Synonym: KGD Hydraulic Fracture @model = Kristianovich-Geertsma-de Klerk

Fracture half-length

(1)	$\begin{array}{l}\displaystyle X_f = 0.539 \, \left( \frac{q^3 E'}{\mu \, h_f^3} \right)^{1/5} \, t^{2/3}\end{array}$

Fracture width at well site

(2)	$\begin{array}{l}\displaystyle w_{f0} = 32.36 \, \left( \frac{q^3 \mu}{E' \, h_f^3} \right)^{1/6} \, t^{1/3}\end{array}$

Average fracture width

(3)	$\begin{array}{l}\displaystyle \bar w_f = \frac{\pi}{5} \, w_{f0}\end{array}$

Net pressure at the wellbore

(4)	$\begin{array}{l}\displaystyle p_{\rm net} = 1.09 \, \left( E'^2 \, \mu \right)^{1/3} \, t^{-1/3}\end{array}$

where

$\begin{array}{l}t = Q(t)/q\end{array}$	injection time
$\begin{array}{l}q\end{array}$	injection rate
$\begin{array}{l}Q(t)\end{array}$	cumulative injection over time $\begin{array}{l}t\end{array}$
$\begin{array}{l}h_f\end{array}$	fracture height
$\begin{array}{l}E' =\frac{E}{1-\nu^2}\end{array}$	plain stress
$\begin{array}{l}E\end{array}$	Young modulus
$\begin{array}{l}\nu\end{array}$	Poisson ratio
$\begin{array}{l}\mu\end{array}$	fluid viscosity

Reference

Geertsma, J., and F. De Klerk. "A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures." J Pet Technol 21 (1969): 1571–1581. doi: https://doi.org/10.2118/2458-PA

Zheitov, Yu. P. and Khristianovitch, S. A.: “The Hydraulic . Fracturing of an Oil-Producing Formation”, Izvest. AKad. Nauk USSR, Otdel Tech Nauk (1955), No. 3, 41.

Barenblatt, G. I.: “The Mathematical Theory of Equi- librium Cracks in Brittle Fracture”, Advances in Applied Mechanics ( 1962) 7, 56.

Khristianovitch, S. A. and Zheltov,4 Yu. P.: “Formation of Vertical Fractures by Means of Highly Viscous Fluid”, Proc., Fourth World Pet. Cong. (1955) II, 579.

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