...
The common model of Hydraulic Fracture Permeability is based on Cozeny-Karman permeability @model:
LaTeX Math Block |
---|
| k = 1014.24 \cdot {\rm FZI}^2 \cdot \frac{(\phi_f -\phi_{f0})^3}{( 1 - \phi_f+\phi_{f0})^2} |
| LaTeX Math Block |
---|
| {\rm FZI} = \frac{1}{\sqrt{F_S} \, S_{gV} \, \tau } |
|
where
In case of proppant-filled fracture the Flow Zone Indicator can be approximated as:
...
For the fluid-filled fracture the Flow Zone Indicator can be approximated as:
LaTeX Math Block |
---|
| {\rm FZI} = \frac{w_f}{2 \, \sqrt{F_S}} |
| LaTeX Math Block |
---|
| F_S \approx 3 \cdot 10^{-6} \, \frac{\phi_{fo}^2}{(1-\phi{f0})^3} |
|
which leads to simple correlation for fracture permeability:
...