Imagine that there are multiple parallel and series first-order reactions. Which reaction is used to represent the reaction rate in the Thiele modulus equation for a sphere, sqrt(k*a^2/D) on pg 46 of the link? The slowest reaction?
E.g.
1) A->B
2) B->C
3) A->D
4) D->C
You can define a Thiele modulus for each chemical reaction separately, you can for one and use stoichiometric relations. It can be defined for one symmetric grain shape, for example, for a semi-infinite cylinder, it can for all three (so called generalized Thiele modulus). In case of consecutive-competing reaction scheme, it is possible for the slowest reaction. It depends on you. It is not always possible to define a Thiele modulus. For equimolar counter-current diffusion or Knudsen diffusion (Fick's type equation) - of course - yes.
Regards,
Here comes the question. Do we need to define a Thiele modulus?
The Thiele module appears in the mass balance equation/equations after it has been transformed into a non-dimensional form, and strictly speaking, after the introduction of dimensionless spatial variable, eg z = r / R. So in the mass balance equation we have one parameter instead of three. The Thiele modulus also specifies the relationship between the chemical reaction and the intraparticle mass transfer.
Does something change when we solve mass balance equations - of course not.
Regards,
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