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.