where
| LaTeX Math Inline |
|---|
| body | --uriencoded--s_{wi}%7Bwl%7D |
|---|
|
is
initial connate water saturation which maybe
...
or
...
...
- like for example in petroleogenetic rocks.
The This model assumes no no free gas presence in pores.
...
| LaTeX Math Block |
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|
s = \frac{s_w - s_{wi}}{1-s_{wiwl}-s_{orw}} |
which changes between
for initial water saturation
| LaTeX Math Inline |
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| body | --uriencoded--s_w = s_%7Bwi%7D%7Bwl%7D |
|---|
|
and
for maximum water saturation | LaTeX Math Inline |
|---|
| body | --uriencoded--s_w = 1- s_%7Borw%7D |
|---|
|
....
| OIL | WATER |
|---|
| LaTeX Math Block |
|---|
| k_{row}(s_o) = k_{rowc} \cdot (1-s)^{n_{ow}} |
| | LaTeX Math Block |
|---|
| k_{rwo}(s_w) = k^*_{rwoc} \cdot (s - s^*)^{n_{wo}} |
|
| | LaTeX Math Block |
|---|
| s^* = \frac{s_{wco}-s_{wi}}{1-s_{wiwl}-s_{orw}} |
|
| LaTeX Math Block |
|---|
| k^*_{rwoc} = k_{rwoc} \cdot \left( \frac{1-s_{wiwl}-s_{orw}}{1-s_{wco}-s_{orw}} \right)^{n_{wo}} |
|
...
| LaTeX Math Block |
|---|
| f_w = \frac{M_{rwo}}{M_{rwo} + M_{row}} = \frac{(s-s^*)^{n_{wo}}}{(s-s^*)^{n_{wo}} + g \cdot (1-s)^{n_{ow}}} |
|
| LaTeX Math Block |
|---|
| \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}
|
|
...
| LaTeX Math Block |
|---|
|
g = \frac{M_{rowc}}{M_{rwoc}} \cdot \left( \frac{1-s_{wco}-s_{orw}}{1-s_{wiwl}-s_{orw}} \right)^{n_{wo}} |
...
