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k_f =  \frac{w_f^2}{12}

and in pressure transient analysis In Well Testing applications it normally behaves as the infinite-value value fracture permeability due to a high contrast with reservoir typical formation permeability.

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

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{\rm FZI} \rightarrow \frac{w_f}{2 \, \sqrt{F_S}}

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F_S \rightarrow 253.56 \, \frac{\phi_{f0}^2}{(1-\phi_{f0})^3}

but this has little practial value.

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