Using the dusty gas diffusion equation in catalyst pores smaller than 50 Å radius

Abstract

When the dusty gas diffusion equation is applied to materials containing pores with radii below 50 Å, the observed diffusion behavior in these smaller pore systems can be quite different from that predicted by the equation. Higher temperatures and in some cases higher pressures tend to lessen the deviations between prediction and experiment. The observed deviations are probably caused by surface transport and by momentum transfer between gas molecules and pore walls during molecular flight. For bimodal materials, an additional factor can be the inapplicability of the equation to systems of parallel micro‐ and macropores. Excellent agreement between theory and experiment occurs for large‐pore unimodal systems.

Real gas transport through nanopores of varying cross-section type and shape in shale gas reservoirs

“…The crosssectional area and perimeter of nanopores are key parameters that affect slip flow [12,30,32]. Gas transport is governed by Knudsen diffusion in nanopores with a radius less than or equal 5 nm at a low pressure [55]. For Knudsen diffusion, the quantitative research is rare in the effect of nanopores type and shape on gas transport capacity [56].…”

Pore structure and kinetics of the thermal decomposition of Al(OH)3

“…The Knudsen diffusion equation was used to calculate the diffusivities associated with the different pore structures, an application justified for the extremely small micropores involved as established by numerous earlier works. Omata and Brown (1972) found, for example, that the regular Knudsen diffusion equation gave eithcr accurate or underestimated diffusivities for a variety of microporous materials, including aluminas. Rao and Smith (1963) obtained good results using this equation to describe hydrogen diffusion through microporous alumina and silica.…”

One‐Dimensional Pseudo‐Homogeneous Packed‐Bed Reactor Modeling: I. Chemical Species Equation and Effective Diffusivity

“…As a result, the following model was created with its derivation explained in a previous paper [52]: w p 1 À 6:85 ln e (28) In 2000, Winterberg et al [4] demonstrate that the quasihomogeneous, one-phase model provides good accuracy in modeling packed-bed reactors with chemical reactions. As a result, the following model was created with its derivation explained in a previous paper [52]: w p 1 À 6:85 ln e (28) In 2000, Winterberg et al [4] demonstrate that the quasihomogeneous, one-phase model provides good accuracy in modeling packed-bed reactors with chemical reactions.…”

“…Efforts in modeling packed-bed reactors started in the late 1960s with the focus mainly on finding tortuosity, diffusion, and thermal conductivity values within the packed bed [27][28][29][30][31][32]. As computational technology improved, researchers began to develop multidimensional models for the chemical species and energy equations including radial effects [10,22,[33][34][35].…”