Viscous fluid in granular material (DAPL)

[jman31415]

I saw the DAPL news story about the oil pipeline and I realized I have no idea how to analyze the problem of a fluid flowing from a boundary into granular material (or however you would classify soil).

Does anyone know of any book or website that discuss the governing (or approximate) equations involved in such a process.

My guess is that the equations are non-solvable but I am curious if there are numerical results and/or solvable approximate toy models.

P.S. I don't want to discuss any politics, just the physics involved with oil flowing into soil.

 

[Chestermiller]

Darcy's law.

 

[jman31415]

Darcy's law.

Thanks, that's exactly what I was looking for.