Catalytic Oxidation of Formic Acid in Water. lntraparticle Diffusion in Liquid-Filled Pores G. Baldi,’ S. Goto,’* C.-K. Chow, and J. M. Smith* University of California, Davis, California 95676
Liquid-phase oxidation with a solid catalyst provides a potential method for the removal of dissolved pollutants. A commercial CuO-ZnO catalyst was found to be effective for converting dilution solutions of a test pollutant, formic acid, to carbon dioxide at 200-240°C. To prevent the presence of a vapor phase the operating pressure was maintained at 40 atm. Rate measurements showed the reaction to be first order with respect to both dissolved oxygen and formic acid concentrations. In the presence of formic acid solutions the catalyst could be reduced when the oxygen concentration was low and oxidized at higher oxygen concentrations. Possibly the activity of the catalyst is explained by an oxidation-reduction mechanism. Measurements with large catalyst particles (0.477-cm diameter) showed severe retardation of the rate; effectiveness factors as low as 0.11 were obtained. Tortuosity factors (-1.0) were lower than would be expected for gas-filled pores. The intrinsic activation energy was about 37 kcal/mol while the apparent value for 0.477-cm particles was 24 kcal/mol.
Biological oxidation is the usual process for removal of organic pollutants dissolved in liquid water. For some waste waters alternate methods are needed. For example, some pollutants with aromatic or naphthenic structures are but slowly decomposed and oxidized by bacteria. Reverse osmosis (Hindin, et al., 1969), autoxidation with air (Prather, 1970), noncatalytic, wet oxidation (Zimmerman, 1958), and photochemical oxidation (Hancil and Smith, 1971) have been proposed as alternated methods. Recently, there has been considerable interest in the process of liquid-phase oxidation with a solid catalyst, but there appears to be no published information available. Operation in the liquid phase with practical sizes of catalyst particles introduces the question of intraparticle diffusion in liquid-filled pores. Data for intraparticle diffusivities in such systems are scarce. The purpose of this study was to evaluate the kinetics of a liquid-phase oxidation process for a highly oxidized pollutant-catalyst system and also to measure quantitatively the importance of intraparticle diffusion in a catalyst with liquid-filled pores. Studies of gas-phase oxidation of organic compounds indicate that many intermediate steps are involved on the route to carbon dioxide. For example, in the oxidation of paraffin hydrocarbons on metal oxides, acids and aldehydes, especially acetaldehyde, are found (Thomas and Thomas, 1967). The further oxidation of acetic acid and acetaldehyde to carbon dioxide has been shown (Margolis, 1971) to involve formic acid and formaldehyde as intermediates. Also, the final oxidation of formic acid to carbon dioxide does not involve stable intermediates. For these reasons formic acid was chosen as the pollutant for our study. The catalyst used was a CuO-ZnO mixture (Girdler G-66B, Chemetron Corp.) whose properties are given in Table I. It was added to the reactor in its unreduced form but pretreatment to obtain stable activity resulted in some change in the oxidation state as discussed in a later section. The rate of oxidation became accurately measurable a t temperatures above 200°C. To prevent vaporization, the operating pressure was maintained a t about 40 atm, well above the vapor pressure of water a t the maximum temperature of 240°C. The rate of oxidation of dilute solutions (50-500 ppm) of formic acid in distilled water was measured in a differential, fixed-bed reactor. The effects of fluid-particle and intraparticle diffusion on
’ On leave from lstituto Politechnico. Torino, Italy. On leave from University of Nagoya, Japan.
the rate were established by varying the liquid feed rate and the size of catalyst particles. Experimental Section A schematic drawing of the apparatus is shown in Figure 1. The formic acid-oxygen feed of desired composition was prepared by continuously saturating an aqueous formic acid solution, in the reservoir (4), with an oxygen-nitrogen gas mixture. The solution was prepared from distilled water and reagent grade formic acid. A cooling coil (3) and circulating pump (1) were used to maintain constant temperature and composition in the reservoir. The feed, at atmospheric pressure, was introduced into the reactor (13) through a piston-type, stainless steel metering pump (5). Pressure fluctuations from the piston pump were almost completely eliminated with the surge tank (6). The operating temperature was reached with electric tape heaters (9) wound around the feed line (Ih-in. 0.d. stainless steel tube). The reactor, inserted in an air constant-temperature bath (12) consisted of a 10-in. section of 0.37-in. i.d., 0.50-in. 0.d. stainless tubing. To avoid channeling, sections of glass beads (80 mesh) were placed before and after the catalyst bed which itself consisted of about equal parts of catalyst particles and glass beads. Since the oxygen was dissolved in the feed solution a t atmospheric pressure and the operating pressure was 40 atm, there was no possibility of gas formation in the reactor. Temperatures were measured with iron-constantan thermocouples (10) placed at the entrance and exit of the reactor. Since formic acid concentrations were low, the temperature rise due to reaction was insignificant. The two thermocouples normally gave readings that differed by less than 2°C. The effluent from the reactor was cooled to room temperature (14), the pressure reduced in a capillary tube (15) and with valves (16, 17), and the flow rate measured in a calibrated rotameter (18). For the kinetics study, the range of concentrations shown in Table I1 were employed at a constant temperature of 225°C. Then the effects of catalyst particle size and temperature were measured at constant feed concentrations of 28.7 X 10-7 mol/cm3 for formic acid and 10.9 x 10-7 mol/cm3 for oxygen. The latter value corresponds to the solubility of oxygen in water at 25°C and 1atm. Analytical Methods. Samples of the reactor effluent were stripped of dissolved C 0 2 and 0 2 with nitrogen. Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4 , 1974
447
He
TT$
From Tab rater To Disch
%-N2 Lliitun
Yatir to Waste
Figure 1. Apparatus: 1, circulating pump; 2, feed sampling line; 3, cooling coil; 4, feed reservoir; 5, pumps; 6 , surge tanks; 7, pressure gauges; 8, rupture disk; 9, heating tapes; 10, thermocouples; 12, constant temperature bath; 13, reactor: 14, heat reactor: 15, capillary; 16, valves; 17 valve: 18, flow meter; 19, pump; 20, stripping column; 21, condenser; 22, drier (silica gel).
Table I. Properties of Catalyst Fresh' Composition, wt% ZnO CUO P o r e volume, cm3/g P a r t i c l e density, g/cm3 Solid -phase density, g/cm3 Porosity Most probable pore d i a m e t e r , Surface a r e a , m 2 / g
A
82.5 16.5 0.24 2.35; 5.29 0.56; 350 35.9
Used
1.90 0.67
From Suzuki and Smith (1971).
feeding water saturated with air. With a liquid flow rate of 2.2 cm3/min and a helium rate of about 50 cm3/min (25"C), the measured concentration of oxygen in the water was 2.70 X 1 0 - 7 mol/cm3 in comparison with the reported solubility a t 25°C of 2.66 x 10-7 mol/cm3 (Seidell, 1958). Catalyst. Properties of the catalyst are given in Table I. The fresh form corresponds to G-66B (Chemetron Corp.) as received. The used form is catalyst that has been pretreated and used for oxidation runs. The particle density and porosity were determined from helium pycnometer and mercury porosimeter measurements. The feed and product streams were acidic (pH -3.5). However, during the maximum operating time for one bed, about 60 hr, no decrease in activity of the pretreated catalyst was detected. It was concluded that dissolution of the metals on the catalyst was not significant up to 60 hr. The acidic water did discolor the glass beads in the reactor. Catalyst Beds. The kinetics of the reaction were studied using granular particles in the 35-42 and 28-32 meshsize ranges (average d, = 0.0380 and 0.0541 cm) at 225°C. For these particle sizes and a t 225°C the results indicated that diffusion resistance was negligible. Diffusional effects were studied using two larger particles. The largest consisted of x lh-in. cylindrical pellets which have an equivalent spherical diameter, d,, = 6V,/S,, of 0.477 cm. To produce an intermediate size these pellets were cut into pie-shaped quarters whose d,, was 0.291 cm. The bed was prepared by mixing as uniformly as possible the catalyst particles with glass beads of two diameters, 0.32 and 0.06 cm. Before preparing the bed the particles were boiled in water for 30 min. Comparison of weights before and after such treatment indicated that the pores were 98% filled with liquid. Preliminary Studies
HCOOH
Table 11. Range of Operating Conditions Mass of catalyst in bed, g Catalyst particle size, average diameter, cm Liquid flow rate, cm3/sec Temperature, "C Feed concentrations (at 25°C): Oxygen, mol/cm3 Formic acid, mol/cm3 Pressure, atm a
0.300- 0.907 0.0380," 0.0541,* 0.291, and 0.477 0.67- 1.4 204-240
+
'/,O,
35 to 42 mesh. 28 to 32 mesh.
Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 4, 1974
H,O
+
CO,
(1
However, it is known (Margolis, 1971; Thomas and Thomas, 1967) that in the gas phase decomposition also occurs by the reactions HCOOH
and HCOOH
2.7 x 10-7 to 10.9 x 10-7 12.2 x 10-7 to 100 x 1 0 - 7 40
These samples were then analyzed for formic acid in a Beckman Model 915 TOC instrument. Samples of the feed were also analyzed for formic acid in the same instrument. Part of the reactor effluent stream was diverted to a stripping column (20). Here helium was used to remove dissolved COz and 0 2 . The gas stream from the stripping column was first passed through a condenser (21) and drier (22) to remove water vapor. Then the CO2 and 0 2 content of the gas was sent to a gas chromatograph. Oxygen and other gases were measured with a 20-ft, 1/4-in. 0.d. column packed with 5A molecular sieve particles (20-60 mesh) and carbon dioxide was determined with a 10-ft, l/4-in. 0.d. column packed with 80-100 mesh Poropak Q. Both columns were maintained a t 95°C. No formic acid was detected in the gas stream from the column. Hydrogen was determined by replacing helium with nitrogen as carrier gas in the chromatograph. The efficiency of the stripping column was tested by 448
-
The reaction for oxidation of formic acid is
-+
-
CO
-
CO:,
H20
+
H,
(2)
(3
Carbon dioxide was produced in all the runs but carbon monoxide was never detected. Hydrogen was observed when the oxygen concentration in the feed was very low (0.56 X 10-7 mol/cm3) but was not detected at normal oxygen levels. Blank runs without catalyst but with glass beads in the reactor showed no CO2 or Hz production or comsumption of oxygen. Hence reactions 1 and 3 occurred heterogeneously on the catalyst surface. Calculation of Rates. In the final data used for kinetic and diffusion studies conversions ranged from 4 to 19% for oxygen and 3 to 14% for formic acid. Hence, rates were calculated from the measured feed and product concentrations with the differential reactor expression
Since oxygen and formic acid (TOC) concentrations were measured, as well as those for carbon dioxide, it was possible to assess the accuracy of the data through mass balances. However, for the final data the rate was calculated from the COz concentrations because these determinations were among the most accurate and, particularly, because the C 0 2 concentration in the feed was essentially
Table 111. Reproducibility Data and Carbon Balancesa T e s t no. 2
T e s t no. 1 Concentrations, (mol/cm3) x io7 COZ 0 2
HCOOH Rate, m o l / ( s e c ) ( g ) Total carbon balance (a) Feed. ( m o l / s e c ) X l o 7 HCOOH COZ (b) Product, ( m o l / s e c ) ~ ' 1 0 ~ HCOOH COZ
Feed
Product
Feed
Product
0.53 11.23 28.30
2.45 9.91 27.00
0.50 10.72 28.90
2.32 9.96 26.40
2.84 x 1 0 - ~
2.69 x i o - ?
25.5 0.5 26.0
26.0 0.5 26.5
24.3
23.8 2.1 25.9
2.2 26.5
a Approximate run conditions: t = 240°C; q = 0.90 cm3/sec; W = 0.609 g; d, = 0.477 cm. * COz and chromatography and HCOOH in a total organic carbon (TOC) analyzer.
zero. This meant that the rate was established primarily from but one analysis, that for CO2 in the product stream. Calibration runs indicated that the average accuracy and reproducibility of rates so calculated were about 10 and 5%, respectively. The accuracy of the rate of oxygen consumption was somewhat less because differences in concentrations were required. Since the TOC measurements were less accurate than the chromatographic analyses, they were not used for rate calculations. Nevertheless, the average deviation between the formic acid consumed (from TOC analyses) and the carbon dioxide produced was less than 10%. Typical data for two runs a t approximately the same conditions are given in Table 111. Catalyst Activity. I t was necessary to pretreat the catalyst in place before constant rates were obtained. For example, if an air-saturated solution (CO, = 2.7 X 10-7 mol /cm3) was fed to a bed of fresh catalyst, the rate of carbon dioxide production was erratic for several hours. Also Rc.o, was more than -2Ro,, as prescribed by the stoichiometry of eq 1. This shows that the catalyst is being reduced. I t was found that stable and reproducible rates could be obtained by first pretreating the catalyst for about 10 hr a t the operating temperature with a feed containing the desired formic acid concentration and with the low oxygen concentration of 0.56 x mol/cm3. Figure 2 shows a typical plot of Reo,, RH,, and -2R0, for a fresh catalyst bed during this period. The presence of hydrogen in the product indicated that at this low oxygen concentration formic acid is decomposed according to eq 3 as well as oxidized according to eq 1. For steady-state behavior of the catalyst the three rates should be related by the stoichiometry of eq 1and 3, that is
Rco2 = - 2 R O 2
-C
RH2
(5)
The data in Figure 2 showed that during the first 6 hr Reo, is greater than that given by eq 5 , corresponding to catalyst reduction. After that time the rates were constant and conformed closely to eq 5 . This suggests that a stable catalyst condition has been reached. The last step in the pretreatment was to operate the reactor with an oxygen concentration corresponding to the desired value. After about 4 hr at the higher concentration stable and reproducible rates of oxidation were observed. When the oxygen concentration was increased, hydrogen could no longer be detected in the product. From the kinetics data reported later for the oxidation reaction it was
0 2
TIME
compositions determined by gas
lhnurrl
Figure 2. Rates of COz, Hz, and 0 2 production during pretreatment with low CO, ( d i j = 0.0541 cm, t = 240"C, Q = 0.9 cm3/sec, P = 40 atm).
estimated that the rate of oxidation according to eq 1 was about 50 times the rate of decomposition (eq 3) at a Co, of 10.9 x 10-7 mol/cm3. Hence, the absence of hydrogen during the oxidation runs was believed to be due primarily to the retardation of eq 3 rather than to the oxidation of the hydrogen formed by decomposition. During the 4-hr period -2Rc1, was greater than RC.o,, indicating that some reoxidation occurred on the catalyst. After 4 hr a new stable state was apparently reached and -2R0, was equal to
Rco,. Oxidation Kinetics The reaction order was evaluated from rate data for different formic acid and oxygen concentrations, all a t 225°C and a t a constant flow rate of 0.9 cm3/sec. For these measurements catalyst particles of the smallest sizes, d, = 0.0380 and 0.0541 cm, were employed. As will be seen later (Figures 4 and 5), a t this flow rate, particle size, and temperature, both fluid-to-particle and intraparticle mass transfer resistances were negligible. The effect of oxygen concentration on the rate is illustrated in Figure 3 where R c ~ o , / C bis~plotted us. the arithmetic average concentration of oxygen in the reactor. The data points are for the specific formic acid concentration of 23.7 x 10-7 mol/cm3. These data suggest that the rate is first order in oxygen. Assuming a first-order dependency Ind. Eng. Chem.. Process Des. Develop.. Vol. 13, No. 4 , 1974
449
1 lo
-0
I
1
I
- Lcrst & w e
I
I
D a b Polnb fm Conibnt
I
I
(-23 7 I IO-' I m18icm3).
Cornlattm of All D a b at 225°C
-
2.0
z
1.5
a
1.0
%
0.5
Y 0 1
0
3
2
I lo7,
7
6
5
4
8
9
0.5
10
1.0
0.75
FLOW RATE ,
I nwk/cm3
Figure 5 . Effect of flow rate (t
Figure 3. Effect of oxygen on rate (at 225°C).
-
I/
\
6
4
-1 0
o
I I
io
0 CaMpt 5110 28-32
I
m
+ 30
UI
50 I
Qblyst
SIZO
m
-z
nnh
-
IW
0
Y
i
0.477 on
cFA IM) C
3
I r
dp = 0.23l cm
0 d
'
35 U msh
70
dp = 0.0541 cm
dp = 0.0541 cm (a11 cmcmtmtioll)
I 5
s
+
a . Least %mi8 Correlatim of All Dab at 225-c
15
, cm3 I soc
= 240°C, P = 40 a t m ) .
10 r
I
1.25
4'
\ '
u
02
= 28.7 I 10-I 8 m o ~ e / c d
'
b e d ) = 10.3 I lo-'#
molo/cm3
iw
lo7, I r k / c d
Figure 4. Effect of formic acid on rate (at 225°C). on Co2, a least-squares analysis was made of the data at 225°C for all formic acid concentrations. The line in Figure 3 represents the linear (in CO,) result so obtained. Figure 4 shows the influence of formic acid concentration. The data points are for the specific oxygen concentration of 10.0 X 10-7 mol/cm3 and indicate a first-order dependency on CFA.Assuming that the rate is first order in both CO, and CFA a least-squares analysis of data a t 225°C for all oxygen and formic acid concentrations gave the solid line shown in the figure. The agreement of the data points for the two sizes of catalyst particles shows that there is no measurable influence of intraparticle diffusion on the rate for these small particles, at least at 225°C.
From the results suggested by Figures 3 and 4 an apparent second-order rate constant can be calculated from the expression
RCO2
kco2 =
(6 )
cFAc02
The influence of fluid-to-particle mass transport would be greatest at high temperature and for the largest particle sizes. Figure 5 shows kco, obtained from eq 6 for data at 240°C and for the two largest particles. No effect of flow rate is indicated. Hence the rate values at Q = 0.9 cm3/ sec shown in Figures 3 and 4 should not be affected by fluid-to-particle mass transport. While our data were insufficient to make definitive statements about the reaction mechanism the pretreatment studies provide some insight into this question. These studies showed that the catalyst could be reduced and oxidized in the presence of formic acid solution. This suggests that lattice oxygen participates in the reaction. Such behavior is not unusual in gas-phase oxidation on solid catalysts. For example, Winter (1958) found that the oxidation of CO on cuprous oxide occurred through an oxygen exchange with lattice oxygen. In terms of an oxidation-reduction mechanism formic acid would react with 450
Ind. Eng. Chern., Process Des. Develop., Vol. 13,No. 4 , 1974
\
04
' \
\
0.3
192
1%
2 00
2M
2.011
2 12
lCWT,
Figure 6. Effect of temperature and catalyst size. an active oxidized site on the catalyst, ultimately producing carbon dioxide and a reduced site. Then oxygen would interact with the reduced site to reform an oxidized site. Effectiveness Factors Figure 6 shows the effect of particle size and temperature on kr02 for the data taken at constant CFA and Co2 for d, = 0.291 cm, 0.477 cm, and a single point (diamond) for d, = 0.0541 cm. Also shown (as squares) for the latter size are the points for the runs at all formic acid and oxygen concentrations employed for the kinetic studies. Tbe single point was obtained about 3 months later by a different investigator using a catalyst bed different from the beds used for the other points f o r d , = 0.0541 cm. The comparison between these data points is an overall measure of the reproducibility of the data. The results in Figure 6 show that intraparticle diffusion is important for the larger particles. For the concentrations of formic acid and oxygen indicated in the figure, oxygen was the limiting component. From the stoichiometry of reaction 1, and eq 6
Hence, the apparent rate constant for oxygen can be cal~ expression culated from k ( .by~ the
ko2 = %kco2 Effectiveness factors were evaluated from K O , values for two particle sizes at the same temperature. In terms of the intrinsic rate constant KO,*, the effectiveness factors for two sizes (denoted by subscripts 1 and 2) may be written
Thiele-type moduli for the second-order reaction are
I
w"
Maymo and Cunningham (1966) have solved the mass balance equations for the relation El = f(m) for a secondorder reaction of the form A B R S in terms of the parameters
+
-
+
3
I1 W
and D,
=
& I -
D~,A
(13)
Equations 8-11 and the relation E, = f ( rn) can be solved for E,,, E12, koz*, De,oz by trial and error or by the graphical, triangle method of Weisz and Prather (1954). Since the accuracy of the solution is poor when both effectiveness factors are small, the computation procedure was used for but two of the possible three pairs of data: (1) dp = 0.0541 and 0.291 cm, and, (2) d, = 0.0541 and 0.477 cm. This choice resulted in rather sensitive calculations since El for d, = 0.0541 was high. For our data the average value of E H was 2.6 and D E = 0.40. The latter result was obtained from molecular diffusivities of dissolved oxygen and formic acid in liquid water as calculated from the Othmer and Thaker equation. This equation has been recommended by Reid and Sherwood (1966) for liquid-phase diffusivities at 10-30°C. Since eq 1 does not follow the B R S, eq 13 becomes, for our stoichiometry of A case
+
-
+
This relation includes the assumption that the ratio of the effective diffusivities of two diffusing components in the same catalyst particle is the same as the ratio of their molecular diffusivities; in other words it was assumed that the tortuosity factor is the same for oxygen as for formic acid. The results for E f , De,oz and ko,* are given in Table IV. The effectiveness factors show that the observed rate is strongly retarded by intraparticle diffusion; d, should be less than about 0.05 cm for the surface to be fully effective. The agreement between the two sets of effective diffusivities is a sensitive measure of the precision of the calculations. Tortuosity factors calculated from the De,02results with the equation
u
.. m
m
0
c?
0
u
Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 4 , 1974
451
EDm,02 6 =De&
(15)
are also shown in Table IV. The average value is slightly greater than unity. This is lower than 8 = 3.9 found by Satterfield, et al. (1968), for the diffusion of hydrogen in the liquid-phase hydrogenation of a-methyl styrene. Kenney and Sedricks (1972) obtained an average tortuosity factor of 1.6 for the liquid-phase hydrogenation of crotonaldehyde. These appear to be the only other determinations available for liquid-filled pores under reacting conditions. Surface migration reduces the tortuosity. However, at the relatively high temperatures and low oxygen concentrations of our work it was unlikely that surface diffusion would be important. In the absence of surface migration tortuosity factors should be a measure of the porous structure with respect to diffusion. The pelletted Pt/ A1203 catalyst used by Kenney and Sedricks had about the same porosity (0.54) as the CuO-ZnO catalyst, and pore sizes were probably of the same order of magnitude. Hence, it is reasonable to expect about the same 6 values (1.6 us. 1.0) for these two catalysts. The Pd/A1203 catalyst pellets employed by Satterfield, et al., also had similar properties, so that the reason for the larger value of 3.9 is not clear. Tortuosities of this magnitude (3-4) have been reported in a number of investigations (Satterfield, 1970) with similar catalysts when the pores were filled with gas. Uncertainties in predicting liquid-phase, molecular diffusivities could contribute to the discrepancy, but this seems unlikely to be the sole cause. Activation Energy Apparent activation energies computed for the slopes of the lines in Figure 6 are d,, c m
E , kcal/mol
0.0541 0.291 0.477
35 27 24
If the effectiveness factor is low enough (-0.2) that the asymptotic relationship ET = l/m is accurate and if De is not dependent on temperature, the activation energy should be one-half of the intrinsic value. The decrease in E with increasing d , observed shown here is less. This is probably because E , for the larger two particle sizes is usually greater than 0.2, and because de,^, is not independent of temperature. An Arrhenius plot of the ko2* data in Table IV gave an intrinsic activation energy of about 37 kcal/mol. Conclusions A commercial CuO-ZnO catalyst was found to be effective for oxidizing in liquid-phase operation at temperatures from 200 to 240°C. Preliminary studies showed that the catalyst is partially reduced in formic acid solutions when the oxygen concentration is low (-0.5 X mol/ cm3) and oxidized at higher oxygen concentrations. No reduction of formic acid to hydrogen or carbon monoxide was observed when the oxygen concentration was high. Rate data for small-size catalyst particles indicated that the reaction was first order in oxygen and first order in formic acid. The activation energy was about 37 kcal/mol. Measurements with 0.291 and 0.477-cm catalyst particles showed severe intraparticle diffusion effects. Effectiveness factors as low as 0.11 were found at 240°C for
452
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4 , 1974
0.477-cm particles, and for this size the apparent activation energy was reduced at 24 kcal/mol. Tortuosity factors were about unity, which is considerably lower than those expected for gas-filled pores of the same type of catalyst. Acknowledgment Substantial financial support was provided by the University of California Water Resources Center, Project W392. Also financial support from the Rotary Club of Torino Nord (Italy) and from the Fulbright Commission for G. Baldi is gratefully acknowledged. The Chemetron Corporation kindly provided the catalyst. Nomenclature C, = concentration of component i, mol/cm3 Dg = diffusivity ratio defined by eq 13 De,, = effective diffusivity, cm2/sec Dm,i = molecular diffusivity, cm2/sec dp = equivalent spherical particle diameter, cm E = apparent activation energy, kcal/mol EB = concentration ratio defined by eq 12 E f = effectiveness factor kcOz = apparent second-order rate constant for C02 production, cm6/(mol) (g) (sec) ko, = apparent second-order rate constant for 0 2 consumption, cm6/(mol) (g) (sec) ko2* = intrinsic second-order rate constant for 0 2 consumption, cm6/(mol) (9) (sec) m = Thiele modulus, defined by eq 10 P = pressure, atm Q = liquid flow rate through reactor, cm3/sec Vp = volume of particle, cm3 R, = reaction rate for production of component i, mol/g sec S, = external surface of particle, cm2 T = temperature, OK W = mass of catalyst, g
Greek Letters 6 = tortuosity factor c = porosity pp = particle density, g/cm3 Subscripts and Superscripts FA = formicacid F = feed P = product S = external surface of catalyst - = averagevalue Literature Cited Hancil, V.. Smith, J. M., lnd. Eng. Chem., Process Des. Develop., 10, 515 (1971). Hindin, E., Bennett, P. J., Narayanan, S. S., Water Sewage Works, 116, 466 (1969) Kenney, C. N., Sedriks. W.. Chem. Eng. Sci., 27, 2029 (1972) Margolis, L. Y . , J. Catal., 21, 93 (1971). Maymo, J. A,, Cunningham, R. E.. J. Catal.. 6, 186 (1966). Prather, 6.V., J. Wafer Pollut. Contr. Fed., 42, 596 (1970). Reid, R. G., Sherwood. T. K.. "The Properties of Gases and Liquids," 2nd ed, p 559, McGraw-Hill, New York, N. Y., 1966. Satterfieid, C. N., "Mass Transfer in Heterogeneous Catalysis." pp 66. 157, M.I.T. Press, Cambridge, Mass., 1970. Satterfield, C. N.. Ma, Y. H.. Sherwood. T. K., Chem. Eng. Symp. Ser. (Brit.), No. 28, 22 (1968). Seidell. A , , "Solubility of Organic and inorganic Compounds," 3rd ed, pP 1228-1229, Van Nostrand, New York. N . Y., 1958. Suzuki, M.. Smith, J. M.. J. Catal., 21, 336 (1971). Thomas, J. M., Thomas, W. J.. "Introduction to the Principles of Heterogeneous Catalysis," pp 315, 383, Academic Press, New York, N. Y . , 1967. Weisz, P. 6.. Prather, C. D.. Advan. Catal., 6, 172 (1954) Winter, E. R. S., Advan. Catal., 10, 196 (1958). Zimmerman, F. J., Chem. Eng., 65, 117 (1958).
Received for reuiew April 26, 1974 Accepted June 17, 1974
