# Lifetime of a hydraulically fractured well

## Input(s)

\(m\): Slope of the Production Decline Curve (bbl/day)

\(Q_{a}\): Production Rate just before the Abandonment of the Well (bbl/d)

\(Q_{0}\): Initial Production Rate following the Hydraulic Fracturing Operation (bbl/d)

## Output(s)

t: Lifetime of a Hydraulically Fractured Well (days)

## Formula(s)

\[
t=\ln \left(\frac{Q_{a}}{Q_{0}}\right) \cdot \frac{1}{|m|}
\]

## Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 86.