Dispersion Knudsen diffusivity

Continuous stirred tank reactor Dispersion coefficient Effective diffusivity Knudsen diffusivity Residence time distribution Normalized residence time distribution... 

Effective diffusivity in Knudsen regime Effective diffusivity in molecular regime Knudsen diffusion coefficient Diffusion coefficient for forced flow Effective diffusivity based on concentration expressed as Y Dispersion coefficient in longitudinal direction based on concentration expressed as Y Radial dispersion coefficient based on concentration expressed as Y Tube diameter Particle diameter... 

Axial dispersion coefficient in entrance region of an open reactor Knudsen diffusivity... 

The analysis in this section focuses on the appropriate dimensionless numbers that are required to analyze convection, axial dispersion and first-order irreversible chemical reaction in a packed catalytic tubular reactor. The catalytic pellets are spherical. Hence, an analytical solution for the effectiveness factor is employed, based on first-order irreversible chemical kinetics in catalysts with spherical symmetry. It is assumed that the catalytic pores are larger than 1 p.m (i.e., > 10 A) and that the operating pressure is at least 1 atm. Under these conditions, ordinary molecular diffusion provides the dominant resistance to mass transfer within the pores because the Knudsen diffusivity,... 

Both diffusion coefficients and mass transfer are important, but they depend on the different solids, drainage (flow), and particles porosity. The effective diffusion involves Knudsen and convective diffusion, which depends on the phase of fluid (gas or liquid) and pore size (large or small). These coefficients are characterized by Peclet number (Pe), which depends on the axial or radial dispersion and diffusivity. Depending on the velocity profile, these coefficients can vary radially or axially. The diffusion and dispersion coefficients can also vary due to its dependence on the radial position. If the coefficients vary along the reactor, as in heterogeneous reactors, for example, the velocity is not constant. Thus, the axial dispersion occurs. 

In adsorbent particles with bi-dispersed pore structures, such as activated carbon, macropores usually act as a path for the adsorbate molecules to reach the interior of the particle. In this case molecular diffusion or Knudsen diffusion takes place in the macropore this is called pore diffusion. 

Assume that Pt was dispersed throughout the pore structure of the entire pellet in Problem 4.1 and apply the Weisz-Prater criterion to determine if mass transport limitations are expected. Do only one calculation using the lowest observed rate. Assume that the average pore diameter in the catalyst is 100 A (10 A = 1 nm), that Knudsen diffusion dominates, and that no external transport limitations occur (Cs = Co). 

Despite the fact Chat there are no analogs of void fraction or pore size in the model, by varying the proportion of dust particles dispersed among the gas molecules it is possible to move from a situation where most momentum transfer occurs in collisions between pairs of gas molecules, Co one where the principal momentum transfer is between gas molecules and the dust. Thus one might hope to obtain at least a physically reasonable form for the flux relations, over the whole range from bulk diffusion to Knudsen streaming. 

Uhlhorn et al [28] reported for a H2/N2 mixture a separation factor of about 9 compared to the Knudsen value of 3.74. As shown in Fig. 9.17 the ratio of the H2 flux over that of the N2 flux decreases from 9 at a pressure of 50 kPa to 5 at 200 kPa. This result is obtained on 7-AI2O3 membranes (thickness 100 pm, pore diameter 2.5-4.0 nm) impregnated with 17 wt% (finely dispersed) Ag. The increase of the H2 flux is obtained by the Ag impregnation. Probably the decrease of the separation factor is caused by a decreasing contribution of the surface diffusion to the total flux with increasing pressure due to saturation of the adsorption. 

Miscellaneous effects A number of factors can influence the effectiveness factor, some of which are particle size distribution in a mixture of particles/pellets, change in volume upon reaction, pore shape and constriction (such as ink-bottle-type pores), radial and length dispersion of pores, micro-macro pore structure, flow regime (such as bulk or Knudsen), surface diffusion, nonuniform environment around a pellet, dilution of catalyst bed or pellet, distribution of catalyst... 

Diffusion Continued) effect of, on activation energy, 104 effect of, on reaction order, 105 effect of, oh reaction rate, 95 importance of, 115 Knudsen, 484 molecular, 484 on surface, 98, 208 Diffusivity. See Effective diffusivity Dispersion (of catalyst), 19 Dispersion coefficients (axial and radial), 287, 493, 497... 

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