Fracture area of a hydraulically fractured formation

Input(s)

qiq_{i}: Injection Rate (m3/min)\left(\mathrm{m}^{3} / \mathrm{min}\right)

WW : Fracture Thickness (ft)(\mathrm{ft})

tt: Injection Time (min)

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

Output(s)

A(t)A(t): Fracture Area in time " t\mathrm{t} " (m2)\left(\mathrm{m}^{2}\right)

Formula(s)

A(t)=[qiW4πC2][ex2erfc(x)+2xπ1]erfc(x)=2πxet2dtx=2CπtW\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.


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