Leverett J-function capillary pressure @model

Physical correlation for capillary pressure on reservoir saturation:

(1)	$\begin{array}{l}\displaystyle P_{cow} (s_w) = \frac{ (\sigma \cos \theta) _{ow} } { \sqrt \frac{k}{\phi}} \; J_{cow}(s_w)\end{array}$

(2)	$\begin{array}{l}\displaystyle P_{cog} (s_g) = \frac{ (\sigma \cos \theta)_{og} } { \sqrt \frac{k}{\phi}} \; J_{cog}(s_g)\end{array}$

where

$\begin{array}{l}\sigma_{ow}\end{array}$	oil-water surface tension	$\begin{array}{l}\sigma_{og}\end{array}$	oil-gas surface tension
$\begin{array}{l}\theta_{ow}\end{array}$	oil-gas contact angle	$\begin{array}{l}\theta_{og}\end{array}$	oil-gas contact angle
$\begin{array}{l}k\end{array}$	absolute permeability to air	$\begin{array}{l}\phi\end{array}$	porosity
$\begin{array}{l}J_{cow}(s_w)\end{array}$	some function of water saturation	$\begin{array}{l}J_{cog}(s_g)\end{array}$	some function of gas saturation

The functions $\begin{array}{l}J_{cow}(s_w)\end{array}$ and $\begin{array}{l}J_{cog}(s_g)\end{array}$ are called Leverett J-functions.

They are individual to every certain rock type, just like relative permeability curves.

There are many correlations for Leverett J-functions and the most popular is Brooks-Corey correlation:

(3)	$\begin{array}{l}\displaystyle J_{cow}(s_w) = a \ ( s_{wn} )^{-1 / \lambda}\end{array}$

where

$\begin{array}{l}s_{wn} = \frac {s_w - s_{wс}}{1-s_{wс}}\end{array}$ – normalised water saturation,

$\begin{array}{l}s_{wс}\end{array}$ – critical water saturation,

$\begin{array}{l}a, \lambda\end{array}$ – model parameters which are set for laboratory data on capillary pressure and/or on resistivity water saturation during SHF.

Model parameter $\begin{array}{l}\lambda\end{array}$ is related to the the size of the pore size distribution.

The most popular value is 2 but it can vary to smaller or higher values.

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Leverett J-function capillary pressure @model