Fracture area of a hydraulically fractured formation
Input(s)
\(q_{i}\): Injection Rate \(\left(\mathrm{m}^{3} / \mathrm{min}\right)\)
\(W\) : Fracture Thickness \((\mathrm{ft})\)
\(t\): Injection Time (min)
C: Fracture Liquid Coefficient \((\mathrm{m} / \sqrt{\min })\)
Output(s)
\(A(t)\): Fracture Area in time " \(\mathrm{t}\) " \(\left(\mathrm{m}^{2}\right)\)
Formula(s)
\[
\begin{gathered}
A(t)=\left[\frac{q_{i} \cdot W}{4 \pi \cdot C^{2}}\right] \cdot\left[e^{x^{2}} \operatorname{erfc}(x)+\frac{2 x}{\sqrt{\pi}}-1\right] \\
\operatorname{erfc}(x)=\frac{2}{\sqrt{\pi}} \int_{x}^{\infty} e^{-t^{2}} d t \\
x=2 C \frac{\sqrt{\pi t}}{W}
\end{gathered}
\]
Reference(s)
Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 12.