Ind. Eng. Chem. Fundam.,Vol. 17, No. 2, 1978
Acknowledgment For financial support J.M.P. is grateful to the National Science Foundation and to Union Carbide Corporation. During his stay at Berkeley, T.O. was the recipient of a fellowship from Asahi Chemical Industry Co., Ltd.
113
James, A. T., Martin, A. J. P., Biochem. J., 50, 679 (1952). Liu, D. D., Prausnitz, J. M., Ind. Eng. Chem. Fundam., 15, 330 (1976). Lyckman, E. W., Eckert, C. A., Prausnitz, J. M., Chem. Eng. Sci., 20, 703
(1965). Maloney, D. P., Prausnitz, J. M., AlChEJ., 22, 74(1976). Newman, R. D., Prausnitz, J. M., AlChEJ., 19, 704 (1973);Erratum, 20, 206
(1974). Tsonopoulos, C., AlChEJ., 20, 263 (1974).
Literature Cited
Received for review October I,1977 Accepted February 6, 1978
Guillet, J. E., "New Developments in Gas Chromatography," Howard Purnell, Ed., Wiley, New York, N.Y., 1973.
Mass Transfer and Contacting Efficiency in a Trickle-Bed Reactor Shush1 Morlta and J. M. Smith* Department of Chemical Engineering, University of California, Davis, California 956 76
A batch-recycle system, in which cu-methylstyrene was hydrogenated with a Pd/A1203 catalyst, was employed to study liquid-particle mass transfer in a trickle-bed reactor. Liquid-full reactor measurements were first made to determine intrinsic kinetics and intraparticle diffusivity in the liquid-filled pores. Data were taken at 32 to 52'C and 1 atm pressure. The results for both liquid-full and trickle-bed operation suggested that the effective mass transfer area between liquid and porous catalysts under reaction conditions was less than the outer surface area of the catalyst particles. However, the latter area may be suitable for correlating dissolution mass transfer data from nonporous particles. Also measurements for catalysts of different activities indicated that in trickle-bed operation the surface of the particles was not completely covered with liquid. Using an approximate model it was found that the fraction, f, of the particle surface covered by liquid did not vary significantly with liquid flow rate. The average value of f was 0.89. Data were taken in the gas-continuous flow regime and showed no significant change in rate of reaction with gas (hydrogen) flow rate.
Interphase mass transfer can severely retard global rates of reaction in trickle-bed reactors (Goto and Smith, 1975) where liquid and gas streams flow concurrently downward over a bed of catalyst particles. While several correlations have been presented (Satterfield, 1975; Charpentier, 1976; Goto et al., 1975) for gas-liquid and liquid-solid mass transfer coefficients, many of these have been for large size particles and all have been based upon mass transfer measurements in the absence of reaction. For example, liquid-solid mass transfer has been studied by solution of solid particles such as p-naphthol into a liquid. The effective surface area for mass transfer in these experiments may be greater than in the reaction case where mass transfer is predominantly on the part of the outer surface of the catalyst particle that is porous. A primary objective of the work reported in this paper was to measure liquid-solid mass transfer rates under reaction conditions with a porous catalyst. In the trickling, or gas-continuous, flow regime (Charpentier, 1976) evidence suggests that the catalyst particles may not be completely covered with liquid. Such partial wetting, or contacting, of the catalyst surface with liquid also can affect the global rate of reaction. Hartman and Coughlin (1972) studied the oxidation of sulfur dioxide in a packed-bed reactor with air and water streams and concluded that the carbon catalyst particles were not completely wet. Satterfield and Ozel (1973) decided from studies on the hydrogenation of benzene with a Pt/A1203 catalyst in a trickle-bed reactor that some part of the outer surface of the catalyst particles was covered by gas, even a t high liquid rates. Similar observations 0019-7874/78/1017-0113$01.00/0
have been reported by Sedriks and Kenney (1972), Germain et al. (1974), and Hanika et al. (1976). A secondary objective of our work was to investigate experimentally this contacting efficiency for a specific system. We studied the hydrogenation of a a-methylstyrene to cumene, C G H & ( C H ~ ) = C H ~ t ( ~HZ(g) ) C6H&H(CH3)2 at near ambient temperatures and at atmospheric pressure. For these conditions this single, irreversible reaction does not occur homogeneously, and the liquid reactant is sufficiently nonvolatile to eliminate gas-phase reaction. With a palladium-on-alumina catalyst the reaction is first order in hydrogen; its kinetics has been investigated (Babcock et al., 1957; Sherwood and Farkas, 1966; Satterfield et al., 1968; Pruden and Weber, 1970; Germain et al., 1974). Our work was done with relatively active catalysts since the chief objective was the evaluation of mass transfer resistances. Hence, effectheness factors in the liquid-filled pores were low. Intrinsic kinetics a t the catalyst sites was first evaluated from data obtained for only liquid flowing upward through a bed of catalyst particles (i.e., liquid-full reactor). Then global rates were measured in a batch-recycle (with respect to liquid) trickle-bed reactor operated with low conversions per pass. By this procedure the rate of reaction was nearly the same throughout the catalyst bed. Rates were determined by analyzing samples of the circulating liquid for cumene at various times. Data were obtained for various liquid flow rates and two catalyst activity levels, since these variables were most important for our objectives. The solubility of hydrogen in a-methylstyrene is so low
-
0 1978 American Chemical Society
114
Ind. Eng. Chem. Fundam., Vol. 17, No. 2, 1978
Table I. Physical Properties of Catalysts
'h
12
Figure 1. Schematic diagram of apparatus: 1,constant-temperature bath; 2, absorber; 3, condenser; 4, dispersion tube; 5, sample valve; 6, trickle-bed reactor; 7, distributor;8, preheater for liquid; 9, pump; 10, rotameter; 11,thermometer; 12, needle valve; 13, valve; 14, catalyst bed; 15, deoxygenerator (palladium catalyst bed); 16, drier (silica gel); 17, soap-film meter; 18, preheater for gas; 19, trap; 20, funnel. (about 2.7 X g-mol/cm3 a t 40 "C and 1 atm) that a single-pass, differential reactor could not be used to obtain accurate rate data in either liquid-full or trickle-bed reactors. Experimental Section Apparatus. Figure 1 shows the apparatus of which the key parts were the reactor (6) and absorber (2) for saturating the a-methylstyrene with hydrogen. The styrene was recycled through the absorber after each pass through the reactor. In this way the hydrogen concentration in the liquid entering the reactor was in equilibrium with hydrogen gas feed. Reactor and absorber were contained in the same constant-temperature bath so that the reaction and absorption temperatures were equal. With this arrangement the hydrogen concentrations in the liquid and gas were nearly uniform throughout the differential reactor and also did not vary during a run. A series of runs was initiated with pure a-methylstyrene and terminated when the cumene concentration reached about 6%. Hence, the styrene concentration was also essentially uniform throughout the reactor and also did not vary significantly during a run. One run lasted for 4 to 6 h during which period four or more samples of liquid were taken from the absorber (line 5, Figure 1)and analyzed for cumene. The auxiliary parts of the apparatus provided for purifying the hydrogen, measuring flow rates, and preheating and pumping the feed streams, as shown in Figure 1. The stainless steel reactor was 2.54 cm i.d. and 30 cm long. For trickle-bed operation, the liquid was introduced through a distributor consisting of five 0.1 cm i.d., 0.5 cm long capillary tubes (stainless steel) placed across the reactor cross section. This gave approximately uniform distribution. The outlet of the tubes was located 0.5 cm above the top of the alumina prepacking. The bed as a whole consisted of three sections: a prepacking length of alumina particles, the catalyst section consisting of the Pd/A1203 particles, and an after section of alumina particles, all supported by a stainless steel screen placed near the bottom of the reactor. The lengths of the prepacking section and the catalyst bed are given in Table 11. The particle sizes (Table 11),tube diameter, and depths of the sections were such that uniform distribution of liquid was expected throughout the catalyst section. This was ascertained from the criteria given by Herskowitz and Smith (1977). The pre- and after-sections consisted of the same size alumina particles as used to prepare the catalyst. The effluent from the reactor was recycled to the absorber where it separated into gas and liquid. The gas, containing small amounts of a-methylstyrene, was cooled in a vertical glass condenser (3) packed with S/s-in. i.d. helices. The styrene condensate flowed back into the absorber, and the remaining
Surface area (Nz adsorption), m2/g 165a Pore volume, cm"g 0.33a Average pore radius, A 60a 3.07 Solid phase density, ps, g/cm3 Particle density, pp, g/cm3 1.53c Bulk density, p ~ g/cm3 , 0.79 Porosity of particle, cp 0.503c 0.4P Void fraction of bed, f B a From Girdler Chemical Inc. Measured. Calculated. gas was discharged. The valves and lines for liquid were &in. 0.d. stainless steel; the lines outside of the constant-temperature bath were insulated with glass wool. For liquid-full runs a different stainless steel reactor (0.93 cm i.d., 16 cm long) was used with a prepacking section of alumina particles and a catalyst bed as listed in Table 11.The liquid was fed to the bottom of the reactor and hydrogen gas was introduced only to the absorber (Figure 1). The liquid was recycled through the absorber; the rest of the apparatus was the same as for the trickle-bed runs. Chemicals. Technical grade a-methylstyrene (Dow Chemical Co.) with a stated purity of 99.2%was used as supplied. The major impurity was isopropylbenzene, and the polymer content was negligible. For catalyst preparation reagent grade palladium chloride and activated y-alumina pellets (3/16 X 3/ls in., T-374, Girdler Chemical Inc.) were used. The stated purities of the H2 (before elimination of oxygen in the deoxygenator, Figure 1) and the nitrogen were 99.999% and 99.996%, respectively. Reagent grade cumene (Aldrich Chemical Co.) and reagent grade p-xylene (Eastman Organic Chemicals) were employed for calibrating the chromatograph for cumene analysis. Catalyst Preparation. Evacuated alumina particles (7 to 10 mesh) were soaked in an aqueous HC1 solution of palladium chloride a t 70 "C for 48 h. After evaporation and thorough drying, the particles were reduced at 370 "C for 24 h in a stainless steel tube through which hydrogen was flowing. After crushing and sieving, two sizes were chosen for the reaction studies: these were particles for which the average sizes of the granules were d, = 0.141 cm (10 to 14 mesh) and d, = 0.0541 cm (28 to 32 mesh). Visual observation indicated uniform dispersion of the palladium throughout the particles. Catalysts of two activities were prepared, containing 0.5 wt % Pd and 2.5 wt % Pd. The measured and available properties of the catalysts are shown in Table I. The properties supplied by the manufacturer are those for the y-alumina. The porosity, particle density, and void fraction were calculated from the solid-phase density and pore volume. Analytical Methods. The concentration of cumene in the liquid was determined by adding to the liquid sample a solution of a known amount of p-xylene in a-methylstyrene. The p-xylene was used as an internal standard. The concentration of cumene was obtained from the ratio of the peak heights of cumene and p-xylene when the sample was chromatographically separated in a l/s-in. 0.d. stainless steel column, 5 f t long, packed with Silicone SE-30, and operated a t 70 OC. A calibration curve was prepared with samples containing known amounts of p-xylene and cumene. The solubility of hydrogen in a-methylstyrene was determined by analyzing liquid samples saturated with hydrogen. The analysis was done chromatographically using a 6-m length of column (0.63 cm o.d.), packed with 20 to 40 mesh, 5A molecular sieve particles and maintained at 100 "C. The liquid was saturated a t atmospheric pressure by bubbling hydrogen through the liquid for at least 10 h. A 1OO-kL sample of the saturated liquid was withdrawn and a 50-wL portion was analyzed by injecting it into a stream of nitrogen as carrier gas.
Ind. Eng. Chem. Fundam., Vol. 17, No. 2, 1978
Table 11. Operating Conditions 1. Mass of catalyst in
Liquid-Full Runs 1.0 (d, = 0.0541) and 2.0 ( d , = 0.141)
reactor, g 2. Palladium Content, wt 0.5 (d, = 0.0541 and 0.141) and 2.5 (d, % = 0.141) 3. Mass of prepacking, g 1.0 (d, = 0.0541) and 2.0 (d, = 0.141) 4. Catalyst particle size, 0.0541O and 0.141b d,, cm 5. Liquid flow rate, QL, 2.0-21.5 (d, = 0.0541) and 2.6-25.1 (dp cm31s = 0.141 6. Reaction temperature, 32.4,40.6, 51.7 (d, = 0.0541) and 40.6 "C (d, = 0.141 7. Total pressure, atm 1.0 1. Mass of catalyst in reactor, g
Trickle-Bed Runs 2.0
2. Palladium content, wt 0.5 and 2.5 %
3. Length of catalyst bed, 0.5
cm 4. Length of prepacking, 5.0 and 10.6 (0.5%Pd), 5.0 (2.5%Pd) cm 5. Catalyst particle size, 0.141 d,, cm 6. Hydrogen flow rate, Qc,0.5-15.0 (0.5%Pd), 5.0 (2.5%Pd) cm3Is 7. Liquid flow rate, QL, 0.5-15.0 (0.5%Pd), 1.0-15.0 (2.5%Pd) cm3Is 8. Reaction temperature, 40.6 "C 9. Total pressure, atm 1.0 a 28 to 32 mesh. 10 to 14 mesh. A calibration curve was prepared using gas samples of 1to 5 WLof hydrogen. The results for the solubility at 1atm hydrogen pressure are represented by the expression (Csat)Hs= (1.84
+ 0.02327') X
g-mol/cm3 (22 O C 5 T I50 "C)
Such small concentrations are difficult to measure accurately, and it is estimated that the maximum error in the above expression could be as much as lo%, even though care was taken in obtaining the data, and reproducibility was about 5%.The solubilities from the above expression are about 30% lower than those of Satterfield et al. (1968), and 20 to 50% higher than the data of Polejes (1959). Operating Procedure. The operating conditions and range of variables studied are given in Table I1 for the liquid-full and trickle-bed runs. To avoid catalyst deactivation and to obtain reproducible rates, it was necessary to pretreat the catalyst bed. The following procedure was found to give good results. After packing the reactor, nitrogen was passed through the bed for 1h and followed by a flow of hydrogen for 30 min to displace air. Next, 600 cm3 of a-methylstyrenesaturated with hydrogen a t 25 "C was charged to the apparatus (to fill the pump) using the funnel (20) shown in Figure 1.Then the flow of hydrogen to the absorber was started and the pump operated until the lines and reactor were filled with liquid. Finally, the catalyst was maintained covered with the Hz-saturated liquid for 12 h. It was particularly important to eliminate simultaneous contact of oxygen (air) and hydrogen with the dry catalyst. A trickle-bed run was started by simultaneously introducing hydrogen flow to the absorber and to the reactor. The first sample of liquid was analyzed for cumene after 30 min and three or more samples were taken at subsequent 1to 2 h intervals. Usually 6 runs could be made before the cumene concentration reached 6%. At that time the reactor was dis-
115
mantled, the liquid was withdrawn, and a new sample, from the same batch of catalyst, was packed in the reactor. When not making a run, the reactor was maintained full of liquid saturated with hydrogen. The mass of catalyst in the reactor was chosen so as to reduce the time of a run to a reasonable level and still keep the hydrogen conversion per pass through the reactor a t an average value of less than 15%. It is essential in interpreting the data that the liquid entering the reactor from,the absorber be always saturated with hydrogen. Preliminary experiments showed that such saturation could be maintained by flowing hydrogen through the absorber a t a rate of 3 cm3/s. This flow rate was 30 times the rate of hydrogen consumption in the reactor a t conditions for which the rate of reaction was a maximum. Experimental R a t e D a t a The rate of reaction, R , was calculated from the change in cumene concentration with time and the known mass of catalyst and total volume of liquid. Thus, for a batch recycle reactor
Since the conversion per pass was very low, concentrations were essentially uniform in all parts of the system. Then the rate calculated from eq 1could be associated with a specific hydrogen concentration. Furthermore, the hydrogen and styrene concentrations did not vary during a run; the maximum conversion of styrene to cumene in one run was 1%.So the data for Cc vs. t were linear and the rate was constant during a run. Such rates of reaction were used to analyze the data obtained for both liquid-full and trickle-bed operation. There have been numerous studies of the intrinsic kinetics of the reaction with Pd/A1203 catalysts, for example, Babcock et al. (1957) and Satterfield et al. (1968). While the results are not entirely consistent, over a narrow range of low hydrogen concentrations, and a t high styrene concentrations, the reaction appears to be first order in hydrogen and is irreversible. First-order kinetics will be assumed in interpreting our data. Liquid-Full Reactor Results Intrinsic Kinetics. For liquid-full operation the rate can be expressed in terms of the mass transfer rate to the catalyst particles, or in terms of the kinetics of the reaction
where CL is the average concentration of hydrogen in the bulk liquid, and ( ~ , u , ) Ris the liquid-particle mass transfer coefficient under reaction conditions. Since the concentration entering the reactor was the saturated value and the change in concentration in the reactor per pass was small
Eliminating C, from the two relationships in eq 2, and using eq 3 for CL, gives (4) At a fixed temperature and pressure ( ~ , u , ) R should be a function of liquid flow rate. Mass transfer correlations (Evans and Gerald, 1953; Hirose et al., 1976; Sherwood et al., 1975; Wilson and Geankoplis, 1966) suggest that ksas is proportional ~ that 0.3 < a < 0.7. Our rate data, plotted according to Q L and to eq 4, gave the best straight lines when a = 0.48. The results
116
Ind. Eng. Chem. Fundam., Vol. 17, No. 2, 1978
Table 111. Liauid-Full Results Catalyst Pd (%)
d,, cm
Temp,
D, x 104,
k, cm3/(g)(s)
(g)(s)/cm3
O C
40.6 0.64 12.0 0.5 0.0541 0.5 0.141 40.6 1.62 12.0 0.5 0.0541 32.3 0.75 9.76 0.5 0.0541 51.7 0.51 15.g6 2.5 0.141 40.6 0.61 82.7 0 Satterfield et al. (1968). Based upon a tortuosity factor of 2.59.
x 104,
DO
t
cm2/s
cm2/s
T
0.131 0.052 0.132 0.124 0.020
0.218 0.278 0.243 0.328b 0.278
1.42 1.42 1.25 1.69 1.42
2.59 2.59
1.0
0.5
0.2
.-
E
0.1
LL m &
.en
0.0: In
B
0.G
0.01
0.001 10
20
50
100
200
500
1wo
2m
Liquid Reynolds' Number, Re
Figure 3. Mass transfer factor,j d , calculated from eq 8 for liquid-full operation.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Q i O . 4 8 , icrn3/rec. ) 4 . 4 8
Figure 2. Rate data for liquid-fulloperation. are shown in Figure 2 for the three temperature levels and for both catalyst activities and particle sizes. The intercepts of the lines in Figure 2 give k q and the slopes established the mass transfer coefficient, (k,a,)R. The intrinsic rate constant k was evaluated from the k q values for the two particle sizes at the same temperature (40.6 "C) and catalyst activity (0.5% Pd). This was done by using the effectiveness factor relationship for a first-order, irreversible reaction on spherical catalyst particles
Equations 5 and 6, applied to both particle sizes, were solved with the known k q values to give k and De. These results as well as the relatively large slopes in Figure 2 show that the measured rate of reaction was severely reduced by external and intraparticle mass transfer. The tortuosity factor was obtained from the equation Dt De
(7)
where D is the molecular diffusivity of hydrogen in a-methylstyrene. Satterfield et al. (1968) measured D vs. tempera-
ture, and their values were used, along with the known results for De and tp, to obtain T = 2.59. With T known and D available, De could be calculated at the other two temperatures and for the other catalyst activity. Then, using eq 5 and 6 and the k q values, k and q were obtained for the other temperatures and the more active catalyst (2.5% Pd). These results are given in Table 111. The intrinsic Eate constants at the three temperatures for the 0.5% Pd catalyst followed an Arrhenius plot and gave an activation energy of 5.0 kcal/mol. Other reported activation energies are 7.6 and 10 kcal/mol by Satterfield et al. (1968) and Germain et al. (1974). The method used for obtaining individual values of k and q is not very sensitive when the catalyst activity is high. Under such conditions the ratio of the q values for two particle sizes approaches the inverse ratio of the particle diameters. For more accurate values of k a less active catalyst should be used. However, for our purpose of interpreting mass-transfer effects in trickle-bed reactors, only the product k q is needed. Hence, high-activity catalysts with the desired large mass transfer resistances could be used. Mass Transfer Results. The mass transfer coefficients (k,as)R obtained from eq 4 and Figure 2 may be conveniently compared with available correlations through j d factors. Such factors were evaluated from the expression
The total external area at was calculated by supposing that the particles are spherical so that at = 6/dp pp. This is the area employed in the various correlations for Id. Values of j d so obtained from our reaction data and the available correlations based upon mass transfer data (in the absence of reaction) are shown in Figure 3.
Ind. Eng. Chem. Fundam., Vol. 17, No. 2, 1978
The mass transfer correlations give values about fourfold larger than those from our reaction results. This difference is too large to be explainable by uncertainties in D or other physical properties. Also, the magnitude of end effects, or unusual flow patterns, are unlikely to be large enough to account for the difference, particularly since the experimental points represent many different bed packings. The agreement of the data for the catalysts containing 0.5 and 2.5%Pd, which gave widely different reaction rates (Figure 2), lends confidence to the experimental results. The other available information on mass transfer with this reaction appears to be that of Biskis (1963) and Biskis and Smith (1963),who used a liquid-full reactor (i.d. = 1 in.), packed with l/S-in. alumina spheres containing 0.5 wt % Pd, and operated a t 55 " C and about 5 atm pressure. Biskis' line for j d , also shown in Figure 3, is much closer to our data points. The large discrepancy between the mass transfer correlations and our j d values (and those of Biskis) is most likely due to differences in effective areas for mass transfer. The correlations are based upon either dissolution of solid particles or reaction with a nonporous solid (Hirose et al., 1976, employed the redox reaction between solid copper and dichromate ions). In these systems the effective surface may well be close to the external surface area calculated from the relation a t = 6/dppp. In contrast, when a reaction occurs predominantly inside the pores of a catalyst particle, mass transfer is constrained to a region close to the pore openings on the outer surface of the particles. Hence, the effective surface area for mass transfer could be considerably less than at, leading to low values for j d as shown in Figure 3. A similar explanation has been proposed for explaining mass transfer effects for disproportionation reactions (Moffat et al., 1970, 1972). More studies are needed on porous catalysts, at conditions where external transport is important, in order to provide a complete explanation for such differences in j d . However, the coincidence of the data for 0.5 and 2.5% P d catalysts in Figure 3 is in agreement with the area explanation. The smaller variation in j d with particle size, evaluated from our reaction data and from those of Biskis, could be due to flow distribution. For example, the tube-to-particle diameter in Biskis' data is small enough (about 8) to lead to excessive flow at the wall (Herskowitz and Smith, 1977) and to give somewhat lower mass transfer coefficients. For our two, very small particles the Reynolds number may not correlate all the effects of particle size. This has been observed for gas-solid systems for external mass transfer by Bar-Iran and Resnick (1957) and by Edwards and Richardson (1968) for axial dispersion. Trickle-Bed Reactor Results When the apparatus was operated as a trickle-bed reactor, global rates were determined at 40.6 "C over a range of gas and liquid flow rates. Pure hydrogen gas and styrene saturated with hydrogen at 40.6 " C and 1 atm were fed to the reactor. Interpretation Based upon Complete Liquid Coverage. The mass balance of hydrogen around the reactor, assuming that all the outer surface of the particles is covered by the liquid flow, is
The average concentration differences in the reactor are related to the inlet and outlet values C L ~ ( =Csat) and CL, by the equations
117
2.0
oto and Smith (1975)
1.0
0.5
b
0.2
m"
s 0.5
0.2
1
2
I
1
I
1
5
10
20
50
Liquid Flow R a t e , QL , cm3/s0c
Figure 4. Apparent mass transfer coefficient ( k s a s ) ~based , on f = 1, in trickle-bed reactor (QG = 5.0 cm3/s).
1
+ (c b - c s ) ] = 2 (Csat + CL,) - c s
(11)
Equation 2 relating C, and CL is valid for trickle-bed operation. The second equality in eq 2 can be combined with eq 9-11 to obtain an expression for C, in terms of CSat.This expression can then be employed for C, in the first equality of eq 2 to give the following equation for the rate in terms of the mass transfer coefficients and Csat
R=
Csat 1 -+ks
1 ( b a s ) ~( h a ~+) 2 Q ~ l m l
(12)
+
or (ksas)R =
1
Csat---1
1
(13)
R k s (kLaL) + 2 Q ~ l m From the trickle-bed data, Csat, QLlm, and R (calculated by eq 1) are known. From the liquid-full runs k q is available. Before eq 13 can be used to calculate (k,aS)R,the mass transfer coefficient from gas to liquid must be evaluated. However, ( K L U L ) was always less than 5%of 2 Q ~ l mso that an approximate value of this quantity is satisfactory. The correlation of Goto and Smith (1975), based upon data for absorption and desorption of oxygen in a trickle-bed packed with small particles (0.0541 to 0.413 cm), was used to estimate ( k L a L ) . The largest terms in the denominator of eq 13 were C,,JR and l / k v , and they were of the same magnitude. The values of (k,a,)R obtained from eq 13 are shown in Figure 4 along with previously published correlations (Van Krevelen and Krekels, 1948; Goto and Smith, 1975).The latter are based upon mass transfer (no reaction) data determined by dissolution of nonporous solid particles. The results for ( k , a , ) could ~ possibly be affected by nonuniform distribution of liquid across the reactor diameter. In a recent paper (Herskowitz and Smith, 1977) it was found that for granular particles for which the ratio of tube to particle diameter was 218, uniform distribution was achieved from a point-source feed after a minimum bed depth of twice the tube diameter. In our experiments a nearly uniform liquid feed was employed, the tube to particle diameter ratio was 18,and a t least the minimum bed depth (including the prepacking section) was used. Hence, the liquid distribution should have been uniform. Also, the values of ( k , a , ) ~and , the effect of liquid flow rate on them, could possibly be influenced by changes in gas and liquid flow
118
Ind. Eng. Chem. Fundam., Vol. 17, No. 2, 1978
pattern in the bed. In the range of flow rates covered in our research the flow would always be in the gas-continuous regime, as summarized by Satterfield (1975) and Hirose et al. (1976). As the data points in Figure 4 show, there was no significant effect of gas flow rate on (k,a,)R. This is in agreement with the conclusion of Hirose et al. (1976) that k,a, was not influenced by gas rate in the gas-continuous flow regime. At the higher liquid rates the experimental points in Figure 4 are again severalfold less than the predicted results from the correlations. However, the differences are somewhat less than the differences for the liquid-full condition shown in Figure 3. Also, the ( k , a , ) ~values for the more active catalyst (2.5% Pd) are greater than those for the 0.5% Pd. These two facts suggest that, in the trickle-bed condition, liquid does not completely cover the outer surface of the catalyst particles and that the part covered by gas contributes to the reaction. The reaction on the gas-covered surface would be greater than that on the liquid, because the mass transfer resistance between gas and particle surface would be less than that between liquid and particle surface. The higher total rate (the measured value, R ) could explain why the deviation of (k,a,)R between our experimental data and the correlations is less for trickle beds than for liquid-full operation. Also, the contribution of the gas-covered surface would be greater for the more active catalyst. This could explain the higher ( k , a , ) R shown in Figure 4 for the 2.5% Pd catalyst. The still large difference between the correlations and data points at high liquid rates is postulated, again, to be due to a lower effective area for mass transfer when a reaction occurs on a porous catalyst. If the surface is partly wet by liquid and partly by gas, ( ~ , u , ) Rcalculated from eq 13 is an apparent value, based upon the surface being completely covered by liquid. There are several reports suggesting that part of the surface is covered by gas and that this part contributes significantly to the total reaction rate (Sedriks and Kenney, 1972,1973; Satterfield and Ozel, 1973;Germain et al., 1974; Hanika et al., 1976).Further, Satterfield et al. (1969) suggested that the effect of liquid rate on global rates of reaction would be small. The data points in Figure 4 also are not particularly sensitive to QL. This could be explained by supposing that increasing the liquid rate does not change significantly the extent of liquid covered surface, but simply increases the thickness of the rivulets, and the velocity of the liquid in the rivulets, flowing down over the particles. Indirect confirmation of this has been noted in liquid-distribution studies (Herskowitz and Smith, 1977). In glass apparatus it was observed that increasing liquid rate in the gas-continuous regime did not change the position of the rivulets. While the individual data points in Figure 4 suggest a minimum in the relationship between apparent ksas and QL, the accuracy of the results may not justify drawing curves in this way. Such a minimum could be explained by a decrease in fraction of gas-covered surface as QL increases, and an increase in ksas for the fraction of liquid-covered surface. However, the subsequent analysis of the data suggests that f is nearly independent of liquid flow rate. Interpretation Based upon Partial Liquid Coverage. An estimate can be made of the fraction, f , of particle surface wet by liquid from the data for the two catalyst activities using the model of Hartman and Coughlin (1972). The chief assumptions, of which the first two seem reasonably applicable for our system, are: (1)the catalyst pores are filled with liquid; (2) on the wetted part of the particle surface, mass transfer is governed by a conventional mass transfer coefficient, k,; (3) there is no resistance to mass transfer a t the gas-covered surface; equilibrium exists between the hydrogen concentration in the gas and in the liquid at the pore mouths. This assumption represents an extreme case. For these conditions the mass balance of hydrogen in the liquid phase, and the rate equations, become
and
+ (1- f)koCsat
R = fk&s
(15)
where ( ~ , u , ) R Lis the mass transfer coefficient on the liquidcovered surface. Using these expressions as replacements for eq 9 and 2 leads to
Equation 16 may be written more conveniently as A=
f
~ (- al b ) - (1 - a b )
(17)
where
(19) b=- R
cs*t
(20)
The quantity A should be independent of catalyst activity. Hence, eq 17 may be written for the 2.5% and 0.5% P d catalysts, and the two expressions for A set equal to each other, to yield
or, solving for f
Since a and b for each catalyst are obtainable from the measured values of R and Csat, and from k v established by the liquid-full data, f can be calculated from eq 22. The results shown in the upper part of Figure 5 indicate that f is essentially independent of liquid rate and has an average value of about 0.89. Hartman and Coughlin (1972) found f = 0.94 at very low liquid rates for oxidation of SO2 with air in countercurrent flow of gas and water through a bed of activated carbon particles. Sedriks and Kenney (1973) reported f = 0.86 for the hydrogenation of crotonaldehyde in a trickle-bed reactor. Schwartz et al. (1976) found f to be equal to 0.65 for nonporous particles and constant over a range of liquid rates. Their measurements were based upon dynamic experiments with an adsorbable tracer in a trickle-bed system. The values of ( ~ , u , ) R L , presumably true liquid-particle coefficients, obtained from eq 16 are shown in the lower part of Figure 5. The correlations based upon mass transfer data are also indicated in Figure 5 . These are the same lines as given in Figure 4. The experimental points are lower for the same reason as mentioned before: a lower mass-transfer area effective when reaction occurs on a porous catalyst. Hirose et al. (1976) found that ksas was somewhat higher in trickle-bed than for liquid-full operation. This is presumably because the actual liquid velocity is higher in the smaller volume fraction occupied by the liquid in the trickle-bed arrangement. In contrast, Goto et al. (1975) found from mass transfer (no reaction) data that k,a, a t low liquid velocities
Ind. Eng. Chem. Fundam.,Vol. 17,No. 2, 1978 ( d p u ~ p J g
