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

where

	effective porosity
	Flow Zone Indicator

with Flow Zone Indicator having a complex dependance on porosity and shaliness:

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 dictates Flow Zone Indicator values at low porosities while second component 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:

{\rm w}_1(V_{sh})  = {\rm w}_{01} \, (1- V_{sh}/V_{sh1})^{g_1}

{\rm w}_2(V_{sh}) = {\rm w}_{02} \, (1- V_{sh}/V_{sh2})^{g_2}

where

	the highest values of weights for shale-free rock matrix
	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