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Yeah, the subject is a bit cryptic.

My system is more or less an external mixed vessel (CSTR) and a tubular reactor (PFR) feeded by the vessel and that discharge in the vessel.

For this reason my system is closed.

I have to simulate the behavior of the PFR in a 1D system. We know from previous studies that the 2D system and 1D system give good match until the length of the PFR is less then a specific value.

I have solved the problem using an external loop made with Matlab in which i pass throught the steps the concentration profiles from the previous outlet to the next inlet. I test it in a stationary model in which the first inlet of the PFR in constant (this means that the external vessel has almost infinte volume so the discharge of the system doesn't change the concentration in it) and it gives great result.

Now I have to consider the time dependant variation of the concentration in the vessel and in the inlet.

Here the problems arise. :|

Someone have some ideas on how to do it?

I can create a time dependant cycle in Matlab passing the information in-out through it but in this case I have to use a really short time step to obtain decent result and this erase all the advantages of a optimized time-dependant analysis. In fact one of the aim of my study is to obtain a very short calculation time (the 2D system works perfectly but it's too slow)

The problem is that the outlet of the last sub-system act on the inlet of the first sub-system via the mixed external vessel and I can't ignore the propagation of the concentration inside the pipe.

This is just a Comsol-Matlab-Programming problem.

Regarding the physical aspect maybe I can solve every time-step as a stationary model if the relaxation time of the system is shorter than the time interval.