Leverett J-function
# Leverett J-function

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

    $J(S_{w})={\frac {p_{c}(S_{w}){\sqrt {k/\phi }}}{\gamma \cos \theta }}$

where $S_{w}$ is the water saturation measured as a fraction, $p_{c}$ is the capillary pressure (in pascal), $k$ is the permeability (measured in m²), $\phi$ is the porosity (0-1), $\gamma$ is the surface tension (in N/m) and $\theta$ is the contact angle. The function is important in that it is constant for a given saturation within a reservoir, thus relating reservoir properties for neighboring beds.

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.

This function is also widely used in modeling two-phase flow of proton-exchange membrane fuel cells. A large degree of hydration is needed for good proton conductivity while large liquid water saturation in pores of catalyst layer or diffusion media will impede gas transport in the cathode.

J-function in analyzing capillary pressure data is analogous with TEM-function in analyzing relative permeability data.

