(1)	$\begin{array}{l}\displaystyle k_f = 1014.24 \cdot {\rm FZI}^2 \cdot \frac{(\phi_f -\phi_{f0})^3}{( 1 - \phi_f+\phi_{f0})^2}\end{array}$

(2)	$\begin{array}{l}\displaystyle {\rm FZI} = \frac{1}{\sqrt{F_S} \, S_{gV} \, \tau }\end{array}$

where

$\begin{array}{l}{\rm FZI}\end{array}$	Flow Zone Indicator	$\begin{array}{l}S_{gV} = \Sigma_e/V_\phi\end{array}$	surface pore area per unit pore volume	$\begin{array}{l}\Sigma_e\end{array}$	pore surface area
$\begin{array}{l}\phi_f\end{array}$	fracture porosity	$\begin{array}{l}F_S\end{array}$	pore shape factor	$\begin{array}{l}V_\phi\end{array}$	pore volume
$\begin{array}{l}\phi_{f0}\end{array}$	porosity cut-off	$\begin{array}{l}\tau\end{array}$	pore channel tortuosity

In case of proppant-filled fracture the Flow Zone Indicator can be approximated as:

(3)	$\begin{array}{l}\displaystyle {\rm FZI} \approx 0.0037 \cdot \frac{d_p}{\tau_p }\end{array}$

where

$\begin{array}{l}d_p\end{array}$	proppant average grain size
$\begin{array}{l}\tau_p\end{array}$	fracture pore channel tortuosity

For the fluid-filled fracture ( $\begin{array}{l}\phi_f = 1\end{array}$ ) the fracture permeability has a simple correlation:

(4)	$\begin{array}{l}\displaystyle k_f = \frac{w_f^2}{12}\end{array}$

In Well Testing applications it normally behaves as the infinite-value fracture permeability due to a high contrast with typical formation permeability.

It can be formally interpreted as the extreme case of finite-conductivity fracture with the following trends:

(5)	$\begin{array}{l}\displaystyle {\rm FZI} \rightarrow \frac{w_f}{2 \, \sqrt{F_S}}\end{array}$

(6)	$\begin{array}{l}\displaystyle F_S \rightarrow 253.56 \, \frac{\phi_{f0}^2}{(1-\phi_{f0})^3}\end{array}$

but this has little practial value.

Page tree

See Also