Initial rate following a hydraulic fracturing operation

Input(s)

$Q_{\text {pre }}$: Rate before the Hydraulic Fracturing Operation (bbl/d)

$r_{e}$: Drainage Radius of the Well (in.)

$r_{w}$: Hole Radius of the Well (in.)

$r_{f}$: Radius of the Fracture (in.)

$k_{f}$: Fracture Permeability $(\mathrm{mD})$

$k_{e}$: Average Formation Permeability $(\mathrm{mD})$

Output(s)

Q: Initial Rate Following a Hydraulic Fracturing Operation (bbl/d)

Formula(s)

$$ Q=Q_{p r e}\left[\frac{\left(k_{f} / k_{e}\right) \log \left(r_{e} / r_{w}\right)}{\log \frac{r_{f}}{r_{w}}+\left(\frac{k_{f}}{k_{e}} \cdot \log \frac{r_{e}}{r_{f}}\right)}\right] $$

Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 84.