Thiele module

The Thiele module is a dimensionless number from the field of chemical macrokinetics , especially the description of pore diffusion (gas-solid or liquid-solid) in solid catalysts . It is named after the chemist Ernest W. Thiele , who introduced it in 1939. ${\displaystyle \phi }$

In heterogeneous catalysis, the inside of a porous catalyst is depleted of the substance to be converted, since it has to diffuse into the solid and its concentration drops. This effect is stronger the thicker the active component of the catalyst, the smaller the diffusion coefficient there and the faster the reaction proceeds. An important key figure for the description is the degree of catalyst utilization, which describes the ratio of the observable effective reaction rate to the maximum conceivable reaction rate in the complete absence of pore diffusion influences. In order to determine this degree of pore utilization, the coupled reaction and diffusion equations are solved and the resulting concentration profile in the solid is solved. By integrating the local reaction rates over the entire volume of solids, the catalyst utilization rate is finally calculated. For simple geometries, i.e. H. spherical, cylindrical and planar bodies as well as the assumption of isothermal energy and simple kinetics, this solution is still possible with analytical methods.

The calculation shows that for simple first-order reactions, the diffusion coefficient, reaction rate constant, pellet size and concentration on the particle form a characteristic dimensionless number which alone determines the concentration profile and thus the catalyst utilization rate. This key figure is the Thiele module.

The Thiele module is defined as:

${\displaystyle \phi =r{\sqrt {\frac {k\cdot c_{s}^{n-1}}{D_{e}}}}}$

${\displaystyle r}$	Pellet radius
${\displaystyle k}$	Rate constant of the reaction,
${\displaystyle c_{s}}$	Concentration on the surface
${\displaystyle n}$	Reaction order
${\displaystyle D_{e}}$	Effective diffusion coefficient

The Thiele module thus describes the relationship between the reaction rate and the mass transport caused by diffusion.

Interpretation:

• Small Thiele module: reaction speed is small - microkinetics limit the reaction
• Large Thiele module: Diffusion speed is low - diffusion limits the reaction

In some literature references, the Damköhler number of type 2 is used instead of the Thiele module . This number has no meaning of its own, it is only defined slightly differently. It applies ${\displaystyle Da_{II}}$

${\displaystyle \phi ={\sqrt {Da_{II}}}}$

There are a number of modified definitions of the Thiele module in order, for example, to better describe geometries that deviate from the ideal spherical shape. In technical chemistry textbooks, especially reaction engineering, there are extensive derivations on this subject.

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

A technical catalyst is generally designed in such a way that it is located in the transition area between kinetic control and diffusion control. A compromise has to be found here, between the utilization of the catalyst by small particles ( small) and practical handling, such as retention in the reactor or the pressure loss in a packing. ${\displaystyle L}$

literature

• M. Baerns, H. Hofmann, A. Renken: Chemical reaction engineering. 2nd Edition. Georg-Thieme-Verlag, Stuttgart 1987.
• G. Emig, E. Klemm: Technical chemistry: Introduction to chemical reaction engineering. 5th edition. Springer Verlag, Berlin 2005.

Web links

• A. Brehm: Mass transport and macrokinetics. (PDF; 838 kB), University of Oldenburg, practical course in technical chemistry.

Individual evidence

1. ^ EW Thiele: Relation between Catalytic Activity and Size of Particle . In: Industrial & Engineering Chemistry . tape 31 , no. 7 , 1939, pp. 916-920 , doi : 10.1021 / ie50355a027 .
2. ↑ This Week's Citation Classic: Thiele E W. Relation between catalytic activity and size of particle . In: Industrial & Engineering Chemistry . No. 2 , January 8, 1979, p. 237 ( upenn.edu [PDF] review of the original article by EW Thiele).
3. ↑ S. Solovyov, A. Goldman: Mass Transport and Reactive Barriers in Packaging . DEStech Publishing Inc., Lancaster 2007, ISBN 978-1-932078-64-0 , pp. 86 .