How to solve this partial differential equation in simulink?

Hello , I want to simulate the following partial equation on simulink , but I dont know if what I already built is fine , I have some struggle with dc/dz ,because it gives me error when I try to build it , so I conected rate transition and discrete derivative ,but dont know it is ok . I am building a fixed bed reactor full loaded with carbon absorbed gold in which a cyanide flow is pumped into and absorbs the gold loading , depleting the carbon . Following the equations:

So i tried finite differences for dc/dz with forward difference for eactor entry , central along the reactor , and backward in the exit, and dc/dt and dq/dt use integrator blocks, I consider Co= 0 and q0=4320. The problem is that when I remove rate transition and discrete derivative in 4th reactor,gives error.

Being that said, is correct to represent dc/dz as following? :

Adjoint the simulink file down here and thanks in advance:

https://riveril123.quickconnect.to/d/s/11jhifsXc7WjjbgDgYlqicG8JX9cxHGm/1KbHfeBHUy1vF0hiTKBsPaD8Nff4HGwg-27UAduxX-Qs

[Chuguang Pan]

As far as I know, the solvers embed in Simulink can only solve ODEs. I think if you want to solve PDEs in Simulink, you should transform PDEs to ODEs.

[Yifeng Tang]

Do you HAVE TO solve this in Simulink? This equation won't be too hard to write and solve in MATLAB. Are you trying to integrate some kind of controller later?