Productivity ratio calculation of a hydraulically-fractured formation

Input(s)

$k_{\text {avgz }}$ : Average Permeability of a Hydraulically Fractured Zone (mD)

$k_{F}$ : Permeability of the Fracture (mD)

$k$ : Permeability of the Formation $(\mathrm{mD})$

$h$ : Formation Thickness (ft)

$W$ : Fracture Thickness $(\mathrm{ft})$

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

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

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

$k_{\text {avg }}$: Average Permeability of a Hydraulically Fractured Formation (mD)

Output(s)

PR: Productivity Ratio of a Hydraulically Fractured Formation (mD)

Formula(s)

$$ P R=\frac{k_{a v g}}{k} $$

or,

$$ P R=\left[\frac{k_{f} \cdot W}{k \cdot h}\right] \cdot \frac{\left[\frac{k h}{k_{f} \cdot W}+1\right] \cdot \ln \left(\frac{r_{e}}{r_{w}}\right)}{\left[\frac{k_{f} \cdot W}{k h}+1\right] \cdot \ln \left(\frac{r_{e}}{r_{f}}\right)+\ln \left(\frac{r_{f}}{r_{w}}\right)} $$

Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 7.