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.

J-function in analyzing capillary pressure data is analogous with TEM-function^[3]^[4] in analyzing relative permeability data.

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).
^ 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.
^ 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.

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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).

[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.

[Mirzaei-Paiaman2020-4] 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.

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References

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