Internal void fraction

With catalyst rings of the size used in industrial operation, pronounced concentration gradients occur inside the catalyst. The effective diffusivity required in the simulation of these gradients was obtained from the molecular and Knudsen diffusivi-ties, the internal void fraction and the tortuosity factor. The latter was determined by the dynamic gas chromatographic method, using the Van Deemter equation. The tortuosity factor was found to vary between 4.39 and 4.99 and to be independent of temperature. 

A recycle reactor containing 101 g of catalyst is used in an experimental study. The catalyst is packed into a segment of the reactor having a volume of 125 cm. The recycle lines and pump have an additional volume of 150 cm. The particle density of the catalyst is 1.12 g cm , its internal void fraction is 0.505, and its surface area is 400 m g . A gas mixture is fed to the system at 150 cm s . The inlet concentration of reactant A is 1.6 mol m . The outlet concentration of reactant A is 0.4 mol m . Determine the intrinsic pseudohomogeneous reaction rate, the rate per unit mass of catalyst, and the rate per unit surface area of catalyst. The reaction isA- - Psov.4 = —1. 

It is hard to find out much about internal holdup. Presumably this will be determined by the internal void fraction of the catalyst, which one may assume is totally filled with liquid phase—at least for reactions in which no phase change to vapor occurs. 

The surface area of n cylindrical pores open at the ends would be rm 2r)L if the pore walls were smooth and there were no pore intersections. However, with a moderately high internal void fraction (e = 0.3A).6) and randomly oriented pores, intersections are frequent, and the wall area of a pore is reduced where two pores intersect. Since any slice through a solid with a random pore structure will have e open fraction, the surface of the cylindrical pores is assumed to be reduced by the same fraction, and the surface is proportional to (1 — e). Allowing for an irregular surface of the pore walls, which increases the area by a roughness factor, r.f., the total surface per gram is... 

Internal surface area, S, = 100 m /g Internal void fraction, e, = 0.60... 

Ca, is the fluid reactant concentration in the pore, Rp the pore radius. D,p in this model may be a harmonic mean of the bulk and Knudsen diflusion coefficient with real geometries it would be a true effective difTusivity including the tortuosity factor and an internal void fraction. D p is an effective diffiisivity for the mass transfer inside the solid and is a correction factor accounting for the restricted availability of reactant surface in the region where the partially reacted zones interfere. For Jt(y) < LJ2 (shown in Fig. 4.5-2) or j>2 < J f e factor ( = 1 for L/ > R y) > L/2 or >i < y < yj the factor = 1 — (40/x) where tgB = (2/L) Ji (y) - (L/2) for y < yi the factor C 0, where R(y) is the radial position of the reaction front. It is clear from Eq. 4.S-1 that no radial concentration gradient of A is considered within the pore. 

The effective diffusivities for transport inside the catalyst were determined from experiments with particle radii varying from 0.35 to 2.3 mm. For butene, for example, the effective diffusivity contains the tortuosity, the internal void fraction, and the molecular and Knudsen diffusivity ... 

In Section 3.4 already the homogeneous medium diffusivity was corrected for the ratio of surface holes to total surface area of the catalyst. For a random pore network this ratio is, according to Dupuit s law, equal to the internal void fraction, es. Another adaptation is required because of the tortuous nature of the pores and eventual pore constrictions. The diffusion path length along the... 

Two types of techniques are commonly used for the determination of the internal void fraction and the tortuosity. The first uses a column packed with the catalyst and having a djdp ratio such that the flow approximates the ideal plug flow pattern, it is conveniently inserted in the furnace of a gas chromatograph that has all the parts for detecting the feed and response signals, besides temperature- and flow controls and six way valves. A narrow tracer pulse is injected in the carrier gas flow and the response is measured at the exit of the column. The pulse widens as a consequence of the dispersion in the bed, adsorption on the catalyst surface and effective diffusion inside the catalyst particle. The tracer does not have to be the component A itself The injected pulse should have an adequate residence time in the column and sufficient widening. Preference is given to transient measurements because steady state operation would not measure the effect of the dead end pores. 

Ammonia synthesis catalysts, after reduction, have a very porous structure. By comparing the particle density of prereduced catalysts (3.70 gcm ) with that of pure iron (7.86 gcm ) we can estimate an internal void fraction, Sj, of 0.47. What is more important, however, the average pore radius is normally in the range of 300-400 A with a very narrow pore-size distribution. This means that activated catalysts have a surface area in the range between 10 and 20 m g" and that nearly all of their active surface is therefore located within the particles. The intrinsic reaction rate must then be related to the ability of the reactants to gain access to the inner catalyst surface and of ammonia to escape to the external surface of the catalyst particle by diffusion through the pores. Similarly, the heat of reaction, which is released inside the catalyst particles, is transferred to their external surfaces by conduction. 

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