Equations are developed for the bulk rote of a gaseous reaction on a porous catalyst whose activity changes with time due to o decrease in active surface. The performance i s evaluated in terms of a pellet effectiveness factor which i s a function of time and a Thiele (diffusionreaction) modulus. By a stepwise numerical technique, the equations can be solved without resort to assumptions regarding the distribution of fouled surface within the pellet. The method is applicable at isothermal conditions for any form of the rate equations for the main and fouling reactions and for any diffusivity-concentration relationship.To illustrate the method, results are given for first-order isothermal reactions for three types of fouling processes. For a series form of self-fouling, a catalyst with the lowest introporticle diffusion resistance gives the maximum activity for any process time. In contrast, for parallel self-fouling a catalyst with an intermediate diffusion resistonce is less easily deactivated and can give a higher conversion to desirable product, particularly at long process times. Page 384A.1.Ch.E. Journal March, 1966 can often be traced to deposition on the cata P yst of a the same reactants as the main reaction ( a parallel fouling PELLET EFFECTIVENESS FACTORSThe e uations can be solved numerically by considerand +. Any point in a lattice is determined by time and radial position. The time increment is labeled n and radial position increment m. Then in difference form Equations (8) and (9) become ing simu 4 taneously three rectangular lattices for CA, CB,

Effective thermal conductivities, k,, were measured for beds of spherical glass beads and steel shot, 29 to 470 microns in diameter. Data were oblained a t low air pressures ( 1 O-* mm. of Hg) to evaluate heat transfer rates through the contact regions of adjacent solid particles, and at pressure from 1 OP2 to 760 mm. of Hg, to ascertain the effects of free molecule conduction. Geometrical considerations were used to develop equations for predicting the effect of pressure on effective conductivity. This approach, which involves no arbitrary constants, agreed well with available data. The solid-to-solid contact heai transfer was found to b e a function of area of contact, characteristics of the surfaces of the particles, and void fraction, E, as well as the solid conductivity, k,. Published data were used to evaluate &, a characteristic parameier of the system which is not a function of k, or E.EAT TRANSFER in heterogeneous fluid-solid systems is impor-H tant in many types of processing-for example, catalytic reactors, heat exchangers, and thermal methods of oil recovery. This study is concerned with beds of fine spherical particles in which the void spaces contain air at pressures from to 760 mm. of Hg. The specific objective was to determine the effect of gas pressure and. hence, fluid conductivity, on the effective thermal conductivity of the bed.Previous investigations of heat transfer in beds of fine particles (7. 2, 9, 70. 73, 78) have been primarilv at atmospheric pressure or with flowing fluids. In attempting to write a mathematical description for the heat transfer rate in beds containing stagnant fluid it has been generally agreed that the transfer of energy occurs by three mechanisms:

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Adsorption rates were measured by a transcient method for nitrogen on beds of porous Vycor glass particles. Nitrogen was adsorbed, from a low concentration in helium, at liquid nitrogen temperature.Equations are presented for the concentration as a function of time and position in the bed, based upon surface adsorption, pore diffusion, or external diffusion controlling the overall process. Analysis of the data with these results indicates that the surface adsorption is a very rapid process and that pore processes determine the rate for particles larger than 0.01 cm. in radius. The effective pore diffusivity was determined to be 0.04 sq. cm./sec. The predominant contribution to the diffusivity is a surface mechanism rather than diffusion in the gas within the pores.Adsorption rates on porous solids are of significance in separation processes, such as drying and hydrocarbon fractionation, and in heterogeneous catalytic reactions. Measured from concentrations in the fluid surrounding the porous particle, these rates reflect the relative resistances of the adsorption step on the solid surface, diffusion in the pores including surface diffusion, and diffusion (external) from the outer surface of the particle into the fluid stream. For physical adsorption activation energies are only a few thousand calories (per gram mole), so that diffusion resistances may be the controlling factor in establishing the measured rate. Little work has been done apparently to compare these three resistances in a quantitative fashion. However Geser and Canjar (10) have obtained data, for the low-temperature adsorption of methane in hydrogen on activated carbon, which suggest that the surface rocess is of negligible resistance present paper is to analyze quantitatively adsorption data by comparison with rate equations based upon the three steps in the overall process. In this way the controlling resistance can be ascertained.A transient method was used to measure low-temperature adsorption rates for nitrogen on Vycor glass. Since the effect of particle size on the resistance of each of the three steps is different, the diameter of the Vycor particle was the major variable in the experimental work.The results of comparing theory with experiment show that the pore processes controlled the rate for the authors' system. Hence the data could be used to evaluate an effective diffusivity for nitrogen in Vycor. A secondary objective of the work was to compare this diffusivity with results obtained from direct diffusion measurements. This procedure provided some information on the importance of surface diffusion.In the experimental procedure a mixture of nitrogen and helium was passed through a fixed bed of Vycor particles, and the concentration of nitrogen leaving the bed was measured as a function of time. To relate these results to the surface and pore processes requires equations which express the concentration as a function of time and position, first for a single particle in the bed and second for the bed as a whole. Edeskuty and Amundson ( 7 ...

Diffusion rates were measured a t atmospheric pressure and room temperature for helium and nitrogen in pelleted silver catolysts. Pellets were prepared from three silver salts giving different micropore characteristics. The dota showed that'the diffusion was of the bulk type and that the micropores had no effect, indicating that mass transfer was predominantly in the macropore region. For each kind of moterial data were obtained for five pellet densities corresponding to macropore volume fractions from 0 up to 0.7. As the problem of reactor design for catalytic reactions has received more exhaustive study, interest has increased in pore diffusion rates. While there have been several studies of mass transfer in individual, porous catalysts and carriers (6, 7, 10, 11, 13, 14, Is), sufficient information has not become available to relate the effective diffusivity to the physical properties of the solid phase, This development is necessary before it will be possible to predict mass transfer rates in a given catalyst and hence evaluate the importance of pore diffusion in the overall reaction rate.In part the hindrance to progress in this area is due to lack of knowledge of the structure of porous catalysts.Conversely diffusion data can lead to a better understanding of the nature of the pores in a catalytic material, particularly if measurements are made on porous materials whose properties are changed in a regular way.The purpose of the present work was twofold: to determine the effect of macropore volume fraction on diffusion rates by studying catalyst pellets of different densities, but prepared from the same microporous powders: to obtain diffusivities for later use in interpretating the significance of diffusion resistance on the over-all rate for a specific reaction. Data were measured for three silver catalysts prepared from salts of phthalic, acedic, and fumaric acids. These catalysts are to be used subsequently for studying the rate of decomposition of formic acid in the gas phase. Since the effect of the properties of the porous solid was of interest, all the measurements were carried out with the helium-nitrogen system. Thus diffusivities were determined for these two gases diffusina, countercurrent to each other through the catalyst pellets.Shinobu Masamune and J. M. Smith are at the