Have you seen these tutorials

https://dealii.org/developer/doxygen/deal.II/step_20.html 
<https://dealii.org/developer/doxygen/deal.II/step_20.html>
https://dealii.org/developer/doxygen/deal.II/step_21.html 
<https://dealii.org/developer/doxygen/deal.II/step_21.html>
https://dealii.org/developer/doxygen/deal.II/step_22.html 
<https://dealii.org/developer/doxygen/deal.II/step_22.html>

They come quite close to your problem.

Best
praveen

> On 16-Oct-2018, at 11:32 AM, Lorenzo Campoli <[email protected]> 
> wrote:
> 
> Dear developers and users,
> 
> I was asked to investigate the viscous finger phenomenon due to water/oil 
> interaction.
> 
> I should adopt the Buckley-Leverett set of equations including capillarity 
> effect with injection/extraction wells in a simple  rectangular domain 
> starting from an homogenous porous medium.
> 
> Has been already done in Deal.II? In case, could you point me there?
> 
> If not done, from which case example I could start to work and modify? Will 
> it be feasable? Which quality/accuracy should I expect in terms of viscous 
> fingers resolution?
> 
> Thank you,
> Kind regards,
> 
> Lorenzo Campoli
> 
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