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(1) k = 1014.24 \cdot FZI^2 \cdot \frac{\phi^3}{( 1 - \phi )^2}



effective porosity


Flow Zone Indicator

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}


\{ {\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

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