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Experimental Criterion for the Absence of Artifacts in the Measurement of Rates of Heterogeneous Catalytic Reactions Rostam J. Madon' and Mlchel Boudart' Department of Chemical Engineering, Stanford University, Stanford, California 94305
An experimental criterion has been developed to assess whether measured catalytic activity is independent of the influence of transport phenomena. A simple theoretical analysis and experimental verification of the criterion have been carried out. This test may be used when heterogeneous catalysis is carried out in batch, continuous stirred tank, and tubular plug-flow reactors, and is best suited to be used with supported metal catalysts. In this case, the test should be performed with two or more samples with different metal loading but of similar metal dispersion. Absence of physical artifacts is established by the constancy of turnover numbers. I f the reaction is exothermic, the test should be repeated at another temperature.
Introduction It has been stated (Boudart, 1972; Carberry, 1966; Satterfield, 1970) that catalytic data should be free from all transport influences to obtain kinetic rate expressions and to yield the correct activity or selectivity of the catalyst. Though the dangers are known, it should be emphasized that scaling down to laboratory studies is fraught with problems to eliminate concentration and temperature gradients both within catalyst particles (intraparticle gradients) and between the external surface of particles and surrounding fluid (interphase gradients). In the past, a number of interesting and useful criteria have been developed to check for the influence of heat and mass transfer on observed catalytic rates. Most of these criteria have been explained in a detailed review by Mears (1971a). Several criteria have been assembled in Table I. The Weisz-Prater criterion (1954) for intraparticle diffusion, for which only directly observable quantities are required, has been criticized for lack of generality by Petersen (1965a). The Petersen criterion (Petersen, 1965a), however, does not contain only observables and is hence more difficult to use. The more generalized criterion of Bischoff (1967), where the integration of the rate expression is involved, or that of Hudgins (1968)and Stewart and Villadsen (1969), where the differentiation of the rate expression is necessary, all suffer from the fact that the rate expression must be known, be it the power law type or the Langmuir-Hinshelwood type law, and if it is the latter then numerical values for all equilibrium constants must be obtained before the criteria can be used. Hudgins (1972) derived a criterion for interphase diffusion, but it suffers from the same problem as stated above. The criteria to check for interphase and intraparticle temperature gradients are due to Mears (1971b) and Anderson (1963), respectively. To use the several criteria, some of the following experimental properties are necessary: effective diffusivity in the pores of the catalyst, the heat and mass transfer coefficients at the fluid-solid interface, and the thermal conductivity of the catalyst. A t the low particle Reynolds numbers used in laboratory packed bed reactors, the accuracy of the value of h obtained from known correlations is subject to question (Madon, 1975). Though numerous studies have been carried out for bulk diffusion and difCorporate Research-Science Laboratories, Exxon Research and Engineering Co., Linden, NJ 07036. 0196-4313/82/1021-0438$01.25/0
fusivities of fluids, it is difficult to obtain the effective diffusivity for different catalysts. Satterfield and Saraf (1965) have shown that diffusional characteristics may change throughout a pellet due to compression of the catalyst powder in a pelletizing machine. Intraparticle criteria include surface concentrations and surface temperatures. These are usually not known and bulk values can be substituted only if there are no interphase gradients. Though the heat transfer criteria can be used to check for temperature gradients in the presence of diffusion, the latter effect could cause the rate and activation energy to be low and the criteria to be obeyed. In the absence of diffusion with the true higher values of the rate and activation energy, the criteria could be disobeyed for the same reaction. Finally, the particle size is another important parameter. Often powders with a wide size range are used in laboratory reaction studies, and Aris (1957) showed that the mean effectiveness factor is given by B = CBia[ i
Aris has warned against using average values for particle size to calculate 7, and in this light the above criteria could not be used except by using the largest and hence the most conservative value for the radius. Besides using the above correlations, experimental tests are often carried out to check for diffusion. In a flow system, if the space velocity is kept constant and then if the conversion remains constant as the flow rate is changed, the influence of external mass transfer is said to be negligible. A similar test is used in slurry reactors where the constancy of the reaction rate is checked as the agitation of the slurry is increased. Chambers and Boudart (1966) have indicated that at the low particle Reynolds numbers encountered in the laboratory the heat and mass transfer coefficients are quite insensitive to changes in flow rates, and hence the above diagnostic test may fail to indicate that the reaction rates are free from interphase concentration gradients. Moreover, this test cannot give any information regarding intraparticle diffusion. If activity of a catalyst is affected by altering pellet size, then this activity is said to be influenced by pore diffusion. However, if there is no change in activity with pellet size one cannot say for sure that there are negligible intraparticle concentration gradients. The influence of internal diffusion in the small pores of a bimodal pore distribution may still be important, and the test may just indicate that there is no diffusional influence in the larger set of pores. @ 1982 American Chemical Society
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Table I. Various Criteria Used t o Check for Transport Effects in Heterogeneous Catalysis For Intraparticle Mass Transfer For Interphase Mass Transfer Hudgins (1972)
Weisz and Prater (1954) R2r
DaII = -G 1 Cs De Weisz (1957) Dan < 6 90.6 G0.3
=-
0.15
