Fracture half-length | | LaTeX Math Block |
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| X_f = \frac{Q}{2 \, w_f \, h_f} |
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Average Fracture width | | LaTeX Math Block |
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| w_f = \frac{2 \pi \, p_{\rm net} \, h_f}{5 \, E'} |
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Net pressure at the wellbore | | LaTeX Math Block |
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| p_{\rm net} = \left( \frac{20}{\pi^2} \cdot \frac{E'^4 \, q \, Q \, \mu}{h_f^6} \right)^{1/5} |
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where
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| borderColor | wheat |
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| bgColor | mintcream |
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| borderWidth | 7 |
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Fracture half-length | | LaTeX Math Block |
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| X_f = 0.524 \, \left( \frac{q^3 E'}{\mu \, h_f^4} \right)^{1/5} \, t^{4/5} = 0.524 \, \left( \frac{E'}{\mu \, h_f^4} \frac{Q^4}{q}\right)^{1/5} = 0.8 \cdot \frac{E' \, Q}{p_{\rm net} \, h_f^2} = \frac{Q}{w_f \, h_f} |
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Fracture width at wellbore | | LaTeX Math Block |
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| w_{f0} = 3.04 \, \left( \frac{q^2 \mu}{E' \, h_f} \right)^{1/5} \, t^{1/5}= 3.04 \, \left( \frac{q \, Q \mu}{E' \, h_f} \right)^{1/5} = \frac{2 \, p_{\rm net} \, h_f}{E'} |
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Average Fracture width | |
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...
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...
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} \, w_{f0} = \frac{2 \pi \, p_{\rm net} \, h_f}{5 \, E'} |
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Net pressure at the wellbore | |
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...
{\rm net} = 1.524 \, \left( \frac{E'^4 \, q^2 \, \mu}{h_f^6} \right)^{1/5} \, t^{1/5} = 1.524 \, \left( \frac{E'^4 \, q \, Q \, \mu}{h_f^6} \right)^{1/5} |
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where | injection time | | injection rate | | cumulative injection over time | | fracture height | | LaTeX Math Inline |
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| body | --uriencoded--E' =\frac%7BE%7D%7B1-\nu%5e2%7D |
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| plain stress | | Young modulus | | Poisson ratio | | fluid viscosity |
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See Also
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Petroleum Industry / Upstream / Well / Well-Reservoir Contact (WRC) / Hydraulic fracture / Hydraulic Fracture @model
[ KGD Hydraulic Fracture @model ]
Reference
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Perkins, Kern and Nordgren
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