I am trying to understand PKN and KGD models for hydraulic fracturing. I am wondering why equations for fracture width and length does not include 'breakdown pressure' (pressure at which fracture initiates? The formula for fracture length for KGD is $$X_f=0.48[\frac{8GQ^3}{(1-v)\mu h_f^4}]^\frac{1}{6} t^\frac{2}{3} $$ where G, Q, $\mu$, $h_f$ and t are shear modulus, injection rate, viscosity, fracture height and time respectivily. Why there is not a threshold value, after which fracture initiates in this formula?
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