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Fracture half-length
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X_f = 0.524 \left( \frac{q^3 E'}{\mu \, h_f^4} \right)^{1/5} \, t^{4/5}
Fracture width at well site
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w_{f0} = 3.04 \left( \frac{q^2 \mu}{E' \, h_f} \right)^{1/5} \, t^{1/5}
Average fracture width
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\bar w_f =  \frac{\pi}{5} \, w_{f0} 
Net pressure at the wellbore
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p_f = 1.524 \left( \frac{E'^4 \, q^2 \, \mu}{h_f^6} \right)^{1/5} \, t^{1/5}

where

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bodyt

injection time

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bodyq

injection rate

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bodyQ(t)

cumulative inecetion over time 

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bodyt

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bodyh_f

fracture height

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body--uriencoded--E' =\frac%7BE%7D%7B1-\nu%5e2%7D

plain stress

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bodyE

Young modulus

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body\nu

Poisson ratio

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body\mu

fluid viscosity


See Also

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Petroleum Industry / Upstream / Well / Well-Reservoir Contact (WRC) / Hydraulic fracture / Hydraulic Fracture @model

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