Assume that for a gaseous irreversible reaction A → B, the reaction and diffusion in a single cylindrical pore results in equimolal counter diffusion, or N_B = - N_A. Then for reactant A, the combined diffusivity in a cylindrical pore is given as

(1)

where is the bulk diffusion contribution and is the Knudsen diffusion contribution.

Here = 0 as N_B = - N_A

Or

(2)

When pore radius is large , = bulk diffusion. If pore radius is very small, Knudsen diffusivity becomes is controlling and

Bulk diffusivity at moderate temperature and pressure can be evaluated using Chapman –Enskog equation. For binary gas mixture of A and B

(3)

Knudsen diffusivity can be evaluated by the following equation:

(4)

The diffusivity of A in multicomponent system containing n components is given as

Here N_i is taken as positive if diffusion is in same direction as that of A and negative if in opposite direction. The D_Ai Ai are the binary diffusivities of component A with respect to component ‘i'. The y_A is molfraction of A and y_i molfraction of ‘i'