A mathematical and kinetics model is presented for reactions catalyzed by solid surfaces where both competitive and noncompetitive odsorption take place, a situation that may be general in reactions between large and small molecules catalyzed by solid surfaces.In the adsorption of large molecules steric hindrance or multiple site adsorption cause maximum surface coverage of such molecules before all sites are occupied. This does not, however, preclude further adsorption of small molecules on the remaining isolated vacant sites nor does it preclude further surface reoction. The overall reaction model for such conditions may be expressed as This particular model has been evaluated for the catalytic hydrogenation of propylene and isobutylene with the expectation that it may be useful in reactions that are of industrial importance. A reaction model based on either competitive adsorption or noncompetitive adsorption alone fails to correlate the experimental data.In these two reactions maximum rates occur a t olefin concentrations below 5 mole % and the catalytic adsorption constants for the olefins are a hundredfold greater than for hydrogen.This reaction model is similar to that proposed by Bond and Turkevich (151, who have further demonstrated through the deutetation of propylene that the actual mechanism of the reaction is much more complicated.In this paper are presented the results of a study of the kinetics of the hydrogenation of propylene and isobutylene gases over a commercial supported platinum catalyst. This study was undertaken to obtain reliable kinetic data on the hydrogenation of olefins and from these to select a mathematical model of use in correlating the rates of similar reactions of commercial importance. These studies are apparently the first ublished on the hydrogenation flow type of reactor.of propylene and isobuty P ene catalyzed by platinum in a PREVIOUS WORKAlthough the catalytic hydrogenation of light olefins. ethylene in articular, has been widely studied, there still for the reaction. The desired kinetic model is a mathematical expression of the reaction rate suitable for design purposes, even though it represents an oversimplification of the actual molecular mechanism involved.Part of the uncertainty in obtaining a reliable model is due to the difEculty of obtaining rate data under isothermal conditions. The hydrogenation of olefins is highly exothermic and when catalyzed by the Group VIII metals (nickel, platinum, palladium, rhodium, and ruthenium) the reaction rate becomes exceedingly rapid. As a result mass and heat transfer resistances at the catalytic surface obscure and complicate the interpretation of the experimental data. For the hydrogenation of ethylene gas over nickel in a stirred fixed volume reactor it has been shown exists consi B erable uncertainty as to the best kinetic model ( 1 ) that the reaction rate depends strongly on the degree of agitation of the gaseous system. An analysis of heat and mass transfer effects in the hydrogenation of propylene over nickel in a fked-b...

Ever since the concept of effectiveness factor was first introduced by Sir James Jeans (15) and further developed by Thiele (23), Wheeler (30), and Aris (I), this subject has been studied by a number of investigators, both theoretically and experimentally ( 2 , 3, 6 to 13, 16 to 22, 24 to 29).With the advent of the electronic digital computer, virtually no problem remains unsolved. However, due to the ease and the increasing use of numerical methods, we have often neglected or abandoned our attempt to obtain analytical solutions which generally offer better insight into the problem and solution. This paper describes the analytical solutions of cases heretofore thought t o be impossible. By the proper use of transformation of variables, the effectiveness factors for the zerourder reaction A -+bRoccurring in the pores of cylindrical and spherical catalyst particles, as well as thin disks, can be obtained. The reactant exhaustion phenomenon associated with this zeroorder reaction will also be discussed. It should be noted that in an important piece of previous work (26), the case of a spherical particle has been solved both numerically and asymptotically. In the latter method an approximation was made such that the starting equation became identical to that for thin-disk geometry. In that case, solutions for effectiveness factors for zero-, fist-, and second-order reactions were obtained. Even so, the mathematical procedure employed was such that the difficult task of obtaining concentration distribution itself was bypassed. In our present work the difficulty has been overcome and a complete set of expressions for pertinent quantities i s tabulated and similarities compared. PROBLEM FORMU LATlONIn solving any problem in the physical sciences, two types of equations are usually required. One, the conservation equation, or the equation of change, describes the system, while the other, the constitutive equation, or the equation of state, describes the properties of the material involved. state equation of continuity ( 4 )In our present case, the equation of change i s the steadywhere NA is the total molar flux (diffusional plus bulk flow) of species A, and R A the molar rate of production of A. The negative sign exists since 4 i s being consumed rather than produced.

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