Leverett J-function

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 }}}{\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.^[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.

References

^ M.C. Leverett (1941). "Capillary behaviour in porous solids". Transactions of the AIME (142): 159–172.
^ J. M. LaManna, J. V. Bothe Jr., F. Y. Zhang, and M. M. Mench, J. Power Sources 271, 180 (2014).

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[1] M.C. Leverett (1941). "Capillary behaviour in porous solids". Transactions of the AIME (142): 159–172.

[2] J. M. LaManna, J. V. Bothe Jr., F. Y. Zhang, and M. M. Mench, J. Power Sources 271, 180 (2014).

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References

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