Can Darcy's law model pseudo-steady and transient state?

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Assuming I have a 1 meter long core. Assume permeability is 1 Darcy, and porosity is 0.2. My injection velocity is about 2 cm/s. The outlet has same pressure as atmosphere pressure. So, actually, for water starts from inlet to outlet, it needs about 1/0.02 =50 s to reach the outlet. I want to see how the fluid velocity change between 0-50 s. But COMSOL only gives me one number of velocity. I assume this velocity is the steady state velocity. How can I get the changes of velocity before it reaches to breakthrough?

Another question is, can COMSOL simulate the skin effect near the wellbore by using Darcy's law?

It's most likely I will not get response from this forum. But whoever reads this post and have similar issue as me, we can try to discuss together.

Thanks in advance.


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