Pressure-dependent Darcy drainage
= Pressure-dependent Darcy drainage
Suppose a porous layer has thickness $h(p)$ and <permeability of a porous medium> $k(p)$, and the pressure drop $p$ acts across its thickness. <Darcy's law> gives the drainage <volume flux>
$$
w=\frac{k(p)}{\mu h(p)}p.
$$
If $k/h=Kp^{-\beta}$, then $w=(K/\mu)p^{1-\beta}$.