# 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.

## Related

### Productivity ratio

An unhandled error has occurred. Reload 🗙