Prater number

The Prater number β _Pr is a dimensionless number of chemical reaction engineering . It describes internal heat transport processes in heterogeneous catalysis and describes the ratio of heat produced by a reaction to heat dissipation in the pellet. It is defined as:

${\displaystyle {\mathit {\beta _{\mathrm {Pr} }}}={\frac {c_{\mathrm {s} }\cdot D_{\mathrm {e} }\cdot (-\Delta H_{\mathrm {R} })}{\lambda _{\mathrm {e} }\cdot T_{\mathrm {S} }}}}$

With:

• λ _e = effective thermal conductivity
• D _e = effective diffusion coefficient
• -ΔH _R = enthalpy of reaction
• c _s = concentration on the outer catalyst surface
• T _s = temperature on the outer catalyst surface

If the Prater number β is 1 (for exothermic reactions) or −1 (for endothermic reactions), the catalyst works isothermally. With a Prater number greater than zero, the catalyst efficiency η can be greater than one as a result of the temperature increase inside the pellet. In this case, the reaction rate inside the catalyst is higher than at the catalyst surface.

literature

• Gerhard Emig , Hanns Hofmann : Reaction technology in: Chemie Ingenieur Technik , Volume 47, Issue 24, pp. 1012-1016, December 1975 doi : 10.1002 / cite.330472405