M1AZDw) \bigg|_{ s_g =s_{gc}}, 1- wwiwl} - s_{orw} } \bigg]^{n_{ow}} |
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M1AZD\bigg|_{ s_g s_{gc}} =,cdot \bigg[
\frac{ s_w - s_{ |
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wiwiwco} - s_{orw} } \bigg]^{n_{wo}} |
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+ s_w {gc}{gc}residual gas saturation to oil displacement | | initial water saturationwс
where Initial water saturation
{wi} maybe is connate water saturation which maybe...
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or
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This model assumes no free gas presence in pores.
Image Added |
Image Removed Typical Oil-Water relative permeabilities
The alternative form of the Oil+Water RPM Corey @model can be presented as a function of normalized water saturation
: LaTeX Math Block |
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s = \frac{s_w - s_{wi}}{1-s_{wl}-s_{orw}} |
which changes between
for initial water saturation LaTeX Math Inline |
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body | --uriencoded--s_w = s_%7Bwl%7D |
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and for maximum water saturation LaTeX Math Inline |
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body | --uriencoded--s_w = 1- s_%7Borw%7D |
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.
In this case equations
LaTeX Math Block Reference |
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and LaTeX Math Block Reference |
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take form: OIL | WATER |
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LaTeX Math Block |
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| k_{row}(s_o) = k_{rowc} \cdot (1-s)^{n_{ow}} |
| LaTeX Math Block |
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| k_{rwo}(s_w) = k^*_{rwoc} \cdot (s - s^*)^{n_{wo}} |
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| LaTeX Math Block |
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| s^* = \frac{s_{wco}-s_{wi}}{1-s_{wl}-s_{orw}} |
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LaTeX Math Block |
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| k^*_{rwoc} = k_{rwoc} \cdot \left( \frac{1-s_{wl}-s_{orw}}{1-s_{wco}-s_{orw}} \right)^{n_{wo}} |
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and fractional flow function is going to be:
LaTeX Math Block |
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| f_w = \frac{M_{rwo}}{M_{rwo} + M_{row}} = \frac{(s-s^*)^{n_{wo}}}{(s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}}} |
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LaTeX Math Block |
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| \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}
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where
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g = \frac{M_{rowc}}{M_{rwoc}} \cdot \left( \frac{1-s_{wco}-s_{orw}}{1-s_{wl}-s_{orw}} \right)^{n_{wo}} |
See also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics[ / Relative Permeability ]/ RPM @model
[ Absolute permeabilityPermeability ] [ Relative Absolute permeability ]