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@wikipedia
The explicit form of physical correlations is given by following analytical formula:
(1) |
P_{cow} (s_w) = \frac{ (\sigma \cos \theta) _{ow} } { \sqrt \frac{k}{\phi}} \; J_{cow}(s_w) |
(2) |
P_{cog} (s_g) = \frac{ (\sigma \cos \theta)_{og} } { \sqrt \frac{k}{\phi}} \; J_{cog}(s_g) |
where
| oil-water surface tension | | oil-gas surface tension |
| oil-gas contact angle | | oil-gas contact angle |
| absolute permeability to air | | porosity |
J_{cow}(s_w) | some function of water saturation | | some function of gas saturation |
The functions
J_{cow}(s_w) and
J_{cog}(s_g) 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) |
J_{cow}(s_w) = a \ ( s_{wn} )^{-1 / \lambda} |
where
s_{wn} = \frac {s_w - s_{wс}}{1-s_{wс}} – normalised water saturation,
s_{wс} – critical water saturation,
a, \lambda – model parameters which are set for laboratory data on capillary pressure and/or on resistivity water saturation during SHF.
Model parameter
\lambda 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.
(4) |
J_{cow}(s_w) = a \ ( s_{wn} )^{-1 / \lambda} |
where
s_{wn} = \frac {s_w - s_{wс}}{1-s_{wс}} – normalised water saturation,
s_{wс} – critical water saturation,
a, \lambda – model parameters which are set for laboratory data on capillary pressure and/or on resistivity water saturation during SHF.
Model parameter
\lambda 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.
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Capillary pressure / Capillary pressure @model