| (1) | 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:
| (2) | 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 {\rm w}_1(V_{sh}) \, \phi_r^{m_1} dictates Flow Zone Indicator values at low porosities while second component {\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:
| (3) | {\rm w}_1(V_{sh}) = {\rm w}_{01} \, (1- V_{sh}/V_{sh1})^{g_1} |
| (4) | {\rm w}_2(V_{sh}) = {\rm w}_{02} \, (1- V_{sh}/V_{sh2})^{g_2} |
where
\{ {\rm w}_{01}, \, {\rm w}_{02} \} | the highest values of weights for shale-free rock matrix |
|---|---|
\{ V_{sh1}, \, V_{sh2} \} | critical values of shaliness at which the corresponding component of Flow Zone Indicator vanishes |
\{ g_1, \, g_2 \} | cementing factors, when low they diminish dependance on shaliness |
This model is very flexible and covers a wide range of practical cases.
When \{ m_1, \, m_2 \} and \{ g_1, \, g_2 \} are small ( \sim 0) the Flow Zone Indicator becomes independent on porosity and shaliness and the model degrades to conventional Cozeny-Karman permeability @model with FZI = \rm const.
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics / Absolute permeability / Absolute permeability @model