Coupled Partial Differential Equations

Hi I am looking to solve the following set of PDEs along with their respective IC's and BC's attached in the file. The system represents equations for mass balance in an adsorption column of length L which contains spherical particles of radius ap.

How should one go about to solve this set ? One of my friends suggested using orthogonal collocation technique but I am not able to get how I can apply this with two spatial coordinates. Many thanks Anshuman

[Marc]

I am gettin dizzy looking at your PDEs. Did you scan this in? The quality is horrible.

I would use MOL... Method of lines. Turn your PDEs into a system of ODEs. I did something like this with Comsol. Packed bed, three phase flow down the column and looking at diffusion into the spherical/cylindrical packed bed.

Good luck