Leverett J-function

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

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

where ${\displaystyle S_{w}}$ is the water saturation measured as a fraction, ${\displaystyle p_{c}}$ is the capillary pressure (in pascal), ${\displaystyle k}$ is the permeability (measured in m²), ${\displaystyle \phi }$ is the porosity (0-1), ${\displaystyle \gamma }$ is the surface tension (in N/m) and ${\displaystyle \theta }$ 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 ${\displaystyle {\sqrt {k/\phi }}}$ 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.[2] 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[3] in analyzing relative permeability data.