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.