Diffusion in porous catalysts

This example illustrates the following point. The variation of D with depends on the importance of bulk diffusion. At the extreme where the Knudsen mechanism controls, the composition has no effect on D. When bulk diffusion is significant, the effect is a function of a. For equimolal counterdiffusion, a = 0 and yJ has no influence on D. In our example, where a = 0.741, and at 10 atm pressure, D increased only from 0.044 to 0.050 cm /sec as y increased from 0.5 to 0.8. 

Also note that under reaction conditions in a pore, as in part (a), the ratio of the diffusion rates of the species is determined by stoichiometry. In contrast, for nonreacting systems at constant pressure, Eq. (11-8) is applicable. 

A considerable amount of experimental data has been accumulated for effective diffusivities. Since reactors normally are operated at steady state and nearly constant pressure, diffusivities have also been measured under these restraints. The usual apparatus is of the steady-flow type, illustrated in Fig. 11-1 for studying diffusion rates of and N2. The effective diffusivity is defined in terms of such rates (per unit of total cross-sectional area) by the equation 

CHAPTER 11 REACTION AND DIFFUSION WITHIN POROUS CATALYSTS 

C—Detector for determining composition of N2 in H2 stream D—Detector for determining composition of H2 in N2 stream —Flowmeters P—Catalyst pellet G —Pressure equalization gauge 

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In the case of nonequimolal cpunterdiffusion, equation 12.2.6 suffers from the serious disadvantage that the combined diffusivity is a function of the gas composition in the pore. This functional dependence carries over to the effective diffusivity in porous catalysts (see below), and makes it difficult to integrate the combined diffusion and transport equations. As Smith (12) points out, the variation of 2C with composition (YA) is not usually strong, and it has been an almost universal practice to use a composition independent form of Q)c (12.2.8) in assessing the importance of intrapellet diffusion. In fact, the concept of a single effective diffusivity loses its engineering utility if the dependence on composition must be retained. 

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. 

This is exactly the situation we considered previously for diffusion in porous catalysts so we multiply r" in the porous wash coat by the effectiveness factor t to obtain... 

Internal diffusion in porous catalysts, if dominant, also reduces the observed activity of the biocatalyst. The decisive coefficient for mass transfer is the effective diffusion coefficient De((, which is defined in Eq. (5.56), where D0is the diffusion coefficient in solution, e the porosity of the carrier, and t the tortuosity factor. 

TABLE 1 Characteristic Timescales for Diffusion in Porous Catalyst Particles. 

A.E. Forrest, Stochastic network modelling of convection and diffusion in porous catalysts, M.Sc. thesis, UMIST (1994). 

Diffusion in Porous Catalyst Affecting Experimental Activation... 

Diffusion in porous catalyst affecting experimental activation energy. In case of a porous catalyst diffusion effects existing therein will also reduce the measured activation energy, depending on the temperature dependence of in... 

Effective diffusivities in porous catalysts are usually measured under conditions where the pressure is maintained constant by external means. The experimental method is discussed in Sec. 11-2 it is mentioned here because under this condition, and for a binary counterdiffusing system, the ratio is the same regardless of the extent of Knudsen and bulk... 

The mathematical equations of the flux relations for the capillary network model as well as the dusty gas model for flow and diffusion in porous catalysts are presented. 

Here we have used the approximation that can be replaced by Dj y and that variations of D y can be ignored within the averaging volume. The fact that only a single tortuosity needs to be determined by equations 1.152 and 1.153 represents the key contribution of this study. It is important to remember that this development is constrained by the linear chemical kinetic constitutive equation given by equation 1.113. The process of diffusion in porous catalysts is normally associated with slow reactions and equation 1.93 is satisfactory however, the first-order, irreversible reaction represented by equation 1.113 is the exception rather than the rule, and this aspect of the analysis requires further investigation. The influence of a non-zero mass average velocity needs to be considered in future studies so that the constraint given by equation 1.97 can be removed. An analysis of that case is reserved for a future study which will also include a careful examination of the simplification indicated by equation 1.117. 

M. Novak, K. Ehrhardt, K. Klausacek, and P. Schneider. Dynamics of non-isobaric diffusion in porous catalysts. Chem. Engg. Sci. 43, (1988) 185-193. 

This simplified diffusivity D a is often used in diffusion in porous catalysts even when equimolar counterdiffusion is not occurring. This greatly simplifies the equations for diffusion and reaction by using this simplified diffusivity. 

Knudsen diffusion in porous catalysts with a fractal internal surface. Fractals, Dutch Antilles, Curacao. 3 (4), 807-820. 

In view of the difficulties in employing a precise description of diffusion in porous catalysts the simple expression... 

We shall only treat the first phase here (a). There is an obvious analogy with reaction and diffusion in porous catalysts, treated in section 5,4.3,1. In principle eqs. (5.46) - (5.51) apply, when is replaced by... 

A dynamic mathematical model of the three-phase reactor system with catalyst particles in static elements was derived, which consists of the following ingredients simultaneous reaction and diffusion in porous catalyst particles plug flow and axial dispersion in the bulk gas and liquid phases effective mass transport and turbulence at the boundary domain of the metal network and a mass transfer model for the gas-liquid interface. 

The very mathematical orientation of chemical reaction engineering led to avant-garde research on American soil. Professor Neil Amundson from Minnesota pubhshed a pioneering work on the stabihty of chemical reactors, and professor Rutherford Aris from the same university published a monumental treatise on reaction and diffusion in porous catalysts. In parallel, the optimization aspects of chemical reactors were developed further by many... 

The subject of reaction and diffusion in porous catalysts is now a well established branch of knowledge discussed in several books such as by Aris [ij and Jackson [2j. Its practical importance has long been recognized since the pioneer work by Thiele [s]. 

Tables of diffusivities in various solids and liquids, including metals, molten salts and semiconductors appears in Poirier and Geiger cited above. Similar information on diffusion in porous catalysts can be found in ...

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