Thiele modulus

The Thiele modulus is a dimensionless parameter in the field of chemical macro-kinetics, especially the description of the pore diffusion ( gas-solid or liquid-solid ) in solid catalysts. It is named after the chemist EW Thiele, who introduced him in 1939.

In heterogeneous catalysis impoverished the interior of a porous catalyst on the substance to be reacted as they have to diffuse into the solid and thereby suffers a drop in concentration. This effect is stronger the thicker the active component of the catalyst is smaller there is the diffusion coefficient and the faster the reaction proceeds. An important indicator to describe is the catalyst efficiency, which describes the ratio of the observable effective reaction rate to the maximum possible rate of reaction during complete absence of pore diffusion effects. To determine this pore efficiency, the coupled and reaction diffusion equations are solved, and so the resulting concentration profile is achieved in the solid. By integrating the local reaction rates on the total solid volume finally calculated the catalyst efficiency. For simple geometries, that is, spherical, cylindrical and planar body and the adoption of the isothermal process, this solution is still possible using analytical methods.

It shows the calculation that the diffusion coefficient, reaction rate constant, pellet size and applied to the particle concentration form a characteristic dimensionless parameter, which determines the concentration profile and thus the catalyst efficiency solely. This figure is the Thiele modulus.

Defines the Thiele modulus is defined as:

So that the Thiele modulus is the ratio between the reaction rate and the mass transport caused by diffusion.

Interpretation:

• Small Thiele modulus: reaction rate is small - microkinetics limits the reaction
• Big Thiele modulus: diffusion rate is small - diffusion limits the reaction

In some references, the Damköhler number 2 type is used instead of the Thiele modulus. This number has no independent meaning, it is only slightly defined differently. It is

There are a number of definitions of the modified Thiele modulus to better describe example geometries that deviate from the ideal spherical shape, can. In textbooks of technical chemistry, specifically the reaction technology, extensive derivations to find on this subject.

The Thiele modulus is linked via the Weisz module to the catalyst efficiency.

A technical catalyst is generally designed so that it is located in the transition zone between kinetic control and diffusion control. So not bad being exploited catalyst material is wasted, on the other hand, the particles are not unnecessarily small, which would increase the flow resistance unnecessary.