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][4] in analyzing relative permeability data.

See also

• Amott test
• TEM-function

References

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).
3. Mirzaei-Paiaman, Abouzar; Saboorian-Jooybari, Hadi; Chen, Zhangxin; Ostadhassan, Mehdi (2019). "New technique of True Effective Mobility (TEM-Function) in dynamic rock typing: Reduction of uncertainties in relative permeability data for reservoir simulation". Journal of Petroleum Science and Engineering. 179: 210–227. doi:10.1016/j.petrol.2019.04.044. S2CID 149962022.
4. Mirzaei-Paiaman, Abouzar; Asadolahpour, Seyed Reza; Saboorian-Jooybari, Hadi; Chen, Zhangxin; Ostadhassan, Mehdi (2020). "A new framework for selection of representative samples for special core analysis". Petroleum Research. 5 (3): 210–226. doi:10.1016/j.ptlrs.2020.06.003.

External links

• http://www.ux.uis.no/~s-skj/ResTek1-v03/Notater/Tamu.Lecture.Notes/Capillary.Pressure/Lecture_16.ppt
• http://perminc.com/resources/fundamentals-of-fluid-flow-in-porous-media/chapter-2-the-porous-medium/multi-phase-saturated-rock-properties/averaging-capillary-pressure-data-leverett-j-function/
• Leverett J-Function in Multiphase Saturated Rocks