Hydraulic fracture efficiency

Input(s)

$x$ : Fracture Length $(\mathrm{ft})$

$t$ : Injection Time (min)

C: Fracture Liquid Coefficient $(\mathrm{m} / \sqrt{\min })$

Output(s)

$\eta$: Hydraulic Fracture Efficiency (\%)

Formula(s)

$$ \begin{gathered} \eta=\left[\frac{1}{x^{2}}\right] \cdot\left[e^{x^{2}} \operatorname{erfc}(x)+\frac{2 x}{\sqrt{\pi}}-1\right] \\ \operatorname{erfc}(x)=\frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^{2}} d t \\ x=2 C \frac{\sqrt{\pi t}}{W} \end{gathered} $$

Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 23.