= Permeability of a porous medium
{title2=$k$}
= Porous permeability
{synonym}
= Intrinsic permeability
{synonym}
<Permeability of a porous medium> is the coefficient $k$ that measures how readily its connected pore geometry transmits a <fluid> in <Darcy law>. Its units are $\mathrm{m^2}$, since $k/\mu$ converts a <pressure gradient> in $\mathrm{Pa\,m^{-1}}$ into a <Darcy velocity> in $\mathrm{m\,s^{-1}}$. Large open, well-connected passages generally give larger <permeability of a porous medium> than narrow or winding passages. <Porosity> alone cannot determine it: two samples can contain the same void volume but have different passage sizes and connectivity.
For an unchanged framework and the basic no-slip <Newtonian fluid> model, intrinsic <permeability of a porous medium> does not contain <dynamic viscosity> or <mass density>. These properties instead enter <hydraulic conductivity> $K=k\rho g/\mu$. At the same horizontal <pressure gradient>, replacing a liquid with another of twice the <dynamic viscosity> halves <Darcy flux> even though $k$ stays fixed. Structural changes, such as swelling or clogging, can change $k$; the independence claim assumes the pore geometry stays fixed.https://books.gw-project.org/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow/chapter/hydraulic-conductivity/{ref}
An <isotropic> sample has scalar <permeability of a porous medium>. An <anisotropic> sample requires a <tensor> $\boldsymbol{k}$ in $\mathbf q=-\boldsymbol{k}(\nabla p-\rho\mathbf g)/\mu$, so discharge need not be parallel to the net driving force. <Layered porous permeability> gives a concrete example: arranging individually <isotropic> materials in horizontal layers produces different vertical and horizontal <effective permeabilities>.
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