The common model One of the models of Hydraulic Fracture Permeability is based on Cozeny-Karman permeability @model:
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| k_f = 1014.24 \cdot {\rm FZI}^2 \cdot \frac{(\phi_f -\phi_{f0})^3}{( 1 - \phi_f+\phi_{f0})^2} |
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| {\rm FZI} = \frac{1}{\sqrt{F_S} \, S_{gV} \, \tau } |
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where
In case of proppant-filled fracture the Flow Zone Indicator can be approximated as:
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{\rm FZI} \approx 0.0037 \cdot \frac{d_p}{\tau_p } |
where
For the fluid-filled fracture () the fracture permeability has a simple correlation:
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k_f = \frac{w_f^2}{12} |
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 trendsfracture the Flow Zone Indicator can be approximated as:
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| {\rm FZI} =\rightarrow \frac{w_f}{2 \, \sqrt{F_S}} |
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| F_S \approxrightarrow 3253.56 \cdot 10^{-6} \, \frac{\phi_{fof0}^2}{(1-\phi_{f0})^3} |
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which leads to simple correlation for fracture permeability:
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but this has little practial value.
See Also
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Petroleum Industry / Upstream / Well / Well-Reservoir Contact (WRC) / Hydraulic Fracture