Desorption reactor design in simulink

Hello, I want to model a desorption reactor with a fixed bed containing gold-laden carbon, through which a desorbing solution passes, which extracts extra gold. I am trying to solve it using a PDE system in which I create multiple nodes, assimilating it as if it were solved using the finite difference method. Using a forward difference for the initial node, a central difference for the intermediate nodes, and a backward difference for the final node. These are relative to a distance differential.The equations are as follows.

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 kg/m3 solution and q0=4.320 kg/m3 carbon. Just considering 5 nodes , shall be more but first i want to make the first five work fine .

And each node consist on the following layout , where can be seen a time integral block term for q(carbon loading) and c(solution loading , it shows also a length step and inputs from the forwarded and current node soluction concentration(in the case of the first node)

My problem is that I am getting the same values on each node, which I don't know if it is right the layout approach, since they should be different with relation to time and besides when i increase or decrease the input stream speed , the values in carbon and solution loading not change at all. thanks in advance

The model file is attached next: Reactor process