Effective permeability ($k_{\mathrm{eff}}$)

An equivalent large-scale permeability of a porous medium relating imposed pressure drop to total Darcy flux through a heterogeneous sample. Parallel flow paths add conductances, whereas successive resistive segments add pressure drops. It depends on direction and boundary conditions; it need not be the arithmetic mean of the local permeabilities.

In a slender layer, two parallel sublayers of fractions $x/L$ and $1-x/L$ have local effective permeability $K(x)=k_{1}x/L+k_2(1-x/L)$. Integrating their successive hydraulic resistance gives the logarithmic mean displayed above. A leading pressure gradient uniform across the thickness does not make parcel paths horizontal; a small transverse velocity preserves mass conservation as the cross-sectional conductance changes.