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.