78
Ind. Eng. Chem. Process Des. Dev. 1988, 25, 76-83
Multiple-Cycle Transient Studies Applied to the Hydrogenation of CO over NickeVSilica Catalysts Pel-Ing Lee and James A. Schwarz' Depariment of Chemical Engineering and Materials Science, Syracuse University, Syracuse, New York 132 10
Temperatwe-programmed desorption (TPD), temperature-programmed reaction (TPR), and muttiple-cycle transient analysis (MCTA) have been used to study the kinetics of hydrogen and carbon monoxide interactions with nickel/silica catalysts. The first two techniques provided valuable kinetic information of the indtvldual steps of adsorption, surface reaction, and desorption. The third technique provided timedependent product data under experimental conditions that are close to steady-state operation of the catalyst. A model of the reaction mechanism is proposed that is consistent with experimental results obtained over a wide range of HJCO ratios, flow rates, and temperatures. In the model, competitive chemisorption of H2 and CO on the Ni surface plays an essential role in determining the rate of hydrocarbon formation. Surface CO is dissociated with the assistance of surface H to produce surface C. This is followed by hydrogenation of surface C at a rate comparable to the CO dissoclation step. The model demonstrates that the surface is predominately covered by CO during the reaction, and a small fraction of the surface is covered by H, which controls the rate of methane formation. The concentration of surface C is determined, from the model, to be about 5 % of the total coverage during steady-state reaction.
The use of transient techniques to obtain kinetic information about reaction mechanisms and possible active intermediates for catalytic surface reactions has received considerable attention in the past 15 years. A review of the literature is summarized in Table I. In particular, a recent review by Falconer and Schwarz (1983) demonstrated the utility of using temperature-programmed desorption (TPD) techniques to studying supported metal catalysts. It was pointed out that quantitative analysis of TPD data from supported metal catalysts to obtain activation energies and preexponential factors is possible only when the assumptions of the differential bed condition and the absence of transport limitations are satisfied. Recent studies demonstrate that by careful design of the experimental apparatus and the experiments, in conjunction with numerical simulation, reliable data on adsorption and desorption kinetics of adsorbates can be obtained (Lee et al., 1984). It is also possible to modify the TPD technique so that reaction occurs between more than one reactant. This technique, referred to as temperature-programmed reaction (TPR), is generally carried out with reactive adsorbates predeposited on the catalyst surface and a reactive carrier gas (McCarty and Wise, 1977; Falconer and Zagli, 1980; Low and Bell, 1979; Zagli and Falconer, 1981; McCarty and Wise, 1979). In addition to the conventional TPR, a second type of programmed reaction can also be investigated. In these experiments, two gases are coadsorbed on the catalyst, heating occurs in an inert carrier, and the rate of product formation is dynamically monitored. These classes of experiments may be referred to as isolated TPR. The isolation techniques greatly simplify the study of complex reaction systems. However, the kinetic parameters obtained from these methods are not unambiguous. Surface concentrations of intermediates are not obtained, and the experimental conditions do not correspond to steady-state reaction conditions. The objective of this research is to determine that yet another transient technique can be conducted within the experimental capabilities of a TPD apparatus. This *To whom inquiries should be addressed. 0196-4305/86/1125-0076$01.50/0
technique, called multiple-cycle transient analysis (MCTA), allows one to study kinetics under conditions that are close to steady-state operation of the catalyst. During the application of MCTA, the response of the system to a small periodic perturbation of the reactant ratio is used to obtain information about reaction kinetics. When the results of MCTA are employed in conjunction with kinetic data from other transient techniques and with mathematical modeling of the reacting system under MCTA conditions, a self-consistent description for a reaction model can be developed. However, the results are subject to the question of the uniqueness of the kinetic model proposed. Many mechanisms may give the same model, and many such models may give adequate agreement with the experimental data. Therefore, the results of experiments reported here are critically analyzed on the basis of a reasonable kinetic model that is selected according to the following criteria: (1)The model should minimize the number of adjustable parameters. (2) The model should reflect both qualitative and quantitative features of the experimental data under different experimental conditions in order to test the consistency of the proposed model with experiments. (3) The rate constants obtained by fitting the experimental data to the model should be chemically reasonable. Reaction System Eighty-two years ago, nickel was discovered to be an effective catalyst for the synthesis of methane from carbon monoxide and hydrogen (Sabatier and Senderens, 1902). However, despite the numerous studies that have been conducted since that discovery, the mechanism of the synthesis is still controversial. Vlasenko and Yuzefovich (1969), Mills and Steffgen (1973), Vannice (1976), Ponec (1978), and Bartholomew (1982) have reviewed mechanisms that can be generally divided into two groups. One involves the formation of an intermediate complex CH,O, on the catalyst surface. The other considers surface carbon, which is formed by dissociation of CO, as the active intermediate. Ho and Harriott (1980) have recently discussed this division. Tables I1 and I11 summarize the salient findings for nickel catalysts by previous investigators. The consensus that 0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25,No. 1, 1986 77 Table I. Summary of Transient Studies forcing function (1976,1978) step and cyclic Bennett (1979,1983) step Biloen et al. (1977) cyclic Dautzenberg et al. step (1982) Fiolitakis and Hofmann (1983) ramp Falconer and Schwarz ramp (1981) Galuszka et al. (1979) cyclic Hegedus et al. (1973,1980,1982) step Happel et al. step Kobayashi and Kobayashi (1974) sinusoidal (1969) Polinski and Naphtali (1969) step Parravano (1972) cyclic Renkin cyclic (1974) Schwarz and Madix (1964) step Tamaru cyclic (1973) Unni et al. (1976,1978) sinusoidal Yasuda authors
parameter gas composition gas composition gas composition gas partial pressure temp temp gas composition gas composition gas partial pressure pressure gas partial pressure concn pressure pressure gas composition pressure (induced by vol variation)
Table 11. CH,O as Intermediate in Methanation Model evidence conclusion postulation CH.0 formation
authors Elvins and Nash Storch et al. Anderson et al. Hamai Pichler Vlasenko et. al.
(1926) (1951) (1949) (1941) (1966) (1964,1965)
Hogan and King
(1972)
Wedler et al.
(1975)
Peebles et al.
(1983)
surface complex formation
Koel et al. Primet et al.
(1981) (1977)
surface complex formation
Farrauto
(1976)
possible complex formation possibIe complex formation heat of adsorption of Hz changed by the presence H, and COSinteraction of CO, and the amount of CO adsorbed is increased by the presence of Hz attractive and mixing effect between surface H, H, and CO, interaction and CO, on Ni (loo),repulsive effect on Ni (111) twice as much Hz adsorbed on the “CO covered” Ni as “CO free” Ni surface CO uptake is increased by the presence of Hz
IR adsorption band for CO shifted by the presence of H microbalance study showed that the weight gain of catalyst below 473 K corresponds to monolayer coverage by CH,O reaction model study reaction model study reaction model study
catalytic decomposition catalytic hydrogenation catalytic hydrogenation water gas shift reaction absorption, desorption, and surface reaction desorption catalytic oxidation catalytic hydrogenation catalytic oxidation and catalytic decomposition adsorption adsorption and heterogeneous catalytic reaction homogeneous catalytic reaction (theoret study) heterogeneous catalytic reaction adsorption and heterogeneous catalytic reaction catalytic oxidation heterogeneous catalytic reaction
CH,O formation Vannice (1975) Langmuir-Hinshelwood reaction to form CH,O McGill and Richardson (1975) Eley-Rideal reaction to form CH,O Polizzotti and Schwarz (1983)
Table 111. Carbon as Intermediate in Methanation Model evidence postulation disproportionation of CO at 473 K on Ni films, carbon-isotope substitution studies showed higher methanation rate for surface C than for surface CO thermal desorption studies of dissociated CO showed two forms of carbon (amorphous carbon and graphitic carbon) temp programmed surface hydrogenation of carbon showed four forms of surface carbon [chemisorbed carbon (a),bulk nickel carbide (Ni-C), amorphous carbon (b), and crystalline elemental carbon] Auger electron spectroscopy (AES) studies showed carbidic carbon (at C/Ni ratio 650 K) reaction modeling study reaction modeling study reaction modeling study reaction modeling study reaction modeling study reaction modeling study isotopic substitution of carbon and oxygen showed irreversible CO dissociation temp program surface reaction of carbon
emerges from a study of the various proposed mechanisms is that CO dissociation yields an active carbon intermediate which is hydrogenated to methane. The questions that often arise are which of these two processes is rate-de-
conclusion authors C intermed Fisher and Tropsch C intermed Araki and Ponec
(1926) (1976)
Ponec C intermed Madden et al.
(1978) (1973)
C intermed McCarty and Wise
(1977)
C intermed Goodman et al.
(1980)
Bartholomew Gardner and Bartholomew Zagli et al. Fitzharris et al. Dalman and Martib Klose and Baerns C intermed Goodman and Yates C intermed Ozdogon et al.
(1981,1982) (1981) (1979,1981) (1982) (1983) (1984) (1983) (1983)
termining and does the rate-determinirigstep change with reaction conditions? The answer to these questions can only be evaluated by considering a general model which allows for both possibilities.
78
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
I
Experimental Section The experimental apparatus consists of three major parts: the gas supply system, the reactor system, and the data acquisition system. The gas supply system is described in detail elsewhere (Lee and Schwarz, 1982; Lee, 1983). The nickel on silica catalyst was supplied by J. L. Carter, Exxon Research and Engineering. The nickel content in the catalyst, after calcination and before reduction, is from 45 to 49 wt %. The metal surface area, determined by hydrogen chemisorption, ranges from 70 to 80 m2/g of catalyst. The total surface area measured by BET varies between 270 and 290 m2/g of catalyst. The porosity is 0.3-0.38 cm3/g of catalyst. The nickel crystallite size which ranges between 20 and 22 8,was determined by X-ray line broadening before the catalyst was reduced. The remainder of this section describes the software and hardware devices that were designed for MCTA studies and the procedures used to conduct these studies. Switching Valves. Programmable switching valves are employed to adapt the TPD apparatus for MCTA studies. Switching the flows between hydrogen and a mixture of hydrogen and helium provides the perturbation to the reactant concentration. The switching time between streams for the valve, which has a zero-volume fitting, was measured to be less than 0.2 s. The hydrogen perturbation reaches 90% of its final value within 2 s. The carbon monoxide feed is equally blended into these streams by using precision cross-pattern valves (SS-4MX). Adjustment of these valves while monitoring the carbon monoxide concentration above the differential reactor allows one to provide a constant fluid-phase concentration of carbon monoxide incident on the catalyst bed. Four Tylan mass flow controllers (FC-260) allow the hydrogen/carbon monoxide ratio and the magnitude of the perturbation to be varied. Sampling Device. The sampling system was designed to enable on-line mass spectrometric detection of the gas composition in a flow system. Sampling a t atmospheric pressure is accomplished by Swagelok cross-pattern valves located directly above and below the reactor. The sampled gas is directed to a buffer chamber where the pressure is maintained a t 300 mtorr (1torr = 133.3 N/m2). Experiments have shown no gas selectivity effects due to molecular weight differences through the cross-pattern valve for buffer chamber pressures higher than 100 mtorr. The sampled gas enters a mass spectrometer chamber through a SS-BOT sampling assembly. This assembly is equipped with controllable orifice valves to prevent selectivity effects of gases during transport into the mass spectrometer chamber. This chamber is evacuated by a 110 L/s turbomolecular pump with a heater, vent valve, and a 3.2 ft3/min direct-drive mechanical pump with isolation valve, thermocouple gauge, and bakeable molecular sieve trap. The trap is routinely baked. The ultimate pressure within the chamber is typically torr and is maintained at lo4 torr during experiments. Data Acquisition System. The data acquisition system is configured around a UTI precision mass analyzer and Spectralink interface. The system allows simultaneous time-dependent data collection of several different species in the gas flow. An Apple 11-Plus microcomputer serves as the host computer which controls the mass spectrometer operation, collects the resulting data, and further manipulates and analyzes the data. Specially developed software serves as a communication vehicle that converts analog signals to ASCII strings and vice versa (Lee, 1983). The estimated data collection time is much less than 0.1 s per m / e peak for single-peak operation and about 0.1 s per
FLOWRATE : 175 CC/MN TEMPE RATVRE. l8GT ,!&RATIO. __
249
WEIGHT OF CATALYST 3Omg DUTY CYCLE 30r/30r
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Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
switches. At point 2, after a delay of 6.45 s due to the flow time from the valve to the catalyst bed and finally to the sampling port below the reactor, the methane peak relaxes with a pseudo-first-order behavior. This relaxation is slightly dependent on temperature. The steady-state values (points 1to 2 and 3 to 4) in the two streams are also temperature-dependent. Figure 2 shows an Arrhenius plot of these steady-state values. The data are well-represented by an apparent activation energy of 24 f 1 kcal/mol. MCTA data were obtained for temperatures from 423 to 500 K, H2/C0 ratios from 1.34/1 to lO/l, and flow rates from 88 to 170 cm3/min. The time-dependent responses of the methane product signal were used in conjunction with kinetic parameters obtained from TPD and TPR studies to propose a model for the methanation reaction consistent with the criteria outlined earlier. Reaction Model The studies by Happel et al. (1980) suggest the possibility of modeling time-dependent product data to elucidate the mechanism of the methanation process. Their model considers reaction steps after the formation of CH, (subscript s denotes surface). The concentrations of surface CO, surface H, and surface C were not considered. In this section, a reaction model is proposed. Kinetic parameters determined by TPD and TPR results are used in the model to determine the time-dependent methane response to the reaction system under MCTA conditions. The influence of experimental conditions such as H2/C0 ratio, temperature, and flow rate are examined by numerical solution of the surface mass balances, and the methane product response is compared with the experimental MCTA results. The following model is proposed for the formation of methane:
20
21
2.2
+lo3
79
23
Figure 2. Arrhenius plots of the steady-state TON for the hydrogen-rich and hydrogen-lean portions of the cyclic perturbation.
is assumed to be covered by C, CO, and H. The time dependence of surface species based on the above model and assumptions can be written as
and the rate of methanation can be written as
1. adsorption and desorption k
CO,,,+ Ni & CO - Ni k-1
(1)
k
H z + 2 N i &k -22 H - N i
(2)
2. initiation of surface reaction
CO - Ni
+ 2H - Ni
k3
C - Ni
3. propagation
CH, - Ni
ki
+ nH - Ni
C - Ni
+ (4-n)H - Ni
4. termination CHI - Ni HzO - Ni
k5
k6
k7
+ H 2 0 - Ni + Ni
+ nNi CHI - Ni + (4-n)Ni CH, - Ni
(3)
(4) (5)
+ Ni
(6)
HzO(,, + Ni
(7)
CH,,,,
In the proposed model, competitive adsorption of Hz and CO is considered in reaction steps 1 and 2. Subsequent steps are written not with the intent to demonstrate the details of elementary reaction steps. For example, step 3 depicts a hydrogen-assistedCO dissociation reaction and the subsequent hydrogenation of the carbon surface intermediate (step 4). The dynamic rate expressions of methanation processes, steps 5 to 7, are assumed to be faster than steps 3 and 4, and the majority of the surface
where 0, denotes the surface coverage of species j . The hydrogen wave form prior to contact with the catalyst is not strictly a square wave. A relaxation period of 1-3 s is observed, depending on the flow rate. This relaxation is caused by interdiffusion between hydrogen and helium during the transport time to the catalyst bed from the switching position. Figure 3a shows the hydrogen relaxation wave, measured directly above the entrance to the reactor. The incident perturbation used for the numerical simulation was that determined experimentally. Equations 8-1 1were solved numerically in conjunction with a convective transport model. A detailed description is given elsewhere (Lee, 1983). Briefly, the model assumes no inter- or intra-particle diffusion limitations and requires a materials balance between surface and gas-phase species. Convective transport is incorporated, phenomenologically, into eq 8-10 by using the ideal gas law and considering the effective partial pressures (per unit time) of reactants within the reactor at its operating temperature and under the flow rate conditions of the experiment. Table IV lists the kinetic parameters, obtained from TPD and TPR experiments (Lee, 1983), used in the numerical simulation. In accordance with the homogeneous-surface postulates, the rate constants k3 and k4 (indicated in Table IV) were assumed to be independent of surface coverage. The activation energies of hydrogen-assisted COSdissociation, E3,and hydrogenation of the surface intermediate, E,, are found from TPR experiments to be 24 and 17 kcal/mol, respectively. The preexponential
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Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
Table IV. Summary of T P D a n d T P R Results perturbation and carrier method variable gas reactive species TPD linear ramp on temp He preadsorbed H,
H, H;!
ureadsorbed C preadsorbed C, and H,
rate constant E , kcalimol A , s-' k2' 0 1.5 X PH2 kzb22(1 - 0.50H2) 1.5 X 1014 k," 0 5X Ppn -kIlb 26(1 - Oca) 3.5 x 1013 k, 18 f 2 -5 x 10s k> 17 i 3 107
H,
preadsorbed C,
k,'
24f 2
He
preadsorbed CO, and H, k3
25 f 2
preadsorbed CO
TPR
linear ramu on temu
-
-
10'0 -5 x 1010
analysis and assumDtion desorption rate isotherms heat rate variation heat rate variation desorption rate isotherms assuming no readsorption desorption rate isotherms assuming no readsorption heat rate variation assuming pseudo-first-order reaction
Adsorption rate constant. *Desorption rate constant. Rate constants used in simulation. Table V. Experimental a n d Simulated T O N (Flow Rate = 170 cms/min) T , "C HZ/CO 160 170 180 TON Experimental 1011 2.2 x 10-3 4.29 x 10-3 7.65 x 10-3 5.7 x 10-3 1.8 x 10-3 3.34 x 10-3 511 1.01 x 10-3 1.7 x 10-3 2.9 x 10-3 211 10/1 5/1
21 1
2 x 10-3
1.12 x 10-3 4.5 x 10-4
TON Model 7.9 x 10-3 4.65 x 103 2.3 x 10-3 1 x 10-3 2.05 x 10-3 4.1 x 10-3
Table VI. Experimental a n d Simulated TON (Flow Rate = 88 cm3/min) T, "C H2/CO 160 170 180 TON Experimental 5.3 x 10-3 1.64 x 10-3 3.05 x 10-3 51 1 3.04 x 10-3 8.4 x 10-4 1.6 x 10-3 211 1.56 X 6.3 x 10-4 9.9 x 10-4 1.3 1.611
-
511
211
1.35/1
1.53 x 10-3 6.84 x 10-3 4.7 x 10-4
TON Model 6.19 x 10-3 3.15 x 10-3 1.45 x 10-3 2.9 x 10-3 2.07 x 10-3 1.0 x 10-3
factors for these two steps, A3 and Ad, and the stoichiometric coefficient n were adjusted to test the consistency of the model results with the time-dependent experimental data for various experimental conditions, such as temperature, H2/C0 ratio, and flow rate. Figure 3b shows a comparison between simulated and experimental results for the rate of methanation in the transient region for two different flow rates. The model reasonably describes the reaction system for both flow rates. The agreement between model and experiment for various experimental conditions such as temperature and H2/C0 ratio is also observed. These results are shown in Figure 4. In the numerical simulation, an iterative process was employed until the proposed mechanism described the experimental results in sufficient detail (90% confidence). The resulting preexponential factors A3 and A4 are in reasonable agreement with those obtained from isolated TPR experiments. The number n is equal to one, indicating that the concentration of surface carbon and the rate of methane formation are both increased as the H2/C0 ratio increases. For n greater than one, the model shows the concentration of surface carbon decreasing with increasing temperature. This is contrary to what would be expected. Tables V and VI show a comparison of the simulated and experimental TON of methane for different
200
2 20
2.6 X 1.8 X 8.5 x 10-3
3.1 X 4.5 x 10-2 2 x 10-2
2.74 X 1.66 X lo-' 7.73 x 10-3
8 x 10-2
5 x 10-2 2.47 X loM2
200
220
2.27 x 10-2 9.3 x 10-3 4.6 x 10-3
1.89 X 3.9 x 10-2 1.95 X lo-'
2.1 x 10-2 1.05 X
6.11 X lo-' 3.2 X 2.37 X
7.6
X
TIME ( s e c . 1 4
Figure 3. (a) Experimental hydrogen wave form incident on catalyst bed for two flow rates (176 and 88 cm3/min). (b) Comparison of simulated and experimental methanation TON during the relaxation period for two flow rates (176 and 88 cm3/min). TON for steadystate region found in Tables V and VI.
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986 81 Hz/CO n 2/1 HIGH FR.
(a1
'
( 0 )
A 211
TIME (sec 1-
k
J 2
r
y
1.0
8
I
0.8I
B
I
bycQ * 211 FR.
I
I
1
(b)
LOW
W
5
-
MODEL EXPERIMENT 0 493 K 0 473K A 453K
0
3
4
L
n !
I
I
I ,I I 2 " 29 TIME (SKI-
I 30
Figure 4. (a) Comparison of simulated and experimental methanation rates during relaxation period at H,/CO = lO/l, 5/1,and 2/1. (Flow rate = 176 cma/min; temperature = 473 K.) TON for steady-state region found in Table V. (b) Comparison of simulated and experimental methanation TON during relaxation period for temperatures 453, 473, and 493 K. (Flow rate = 176 cm3/min; H2/C0 = 2/1). TON for steady-state region found in Table V.
0.81
I
433 443
I
I
I
453
463
473
TEMPERAnJRE-
I
(K)
Figure 6. Concentration of surface species determined from simulation for (a) flow rate = 176 cm3/min and (b) flow rate = 88 cm3/ min. Temperatures range from 433 to 493 K,and H,/CO = 2/1.
Lbw F.R.
433 443
463
-
483 493 I Figure 5. Concentration of surface species determined from simulation for (a) flow rate = 176 cm3/min and (b) flow rate = 88 cm3/ min. Temperature range from 433 to 493 K and H2/C0 = 5/1. 453
TEMPERANRE
Jo
483 493
I
I.,
473
(K
conditions. Over the ranges of temperature from 423 to 493 K, H2/C0 ratios from 1.34/1 to l O / l , and flow rates from 88 to 170 cm3/min, the simulated TON is in good agreement with experimental results. Discussion Systematic studies involving TPD, TPR, MCTA, and computer simulation has resulted in a methanation model that provides information about the concentration of
433 443
453
463
473
483 493
TEMPERATURE4( K )
Figure 7. Concentration of surface determined from simulation for (a) flow rate = 176 cm3/min and (b) flow rate = 88 cm3/min. Temperatures range from 433 to 493 K,and H2/C0 = 10/1.
surface intermediates under reaction conditions. Figures 5-7 give the concentration of surface species (Oca, Oc, and 0,) determined from the simulation for different reaction conditions. For all the conditions studied, 85%-95% of the surface is covered by COS. Surface hydrogen occupies 3.5%-10.0% of the surface. The concentration of surface CO, ecO, decreases as the temperature increases, while the
82
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986
concentrations of surface H, OH, and of C,, Oc, increases as the temperature is increased. This trend is independent of the H2/C0 ratio in the range from 10/1 to 1.34/1 and flow rates from 88 to 170 cm3/min. These results agree with the general observations of a higher methane TON a t higher temperatures within the reaction conditions reported here. The OH and Oc change proportionally as a function of the H,/CO ratio, which also results in an increase in the methane TON, as shown in Tables V and VI. The steady-state results of Polizzotti and Schwarz (1983), Vannice (1975), and others (Rabo et al., 1978; Gardner and Bartholomew, 1981; Dalla Batta et al., 1975; Fitzharris et al., 1982) have shown that the methane TON over Ni catalysts increases as the H2/C0 ratio is increased. There is a subtle variation in the coverage of all surface species as the flow rate is changed. A t the same H 2 / C 0 ratio, Figures 5 and 6 show a decrease in OCo and an increase in OH and 8C as the flow rate is decreased. This indicates that H2 adsorption is more dependent on flow rate than CO,,, alsorption is. More H2(giis adsorbed at lower flow rates, and it can then assist dissociation of surface CO to produce more surface C. This flow rate dependence of H2(Band CO,,, agrees with previous TPD analysis of this study by Lee et al. (1982,1983, and 1985). The population of surface carbon (less than 5%) over a wide range of reaction conditions agrees with the report on Ni( 100) by Goodman et al. (1980) using Auger electron spectroscopy. Bartholomew, Goodman, and others have suggested that catalyst deactivation could possibly be related to the concentration of surface inactive carbon. The lack of information about the dependence of the concentration of surface C on reaction conditions has made verification of this proposition difficult. Experimental studies in this work have focused on reaction conditions where deactivation does not occur. The transformation of surface-active carbon into inactive carbon is not considered. It is believed that this process is important at temperatures higher than 550 K and Oc higher than 25% (Goodman et al., 1980). In these studies, the simulated processes occurring a t temperatures lower than 500 K result in a model that agrees quantitatively with experimental data. Conclusions The proposed model well represents the experimental data obtained under the following reaction conditions: temperatures from 423 to 500 K, H2/C0 ratios from 1.34/1 to l O / l , and flow rates from 88 to 170 cm3/min. The model considers the competitive adsorption of CO,,, and H2(), hydrogen-assisted dissociation of surface CO, and hydrogenation of surface carbon, with the latter two steps occurring a t comparable rates. The overall reaction model is supported by the following facts: First, it is consistent with the observations of surface interactions between Ha and COS from infrared and steady-state adsorption studies (Primet et al., 1977). Second, the activation energies reported by Galuszka et al. (1981) and Lee (1982) for disproportionation of COS (25-33 kcal/mol) and by McCarty and Wise (1977) for the hydrogenation of surface carbon (17-22 kcal/mol) both differ from the activation energy for the methanation reaction a t steady state (21-25 kcal/mol) as reported by Ho and Harriott (1980), Vannice (1975), and Polizzotti and Schwarz (1983). This indicates the possible existence of another reaction step, excluding the competitive adsorption of H2@, and CO,,, and the hydrogenation of surface carbon, which has an activation energy close to the steady-state value.
Third, the differences in the flow-rate dependence of adsorption of H2, and CO,,, and their competitive adsorption on the cafalyst surface have shown that the lower rate favors hydrogen adsorption and consequently increases the coverage of surface carbon and the TON of methane. The dissociation of COSwithout the participation of surface H would be contrary to the experimental results. The concentration of surface hydrogen, OH, can be considered reaction-limited. The participation of surface H in the two slowest steps and its relatively low coverage compared with that of surface CO make the concentration of surface H important in determining the overall reaction rate. Surface CO occupies most surface sites, thus effectively blocking the sites available for H2 adsorption. This observation is consistent with the inhibiting effects as a function of CO,,, pressure and the enhancing effect with increasing H2,, pressure as reported by Vannice, Ho and Harriott, Polizzotti and Schwarz, and others (Kemball, 1953; Ross, 1981). These authors have used the following empirical equation for data correlation: TONCH,= APH?PCO~ exp[-(mc~JRT)I
(12)
The reported values for X are between 0.6 and 1.0 and for Y between -0.3 and -0.5. Fourth, the effects of the H2/C0 ratio on the steadystate activation energy and the number n for the stoichiometric coefficient in the surface-reaction step are also supported by the above arguments. Polizzotti and Schwarz have reported a gradual decrease (24-19 kcal/mol) in the steady-state activation energy as the H2/C0 ratio increases (1/1to 30/1). As interpreted by the model proposed in this study and with n equal to one, the higher I-12/C0ratio results in a higher population of surface carbon, which in turn increases the importance of reaction step 4,which has an activation energy of 17 kcal/mol. The effect is to reduce the apparent activation energy from its measured value of 24 kcal/mol when a higher H2/C0 ratio is used. Finally, the consistency of the time-dependent data over the transient region, as shown in Figures 3 and 4, indicates that the proposed model well represents the reaction system. These simulated results have been determined by using experimental rate parameters in the proposed model. Although the methodology is projected to suggest a conclusive model, it is not intended to demonstrate the details of elementary reaction steps in the system.
Acknowledgment This work was supported by the National Science Foundation under Grant CPE-8119231. We also acknowledge the support and interest from the Syracuse University Institute for Energy Research and the Texaco Foundation. Registry No. CH,, 74-82-8; CO, 630-08-0; Ni, 7440-02-0.
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Received for review May 3, 1984 Revised manuscript received April 1, 1985 Accepted May 10, 1985
Condensation of Vapor Mixtures. 1 Nonequilibrium Models and Design Procedures Ross Taylor, Ramachandran Krlshnamurthy,t and John S. Furno' Department of Chemical Engineering, Clarkson University, Potsdam, New York 13676
Rajamanl Krlshna Indian Institute of Petroleum, Dehradun 248005, India
Nonequilibrium models of multicomponent condensation are reviewed with particular attention to the various ways in which the rates of condensation can be calculated. Ways of solving the mixed set of differential and algebraic equations that constitute the model are discussed, and it is suggested that differential conservation equations be approximated by finite differences and the resulting set of only algebraic equations solved simultaneously (using Newton's method) with the nonlinear equations representing the processes of interphase transport and interfacial ' equilibrium. WRh regard to the various models of vapor-phase transport, it is shown that simple effective diffusivity models may lead to significant over- or underdesign when compared to more soundly based models which take vapor-phase diffusional interaction effects into account. I t is also demonstrated that there is little to distinguish models based on the use of the Chilton-Colburn analogy to obtain the heat- and mass-transfer coefficients from turbulent eddy diffusivity models when both are used to predict the performance of multicomponent condensers.
Introduction Condensation of vapor mixtures is an operation of great significance in the chemical process industries. The two words "vapor mixture" cover a wide range of situations. One limit of this range is one in which all components have Present addreas: BOC Group, Technical Center, M u r r a y Hill, NJ 07974.
* Present address: General Electric Corporate Research and Development, Schenectady, NY 12301. 0196-4305/86/1125-0083$01.50/0
boiling points above the maximum coolant temperature; in this case, the mixture can be totally condensed. The other limit is a mixture in which at least one cqmponent in the initial vapor stream has a boiling point lower than the minimum coolant temperature and, also, is negligibly soluble in the liquid condensate formed from the other components and hence cannot be condensed at all. Examples of such components include nitrogen and helium. An intermediate case of some importance is typified by a mixture of light hydrocarbons in which the lightest members often cannot be condensed as pure components 0 1985 American Chemical Society
