proposed by Herz and Marin (1980) was required to describe the transient data, which illustrates the power of transient kinetic methods. Features of the model are reversible adsorption of CO and molecular adsorption of O , followed by instantaneous dissociation (Campman, 1996). One reaction path, step 4, contains the Langmuir-Hinshelwood reaction between adsorbed CO and O adatoms. The product CO is allowed to adsorb reversibly on the support, step 7. The kinetic parameters of CO adsorption/desorption were determined from in dependent experiments and were hardly depending on temperature. To account for the observed adsorption of CO on sites covered with oxygen and the subsequent production of CO , a second reaction path was included,
Table 2 Elementary steps and reaction paths Elementary reaction k
CO#* 8 CO* k
N1
N2
Step number
2
0
1
1
1
2
1
1
3
2
0
4
0
2
5
0
2
6
0
0
7
\
k
O #* P O * k
O *#* P 2O* k
CO*#O* P CO #2* k
CO#O* 8 OCO* k
\
k
OCO* P CO #* k
CO #) 8 CO ) k \ 2CO#O P2CO
Note: (*) Site on Pt and ()) Site on c-/Al O .
see steps 5 and 6, where gas phase CO is reversibly adsorbed as an OCO* species that might produce CO (Nievergeld, 1998). The same interpretation was used by Nibbelke et al. (1998) to quantify the CO oxidation over a commercial Pt/Rh/CeO /c-Al O catalyst. It is in line with suggestions by Barshad et al. (1985), who observed new peaks in time-average IR spectra during periodic operation, when compared to the steady-state. They concluded that CO adsorbs both on oxygen covered sites and on platinum oxides. The latter can be excluded in the present study. Platinum oxides are formed at a timescale of minutes (Turner and Maple, 1984), where the timescale of the applied oscillations is in the order of seconds. Consequently, the amount of oxides, if present, should be constant in time as the oxide formation is in the sliding regime (Matros, 1984). Since no adsorption of oxygen on oxides takes place and the reduction of the oxides also proceeds at a timescale of minutes, the oxygen adsorption capacity would be smaller than the CO adsorption capacity. It was observed, however, that equal amounts of CO were produced during each of the half-cycles of an oscillation period. All rates were expressed in accordance with the law of mass action. The rate coe$cient for the chemisorption of CO and O is obtained from collision theory:
R¹ 1 k" s , G ¸ 2nM G R G where s refers to the sticking probability on a clean G surface. Because of asssumed instantaneous dissociation
J.H.B.J. Hoebink et al. /Chemical Engineering Science 54 (1999) 4459}4468 Table 3 Final kinetic parameters estimates with corresponding 95% con"dence intervals obtained from regression of experimental data at 4 temperatures with the kinetic model of Table 2 Parameter
Unit
Value
s !A B !E B !b B !s - A *& E *& b *& k k \ k k k \
* s\ kJ mol\ kJ mol\ * s\ kJ mol\ kJ mol\ m mol\ s\ s\ s\ m mol\ s\ s\
0.186$0.002 6;10$1;10 119.7$0.7 14.6$0.1 5.26;10\$0.05;10\ 3.7;10$0.5;10 43.9$0.6 9.35$0.05 219$4 0.040$0.001 1.75$0.04 0.864$0.009 0.809$0.006
of oxygen, the rate constant k is set to in"nity, which makes the chemisorption of O "rst order in the vacant sites (Oh et al., 1986) and causes an overall steady-state rate proportional to p /p (Campman, 1996). - !The desorption coe$cient of CO is obtained from
E !b h B !- !- , k "A exp ! B !\ B !R¹ which accounts for surface non-uniformity or interaction of adsorbed CO molecules. The coe$cient of the surface reaction between CO* and O* is described in an analogous way:
E !b h *& !- . k "A exp ! *& *& R¹ All other parameters were considered as independent of temperature. Final kinetic parameter estimates with their 95% con"dence intervals, obtained via multiresponse nonlinear regression of the experimental data with the kinetic model, are shown in Table 3. Fig. 8A}C show a comparison of experimental data and model predictions. The agreement in general is satisfactory. All parameter estimates are well in the range calculated from the transition state theory (Zhdanov, 1988) and close to values reported in the literature. The sticking probability of CO on a clean surface, s , is lower than !the value reported by Herz and Marin (1980) but much higher than the value reported by Graham (1993). The activation energy and the pre-exponential factor of the CO desorption are in good agreement with literature data (Herz and Marin, 1980; Campman 1996). The estimated value of b which accounts for the dependency B !of the activation energy on the degree of coverage, is only half the value reported by Zhdanov and Kasemo (1994) and Oh et al. (1986) for the CO oxidation over Rh/Al O .
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The sticking probability of O on a clean surface is smaller than the value obtained by Herz and Marin (1980). They assumed, however, a second order oxygen adsorption in their kinetic model and this leads to a higher value of s . The activation energy of the surface - reaction is lower than the value of Herz and Marin (1980) but is close to the result of Graham (1993). The value of the pre-exponential factor of the surface reaction is in good agreement with the value of Herz and Marin (1980) but smaller than the value reported by Graham (1993). The value of b agrees well with the value of Zhdanov *& and Kasemo (1994). Graham (1993) mentioned much higher values for the rate coe$cients of CO adsorption on and desorption from the support. Their values suggest that the sorption takes place on a time-scale of less than 0.1 s. However, the values of the estimates shown in Table 3 are in agreement with transient experiments conducted with a feed containing CO only which showed that the time-scale of adsorption and desorption is approximately 1 s. In the literature no values of the parameters of steps 5 and 6 are reported. The estimates are in line with the observations of Barshad et al. (1985). They suggested a rather low value of h and a poten-!tially fast reaction of OCO* to CO , indicating a relative ly low value of the equilibrium constant and a high value for the rate coe$cient for the desorption of OCO*, k . 7. Conclusions A simulation study was performed, with CO oxidation as an example, to explore how feed composition cycling can be a!ected by di!usion inside catalyst pellets. For a typical case as met when performing kinetic experiments in micro "xed bed reactors, intrinsic kinetics might be obtained from composition cycling experiments. A prerequisite is that the time scale of cycling is much larger than the time scale of di!usion inside the catalyst, provided the elementary reaction steps are in the dynamic regime. Cycling frequencies above 10 Hz seem not relevant as damping and phase shift of the imposed oscillations would occur inside the catalyst. An experimental set-up was presented, which allows cycling of the feed for transient operation of "xed bed microreactors at frequencies up to 10 Hz. This maximum frequency was bound by instrumental analysis, e.g. the sampling frequency of the applied mass spectrometer. Application, however, of higher frequencies seems not useful in view of the timescale of di!usion that is usually met in laboratory catalytic "xed bed reactors. The transient oxidation of CO by O over Pt/c-Al O was studied with this set-up. The results gave evidence that CO may adsorb on oxygen covered sites under simultaneous production of CO . O does, however, not adsorb on CO covered sites, which causes a delay in the transient of the CO production. A kinetic model
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including rate parameters was presented, which gives an adequate description of the experimental data and provides much more detailed information than could be obtained from steady-state experiments.
Acknowledgement The authors gratefully acknowledge the major e!orts of M.A.J. Campman for the development and design of the reactor and its set-up. They are grateful to the Dutch Technology Foundation STW for the "nancial support. Dr E.S. Lox from Degussa A.G. is acknowledged for providing the catalyst samples.
Notation
A B A *& A a B C E G C N G D E B E *& F T f k ? k G k \ k ¸ R M G N G R t t t t < x
preexponential factor for CO desorption, s\ preexponential factor for surface reaction, s\ external surface of the catalyst, m speci"c surface area of the catalyst, m m\ amplitude of imposed oscillation, dimensionless gas phase concentration of component i, mol m\ concentration of component i inside pellet pores, mol m\ e!ective di!usivity, m m s\ activation energy for CO desorption, kJ mol\ activation energy for surface reaction, kJ mol\ volumetric #ow rate, m s\ cycling frequency, s\ adsorption rate coe$cient, m mol\ s\ adsorption rate coe$cient of CO or O , m mol\ s\ desorption rate coe$cient of CO, s\ rate coe$cient of the surface reaction, s\ active sites per unit speci"c surface area, mol m\ molecular weight of component i, kg mol\ di!usive #ux of component i through gas phase/catalyst interface, mol m\ s\ gas constant, J mol\ K\ time, s timescale of the oscillation, s timescale of di!usion, s timescale of adsorption of component A, s reactor volume, m pellet coordinate, m
Greek letters b
coe$cient, accounting for surface non-uniformity or interaction of CO molecules, dimensionles
e @ e N h G *
interpellet void fraction, m m\ intrapellet void fraction, m m\ degree of surface coverage of species i vacant site dimensionless
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