| LaTeX Math Block |
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|
k = 1014.24 \cdot FZI^2 \cdot \frac{\phi^3}{( 1 - \phi )^2} |
where
with Flow Zone Indicator having a complex dependance on porosity and shaliness:
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FZI(V_{sh},\phi_r) = {\rm w}_1(V_{sh}) \, \phi_r^{m_1} + {\rm w}_2(V_{sh}) \, \phi_r^{m_2} |
for each lithofacies individually.
Usually, the first component
| LaTeX Math Inline |
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| body | {\rm w}_1(V_{sh}) \, \phi_r^{m_1} |
|---|
|
dictates
Flow Zone Indicator values at low
porosities while second component
| LaTeX Math Inline |
|---|
| body | {\rm w}_2(V_{sh}) \, \phi_r^{m_2} |
|---|
|
takes over at high
porosities.
This allows to cover a wider range of porosity variations comparing to single-component Cozeny-Karman permeability @model.
The dependance of weight coefficients on shaliness can be often approximated as:
| LaTeX Math Block |
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|
{\rm w}_1(V_{sh}) = {\rm w}_{01} \, (1- V_{sh}/V_{sh1})^{g_1} |
| LaTeX Math Block |
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|
{\rm w}_2(V_{sh}) = {\rm w}_{02} \, (1- V_{sh}/V_{sh2})^{g_2} |
where
| LaTeX Math Inline |
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| body | \{ {\rm w}_{01}, \, {\rm w}_{02} \} |
|---|
|
| the highest values of weights for shale-free rock matrix |
|---|
| LaTeX Math Inline |
|---|
| body | \{ V_{sh1}, \, V_{sh2} \} |
|---|
|
| critical values of shaliness at which the corresponding component of Flow Zone Indicator vanishes |
|---|
| cementing factors, when low they diminish dependance on shaliness |
|---|
This model is very flexible and covers a wide range of practical cases.
When
and
are small (
) the
Flow Zone Indicator becomes independent on
porosity and
shaliness and the model degrades to conventional
Cozeny-Karman permeability @model with
.
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Absolute permeability / Absolute permeability @model
