Problem set up.

In this section we consider that there is a liquid and a solid phase.  The solid phase is a catalyst and it is mass transfer to this catalyst influences the reaction.  First this mass transfer will be steady.  Later it will be oscillatory.

The reaction is now a + b --> d+ e.  The reaction to make e occurs only on the surface of the catalyst.  The reaction to make d occurs in the bulk.  We can now consider the selectivity of the two products by looking at the homogeneous versus heterogeneous reaction rates.  Note that mass transfer will play an important role as well in the synthesis of e.    

First we have an equation for a.  The new term is the transfer of a from the liquid phase to the solid phase as governed by concentration and a mass transfer coefficient ka.  

Since there are two phases, we need to keep track of the "a" on the solid phase.  "cas" is the concentration of on the catalyst.  The reaction term depletes a from the solid and the mass transfer term enhances it.   

Here are the analogous equations for b.

Here are the two equations for the product, e.

Finally we need only 1 equation for d as it is formed in the liquid phase.  (We could consider d adsorbing onto the catalyst and doing nothing -- which it might.   But then again we have not considered an adsorption onto the walls of the reactor for a, b, e and this occurs also.  

Here is the complete two phase equation set.