Leverett J-function

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In petroleum engineering, the Leverett J-function is a dimensionless function of water saturation describing the capillary pressure^[1],

$J(S_w) = \frac{p_c(S_w) \sqrt{k/\phi}}{\sigma \cos \theta}$

where $S w$ is the water saturation measured as a fraction, $p c$ is the capillary pressure, $k$ is the permeability, $φ$ is the porosity, $σ$ is the surface tension and $θ$ is the contact angle.

The Leverett J-function is an attempt at extrapolating capillary pressure data for a given rock to rocks that are similar but with differing permeability, porosity and wetting properties. It assumes that the porous rock can be modelled as a bundle of non-connecting capillary tubes, where the factor $\sqrt{k/\phi}$ is a characteristic length of the capillaries' radii.