EXPERIMENTAL TECHNIQUES
An Improved Single-Pellet Reactor to Study the Interaction of Kinetics with Mass Transfer Effects in Heterogeneous Catalysis 1. Louis Hegedus and Eugene E. Petersen” Department of Chemical Engineering, University of California, Berkeley, Calif. 94720
A description of a new single-pellet reactor is presented along with a critical analysis of its operating characteristics. The reactor allows the measurement of reactant or product concentrations at the center plane of a catalyst pellet of flat slab geometry without the necessity of sample withdrawal. This is achieved by quantitative infrared spectroscopic analysis of the center-plane concentration. Special construction allows the in sifu reactivation of the catalyst pellet up to about 500°C.The supplemental measurements of the concentration a t the center plane of the catalyst pellet permit the simultaneous determination of effective diffusivities in the porous catalyst and the catalyst’s activity. The reactor is also useful to study the deactivation kinetics in catalyst pellets. A review of the pertinent literature and a brief summary of the theoretical aspects are also presented.
T h e r e is a continuing interest among researchers working in heterogeneous catalysis to find better experimental reactors which allow the determination of the parameters of mathematical models describing kinetic and mass transfer effects in catalyst pellets. If one aims to describe a catalytic surface reaction in terms of a mathematical model, actual surface concentrations are best suited for t h a t purpose. However, such information is usually not accessible due to experimental difficulties and one has to be satisfied with concentrations measured in the gas phase. - i n even more complicated situation arises when interaction between the surface reaction and pore diffusion mass transfer takes place in the catalyst pellet. I n this case, t h e mathematical expression describing the kinetic rate has to be incorporated into a conservation equation which also accounts for the diffusion process. The experimentally evaluated concentrations a t the outside of catalyst pellets often do not represent sufficient information to describe accurately t h e intrapellet phenomena. The purpose of this paper is to describe a n experimental reactor which provides information about concentrations a t the center plane of catalyst pellets. T h e authors’ aim is to put this technique in historical perspective and to shoTv t h e unique advantages of it for certain catalytic studies. Furthermore, it is to report about recent improvements in the experimental technique, along 1% ith selected results to illustrate the utility of this single-pellet reactor. Concentration measurements inside catalyst pellets hvere first proposed by Zeldovich (1939). Zeldovich envisioned a catalyst pellet of flat slab geometry. The front face of t h e pellet is exposed to the stream of the reactants, while the rear side faces a closed chamber-we will call i t the centerplane chamber.
The concentration a t the pellet’s surface facing the closed chamber equals the concentration which would prevail a t the center of a pellet of twice that thickness. This can be visualized by the symmetry of a catalyst pellet positioned in a uniform external concentration field. Later i t will be shown t h a t the time scale of the gas phase diffusion in the centerplane chamber allows the assumption t h a t i t is completely mixed. For practical purposes, the pellet’s shape is restricted to a flat slab which can be mathematically approximated by an infinite flat slab with finite thickness L. Information derived using this reactor (effective diffusivity, kinetic reaction order, rate constant, transient activity behavior) can of course be used for pellets of any shape. Zeldovich’s idea was apparently first carried out in practice by Roiter, et al. (1950). Roiter oxidized acetylene with air over a n asbestos-supported MnO2 catalyst. The center-plane chamber was open, since samples had to be n i t h d r a n n for chemical analysis. The mathematical problem arising due to the finite flux across the center plane was circumvented by Roiter in a n ingenious way. T h e temperature of the pellet was raised gradually until the net flux of acetylene across the center plane became zero, At this temperature, the measured net acetylene consumption in the bulk was solely due to the reaction n ithiii the pellet. Roiter used this information to evaluate the kinetic order of t h e reaction. The same reactor was used by Roiter to determine the effective diffusivity of the reactant in the pellet. This was done at a lower temperature where the eatent of the reaction could be neglected. I n a later work (Korneichuk, et al., 1955), Roiter returned once again to the single-pellet reactor to study the effect of pore diffusion on the selectivity of napthalerie olidation over Ind. Eng. Chern. Fundam., Vol. 1 1 , No. 4, 1972
579
of this paper, a brief introduction into the theoretical aspects will be presented in order to review the mathematical framework and to familiarize the reader with the types of problems which can be solved using this reactor.
Chamber
c, (L)
Theoretical Aspects of the Single-Pellet Reactor
0 L Figure 1. Coordinate system for eq 1-3
A simplified sketch of the reactor is shown in Figure 1. It serves to illustrate the coordinates used in subsequent equations. For a general reaction of order n and simple kinetics A .--,B, the steady-state conservation of species A in the pellet can be expressed by the well-known equations
as first shown by Thiele (1939) and Zeldovich (1939). I n eq 1 2, and 3
0.05
0.1
0.5
1.0
5.0
10.0
h Figure 2. Center-plane concentration vs. Thiele parameter for various reaction orders
VZOScatalyst. Roiter’s experimental procedure was rather cumbersome and i t does not seem to be very useful for isothermal studies. Balder and Petersen (1968a) realized the advantages of a closed center-plane chamber. They built a reactor with a relatively small volume behind the pellet, which was sampled by a syringe for gas chromatographic analysis. Balder and Petersen (1968b) treated the appropriate conservation equations rigorously and showed t h a t this type of reactor can be advantageously used to determine reactive effective diffusivities, kinetic reaction orders and to distinguish qualitatively between uniform and pore-mouth poisoning. Hahn and Petersen (1970) used a modification of the singlepellet reactor to demonstrate the nonuniformity of a poisoning wave proceeding across the catalyst pellet. I n their modification, i t was possible to switch the center-plane chamber from one side of the pellet to the other by a combination of valves. Dougharty (1970), using Balder’s data, evaluated the parameters of a n empirical catalyst deactivation model and showed the utility of the center-plane concentration measurements for that purpose. Further studies related to catalyst poisoning and using the single-pellet reactor are currently being carried out by the authors of this article. Interesting results (to be published a t a later time) were obtained by a convenient modification of the reactor, which now allows the measurement of concentrations in the center-plane chamber without the necessity of withdrawing a sample. This was carried out by quantitative infrared spectroscopy. The withdrawal of samples had to be eliminated because it perturbed the system by introducing a net flux across the center plane when withdrawing the sample. The new reactor can also be used for i n situ reactivation of the catalyst pellets up to about 500°C. I n the subsequent part 580 Ind. Eng. Chem. Fundam., Vol. 11, No. 4, 1972
where h i s the Thiele parameter (Petersen, 1965). If the overall rate of the reaction is expressed as @ =
&@lo
=
&kCAn(0)vpellet
(5)
(where & is the effectiveness factor), the relationship between the center-plane concentration 4 ~ ( 1 )and the Thiele parameter h is analytically obtainable for several values of n, such 0, - 1 / 2 J -3/4, - 1 , -2 (Bischoff, as 5, 3, 2, 1, l/3, 1965; Hegedus and Petersen, 1971; 1Iehta and Ark, 1971; Thiele, 1939). Some results of these calculations are summarized in Table I. Figure 2 shows some of the solutions. I n a general case, one might prefer a numerical approach of solution. The dependence of the Thiele parameter on the external reactant concentration (4) allows the determination of the kinetic reaction order by simply varying the bulk concentration CA(O) and observing the behavior of the center-plane concentration c A ( 1 ) (Balder, 1967). Once the kinetic reaction order is known, the Thiele parameter is uniquely defined by the magnitude of the center-plane concentration. The uniqueness does not hold for negative-order reactions, where multiple solutions can arise (Hegedus and Petersen, 1972; Mehta and Aris, 1971). For a first-order reaction, the solution of (I), (a),and (3) 1s ‘A(q)
cosh [h(l - q ) ] cosh ( h )
(7) &=-
tanh ( h ) h
If the overall rate @ is measured, along with the bulk and center-plane concentrations, eq 4, 5, 7, and 8 allow the determination of k , a A , e f f , h, and &. Center-plane concentration measurements can have unique advantages over competitive methods to evaluate the parameters describing the reacting system. The usual ways to determine these parameters are the following. (a) If Deffis
Table I. Analytical Solutions for the Thiele Parameter in Terms of the Center-Plane Concentration for Various Reaction Orders n a
n = 2b
n = l
n=O
n
=
-l/~
n = -1
72 =
-2
For n = 5, 3, and I/;, see Bischoff (1965). For a more general treatment of eq 1, 2, and 3, see Mehta and Aris (1971). * I n both cases, F is the elliptic integral of the first kind and K is the complete elliptic integral of the first kind.
measured independently and the order of the reaction is known, one single activity measurement allows the calculation of k , h, and E . (b) If D,ff is unknown, the so-called size reduction test can be applied. The overall reaction rate a t two particle sizes will be determined and the parameters will be evaluated based on the known relationship of E and h for the particular value of the kinetic reaction order n. I n the first case, t h e independently evaluated effective diffusivity might not accurately fit t h e data, if concentration dependence is observed. I n the second case, two kinetic experiments are needed, sometimes introducing large errors due to the irreproducibility of catalyst activity. Using the single-pellet reactor, only one experiment is necessary to determine the value of k , Q f f , h, and E , provided again t h a t the kinetic reaction order n is known. T h e reaction order n can be determined most accurately by following the variation in t h e overall rate of reaction as a function of the bulk phase concentrations, although in principle the order can be estimated by observing the center-plane concentration a t various values of the bulk concentration (Balder, 1967). -4lthough there are practical limitations on the size of pellet t h a t can be used in a single pellet reactor owing to the need to measure center-plane concentrations, this limitation is
not serious bkcause the parameters deduced from measurements of a larger pellet are independent of the size. Therefore the performance of any size pellet can be predicted from the measured parameters. The single-pellet reactor can also be utilized to study catalyst deactivation phenomena, since a t constant effective diffusivity, the activity of the catalyst pellet is uniquely defined by the center-plane concentration of the pellet. Changing center-plane concentration is a convenient way t o follow changes in the catalyst’s activity (Balder, 1967; Balder and Petersen, 1968b; Dougharty, 1970, Hegedus and Petersen, 1972). Experimental Realization of the Single-Pellet Reactor
4 differential batch reactor was selected for the experiments. The recirculation scheme is similar to that wed by Balder (1967). The nen reactor itself is shown in Figure 3. The pellet is pressed directly into the stainless steel cylinder reactor chamber of 0.93 em diameter. During the pelletirig process, the q-alumina adheres strongly to the stainless steel in such a way as to form a seal which exhibits no bypassing. The end faces of the thick-walled cylinder are polished as they Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
581
P ( L p is such that it allows a correction for the total volume o f the center-plane chamber) Figure 5. Geometry of the center-plane chamber, for transient diffusion studies 0.6cm
1
-
I Figure 3. Cross section of half of the single-pellet reactor used in the authors’ studies
E IO
Bulk Propane Concentration
m
-
4
fl
- -
a-
Center-Plone Cyclopropane Concentration I
IO0
I
I
200 xx) Time (min)
I
400
1 500
Figure 4. Bulk propane and center-plane cyclopropane concentrations during a poisoning experiment in the singlepellet reactor
are the two heads to which the cylinder is sealed b y the pulling force of three threaded rods. The seals are rings of 0.025in. diameter gold wire. Gold rings proved to be excellent seals for both vacuum and above atmospheric pressure operation, even a t temperatures around 500°C. Extreme care is needed when pressing the pellets. Complications arising due to nonuniform density in catalyst pellets have been discussed by Satterfield (1970). I n order to minimize nonuniformities, the pellets are pressed in a floating die; the cylinder’s ends do not touch the die during pressing. This ensures symmetrical force dissipation in the pellet. About 10 min is allowed for the pressure to equalize in the pellet. On both faces of the pellet, thin skins of about 0.1 mm thickness are removed before the catalytic experiments. Upon removal of these skins, the pellet’s density was considered to be reasonahly uniform for the experiments. However, no pelleting process produces absolutely uniform densities throughout the pellet. 582 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
The reactor cylinder is surrounded by a stainless steel mantle containing a Sichrome wire coil for heating purposes. The center-plane chamber has a total volume of 2.43 em3 and is shaped in such a way that the beam of an infrared spectrophotometer can pass through it. At 70 mm path length, hydrocarbons a t about 100 Torr total pressure can be easily analyzed by quantitative infrared spectroscopy. For example, 1 Torr of cyclopropane can be analyzed in the presence of 99 Torr of propane. The ends of the center-plane chamber’s infrared tube are covered by CaF2 or XaC1 windows, sealed by silicone rubber rings. CaFz is used between 2.5 and 8.5 p , while NaCl can be used between 2.5- and 14-p wavelengths. The reactants are introduced to the pellet’s surface through a jet a t a velocity high enough to eliminate external mass transport effects. The reactor’s temperature can be effectively controlled to =tO.l”C,with the help of a hot air recirculating oven, between 35 and 80°C. For reactivation (up to 5OO0C), the Xichrome wire coil is used which surrounds the reactor cylinder. The reactants are recirculated by a large-volume (10,687 cm3) reciprocating pump with Teflon sealing rings. T h e large volume is necessary to maintain a reservoir for reactants during a n experiment of longer duration (deactivation studies). The pump was constructed and described by Balder (1967). d pneumatic rectifier maintains unidirectional flow in the recirculation system. The pump is maintained a t the temperature of the reactor (between 35 and 80°C’ =t 0.1” C) . Bulk concentrations are measured by a gas chromatograph. A digital computer data acquisition system was constructed and conveniently used for integrating the chromatographic peaks (Hegedus and Petersen, 1971) T h e pellet can be activated and reactivated in the cylindrical reactor without removing it from its place. Both pellet faces are exposed to the gas stream used for reactivation (Hz or air). The reactor’s use will now be illustrated by a n example. The hydrogenolysis of cyclopropane was studied over a n q - X l d h supported Pt catalyst a t 50°C. This reaction is first order in cyclopropane a t a large excess of hydrogen. The hydrogen order is negative and unknown. Due to its large excess, the hydrogen concentration is practically unchanged and numerically i t becomes incorporated into the rate constant k . Before use the pellet was reactivated a t 400°C during 12 h r of exposure of both pellet faces to a hydrogen stream. The catalyst pellet was 0.374 ern long and its diameter was 0.930 em. Its weight was 0.2929 g, giving a calculated density of 1.170 g/cm3. I
Table II. Calculated Transient Response of the Center-Plane Chamber to a Step Concentration Increase at the Pellet’s Surface Time, sec
C AX ~ 106,mole/cm3
CAX ~ 106, mole/cm3
Step change,
%
SLLZs!
x
100
CAI
5
0.171
0.1795
5
10
0.171
0.1795
5
60
0.171
0.1795
5
5
0.171
0.1881
10
10
0.171
0.1881
10
L1
60
0.171
0.1881
10
LZ L1 L2
L1 L2 L1 LZ LI LZ L1
L2
The concentration of the propane in the bulk gas phase was monitored by gas chromatography and the concentration of cyclopropane was measured in the center-plane chamber by quantitative infrared spectroscopy. T h e results are shown in Figure 4. The data reveal t h a t a deactivation takes place during the period of 9 hr. From the initial concentration data, the initial values of h, E, a ) A , e f f , and k can be determined, using the treatment explained earlier. The following data were measured : initial rate, 7.127 X lo-’ mole/sec; C,(O), initial, 4.961 X 10+ mole/cm3; and C A ( L ) ,initial, 0.171 X mole/cm3. Calculated results are h, 4.05; E , 0.247; k , 2.289 sec-l; and a ) A , e f f 0.0195 cm2/sec. T h e significance of these numbers depends on the validity of t h e various assumptions and approximations included in the mathematical model which was used t o calculate t h e results (eq 1-3). I n the subsequent section of this paper, these assumptions will be examined in more detail. Analysis of the Performance of the Single-Pellet Reactor
T h e assumption of a n isothermal catalyst pellet was investigated by Balder (1967) for the same catalyst and model reaction used by the present authors. Implanting thermocouples into the pellet, Balder found no measurable temperature gradient. T h e increased heat transfer provided by the thicker wall of the new single-pellet reactor makes the isothermal pellet assumption even more justified than before. T h e cyclopropane hydrogenolpsis is accompanied by a mole number change upon conversion. I n large excess hydrogen concentrations, as used in the experiments, the effect of contraction is expected to be minimal. T h e ternary diffusivity of cyclopropane in a mixture of hydrogen and propane can be considerably concentration dependent. This effect was investigated by Balder (1967) in more detail; he concluded t h a t in large excess of hydrogen, the diffusivity is essentially independent of the composition, if the composition is expressed on a hydrogen-free basis. Another complicating factor might be the change of kinetic order upon conversion within the catalyst pellet. If the kinetic order is a known function of t h e conversion, or If Langmuir-Hinshelwood-type rate models are available, one can incorporate them into the mathematical problem and solve numerically. However, in t h e case of this example, a large excess of hydrogen maintains the rate expression to be first order in terms of cyclopropane concentration. I n studying transient activity phenomena, the assumption
-2.56 -4.71 -1.337 -4.57 0.00 -1.783 -4.90 -9.05 -2.55 -8.80 0.00 -3.45
of complete and instantaneous mixing in the center-plane chamber has to be investigated. For this purpose, the transient diffusion problem in the center-plane chamber was studied. Figure 5 depicts the assumed equivalent geometries representing two extreme cases, characterizing the centerplane chamber. T h e response of concentration a t z = 0 to step disturbance a t z = L can be found in the work of Crank (1956). Two extreme chamber geometries are considered in order to keep the problem one-dimensional. The diffusivity of cyclopropane in a mixture of hydrogen and propane was estimated by the method of Slattery for the binary pairs, which then were substituted into Wilke’s formula to estimate t h e ternary diffusivity (Sherwood and Reid, 1966). For this example, the ternary diffusivity of 34.46 Torr of cyclopropane in the mixture of 800 Torr of H2 and 65.54 Torr of propane was found to be 0.347 cm2/sec a t 50°C. The results for various step changes are given in Table 11. C A~ C Ais~ t h e step disturbance. As it can be seen from there, t h e response time is in the order of a few minutes, if 99% relaxation is required. Since the deactivation process studied has a time scale of many hours, the center-plane chamber can be assumed to be essentially well mixed. Therefore it follows t h a t in the order of 60 sec the center-plane concentration has approached its steady-state value to within a few per cent. This steady-state value is the solution of the Thiele problem at zero time. The limiting time constant of the present system is related to the mixing in the large reciprocating pump. U p to 15 min is necessary to achieve complete mixing of a n injected cyclopropane pulse. If t h e transient phenomenon (catalyst deactivation) observed is slow enough, this time constant does not introduce a significant error. I n other cases, a modification of the reciprocating system might be advisable. Nomenclature
C = concentration, mole/cma Deff= effective diffusivity, cm2/sec = effectiveness factor, defined b y eq 5 G h = Thiele parameter, defined b y eq 4 k = kinetic rate constant = characteristic length, cm L n = kinetic reaction order CR = reaction rate (overall), mole/sec a,,= kinetic reaction rate, mole/sec V = volume, cm3 z = distance, cm Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
583
GREEKLETTERS 7
ic.
= =
dimensionless distance, defined by eq 4 dimensionless concentration, defined by eq 4
literature Cited
Balder, J. R., Ph.D. Thesis, University of California, Berkeley, Calif.. 1967. Balder, J. R., Petersen, E. E., J . Catal. 11,202 (1968a). Balder, J. R., Petersen, E. E., Chem. Eng. Sci. 23, 1287 (196813). Bischoff, K. B., A.I.Ch.E. J . 11 (2), 351 (1965). Crank, J., “Llathematics of Diffusion,’, p 45, Oxford University Press, London, 1956. Dougharty, K.A., Chem. Eng. Sei. 25,489 (1970). Hahn, J. L., Petersen, E. E., Can. J . Chem. Eng. 48, 147 (1970). Hegedus, L. L., Petersen, E . E., 1.Chromatogr. Sci. 9, 551 (1971). Hegedus, L. L., Petersen, E. E., Chern. Eng. Sci. in press (1972).
Korneichuk, G. P., Zhigailo, J. V., Roiter, V. A., Garkavenko, I. P., Zh. Fiz. Khim. 24 (6), 1073 (1955). Mehta, B. N., Aris, R., Chem. Eng. Sci. 26, 1699 (1971). Petersen, E. E., “Chemical Reaction Analysis,” Prentice-Hall, Englewood Cliffs, N. J., 1965. Roiter, V. A., Korneichuk, G. P., Leperson, M. G., Stukanowskaia, N. A., Tolchina, B. I., Zh. Fiz. Khim. 24 (4),459 (1950). Satterfield, C. N., “Mass Transfer in Heterogeneous Catalysis,” I1I.I.T. Press. Cambridge. Mass.. 1970. Sherwood, T. k, Reid, R. C., “The Properties of Gases and Liquids,” McGraw-Hill, New York, N. Y., 1966. Thiele, E. W., Ind. Eng. Chem. 3 1 (7), 916 (1939). Zeldovich, J. B., Zh. Fzz. Khzm. 13 (2), 163 (1939).
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RECEIVED for review September 30, 1971 ACCEPTED June 6, 1972 Financial support was provided in part by a grant from the National Science Foundation.
Apparatus for the Determination of the Solubility of Hydrogen in Molten Salts Anthony P. Malinauskas,* Donald M. Richardson, Jouko E. Savolainen, and James H. Shaffer Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830
A two-chamber apparatus has been developed for the determination of the solubility of hydrogen in molten salts over wide ranges of temperature and pressure. Illustrative data are presented for the solubilities of helium and hydrogen in a LiF-BeFz eutectic at 600°C.
Determinations of hydrogen solubilities in molten salts are complicated by two factors. I n the first place, the gas is ordinarily more soluble in the candidate materials for apparatus construction than in the molten salt itself. Secondly, these same construction materials are usually quite permeable to hydrogen a t the temperatures of interest. Consequently, no data exist concerning the solubility of hydrogen in molten salt systems although, as summarized recently by Cleaver and Mather (1970), solubility measurements have been made for other gases of either technological or theoretical significance. One aspect of nuclear reactor technology involving molten salt systems as fuel and heat transfer media requires data relative to the solubility of hydrogen in these fluids, and for this reason the apparatus design reported here had been developed. The two-chamber concept upon which the design is based was first described in the open literature b y Grimes, et al. (1958)’ but the method was actually developed by R’ewton and Hill (1954). Aside from the use of a n alternate and inherently more accurate analytical method for determining t h e quantity of gas dissolved in the salt, the modifications to the previous design which are presented here were necessitated because of the employment of hydrogen. The Solubility Apparatus
The operational principle on which the apparatus design is based involves the saturation of the liquid with the gas in one chamber of the apparatus, then transfer of a known amount of this saturated fluid into a second chamber where 584 Ind. Eng. Chem. Fondam., Vol. 1 1 , No. 4, 1972
the dissolved gas is stripped from the solvent and collected for measurement. The two-chamber apparatus which is employed in these operations is sketched in Figure 1. The main portions of the solubility apparatus, i.e., the two chambers and the salt transfer line, are constructed of Hastelloy K,a nickel-base alloy containing 7y0chromium, 4% iron, and 12-170/, molybdenum. This alloy was chosen for reasons of compatibility with the salts of interest to this work. The remaining portions of the apparatus, which are maintained at ambient temperature, are constructed either of copper tubing or Pyrex glass tubing. The saturator chamber is a doubly-contained vessel consisting of a 4-in. 0.d. cylinder, 14.5 in. long, which was fabricated from 0.056-in. plate and which is centrally positioned within a 16-in. length of a 4.5-in. 0.d. cylinder constructed from ’/*-in. plate. Penetrations are provided for a 1/4-in. Hastelloy N tubing dip leg through which the saturating gas is admitted into the chamber, a level indicator I in Figure 1, and a thermocouple well located a t T. The stripper chamber is doubly contained also; it consists of a 12.5-in. length of 3-in. 0.d. cylinder constructed of 0.056-in. plate which is centrally located within a container which is identical with the outer container of the saturator section. The stripper chamber likewise contains three penetrations; two of these serve as the entrance and exit ports for the sparge gas, whereas the third penetration serves as a charging port for the salt. Transfer of the molten salt from the saturator to the striptubing per and vice versa occurs through 1/4-in. Hastelloy which is enveloped b y a length of 1-in. Hastelloy PI’ pipe from
