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where
s_{wi} is initial water saturation which maybe equal to critical
s_{wсo} or less than critical
s_{wi} < s_{wco} like for example in petroleogenetic rocks.
The model assumes no gas presence in pores.
The alternative form of the Oil+Water RPM Corey @model can be presented as a function of normalized water saturation
s :
(3) |
s = \frac{s_w - s_{wi}}{1-s_{wi}-s_{orw}} |
which changes between
s = 0 for initial water saturation
s_w = s_{wi} and
s = 1 for maximum water saturation
s_w = 1- s_{orw}.
In this case equations
(1) and
(2) take form:
OIL | WATER |
---|
(4) |
k_{row}(s_o) = k_{rowc} \cdot (1-s)^{n_{ow}} |
|
(5) |
k_{rwo}(s_w) = k^*_{rwoc} \cdot (s - s^*)^{n_{wo}} |
|
|
(6) |
s^* = \frac{s_{wco}-s_{wi}}{1-s_{wi}-s_{orw}} |
|
(7) |
k^*_{rwoc} = k_{rwoc} \cdot \left( \frac{1-s_{wi}-s_{orw}}{1-s_{wco}-s_{orw}} \right)^{n_{wo}} |
|
and fractional flow function is going to be:
(8) |
f_w = \frac{M_{rwo}}{M_{rwo} + M_{row}} = \frac{(s-s^*)^{n_{wo}}}{(s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}}} |
|
(9) |
\dot f_w = \frac{d f_w}{ds} = g \cdot (s-s^*)^{n_{wo}-1} \cdot
\frac{\n_{wo} (1-s)^{n_{ow}} + n_{ow} (s-s^*) (1-s)^{n_{ow}-1}
}
{\left[ (s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}} \right]^2}
|
|
where
(10) |
g = \frac{M_{rowc}}{M_{rwoc}} \cdot \left( \frac{1-s_{wco}-s_{orw}}{1-s_{wi}-s_{orw}} \right)^{n_{wo}} |
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Relative Permeability / RPM @model
[ Permeability ] [ Absolute permeability ]