Madon-Boudart criterion

A minor complication arises when dealing with exothermic reactions, since the effectiveness factor for a catalyst pellet experiencing transport limitations can still equal one. To eliminate any ambiguity associated with this rare condition, the Madon-Boudart criterion for an exothermic reaction should be repeated at a different temperature. 

The simplicity and general utility of the Madon-Boudart criterion make it one of the most important experimental tests to confirm that kinetic data are free from artifacts. It can be used for heterogeneous catalytic reactions carried out in batch, continuous stirred tank, and tubular plug flow reactors. 

A good illustration of the Madon-Boudart criterion is the liquid-pha.se hydrogenation of cyclohexene to cyclohexane over supported Pt/Si02 catalysts that differ in Pt loading by a factor of 4 [R. J. Madon and M. Boudart, hid. Eng. Chem. Fundam.. 21 (1982) 438]. 

Figure 4.11. The Madon-Boudart criterion applied in a study of the liquid-phase hydrogenation of cyclohexene on Pt/Si02 catalysts. Reaction conditions Ph2 = 101.3 kPa, solvent =20cm cyclohexane, (a) Catalyst particle size > 200 mesh, 2cm cyclohexene added at 275 K and 0.5 cm cyclohexene added at 307K (b) 0.5 cm cyclohexene added. (Reprinted from ref. 63, copyright 1982, with permission from American Chemical Society)...

Intraparticle Resistance. The Koros/Nowak (ref. 7) or Madon/Boudart (ref. 8) criterion states that, in the absence of mass transfer influences, the activity of a heterogeneous catalyst should be proportional to the number of active sites. In other words, the observed turn-over frequency (TOF) should be independent of the particle size if there is negligible intraparticle resistance since all active sites are fully effective. 

To verify the absence of any heat transfer effects, the Madon-Boudart method can also be utilized. If plots of In vs. In L are obtained at two or more temperatures, and the slopes are unity at each temperature, then thermal gradients, as well as concentration gradients and other artifacts such as poisoning, can also be ruled out [63]. If the reaction order is known, the criterion in equation 4.73 can also be used to check for isothermal operation. 

However, this criterion also has its limitations, as it is not always easy or possible at all to prepare catalyst samples with different concentration of the active material without simultaneously changing some other important properties of the catalyst, for example its diffusional characteristics. Details about the application of the Koros-Nowak criterion, as well as some methods how to prepare the required catalyst samples, can be found in the original paper by Koros and Nowak [64] or in a more recent article by Madon and Boudart [74]. 

Madon and Boudart propose a simple experimental criterion for the absence of artifacts in the measurement of rates of heterogeneous catalytic reactions [R. J. Madon and M. Boudart, Ind. Eng. Chem. Fundam., 21 (1982) 438]. The experiment involves making rate measurements on catalysts in which the concentration of active material has been purposely changed. In the absence of artifacts from transport limitations, the reaction rate is directly proportional to the concentration of active material. In other words, the intrinsic turnover frequency should be independent of the concentration of active material in a catalyst. One way of varying the concentration of active material in a catalyst pellet is to mix inert particles together with active catalyst particles and then pelletize the mixture. Of course, the diffusional characteristics of the inert particles must be the same as the catalyst particles, and the initial particles in the mixture must be much smaller than the final pellet size. If the diluted catalyst pellets contain 50 percent inert powder, then the observed reaction rate should be 50 percent of the rate observed over the undiluted pellets. An intriguing aspect of this experiment is that measurement of the number of active catalytic sites is not involved with this test. However, care should be exercised when the dilution method is used with catalysts having a bimodal pore size distribution. Internal diffusion in the micropores may be important for both the diluted and undiluted catalysts. 

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