Rate of growth per unit of exploration length

Input(s)

$F$: Total Meterage Drilled up to date and expected to be drilled at the end Discovery ( $\mathrm{ft}$ )

$F_{D}$: Total Meterage Drilled up to the date of Discovery (ft)

$r$: The Ratio of Reserves Discovered in $F$ Meterage to the $F_{D}$ Exploration Metrage (fraction)

$r_{u}$: Latest Rate of Growth for Discovered Resources (fraction)

$b$: Ratio Constant (dimensionless)

Output(s)

$\frac{d r}{d\left(F-f_{D}\right)}$: Increase in Rate of Growth per Additional Unit of Length Drilled $(\mathrm{bbl} / \mathrm{ft})$

Formula(s)

$$ \frac{\mathrm{dr}}{\mathrm{d}\left(\mathrm{F}-\mathrm{F}_{\mathrm{D}}\right)}=\mathrm{b}\left(\mathrm{r}_{\mathrm{u}}-\mathrm{r}\right) $$

If There is no Extra Exploration $\left(F-F_{D}=0 ; r=1\right)$;

$$ \mathrm{r}=\mathrm{r}_{\mathrm{u}}-\left[\left(\mathrm{r}_{\mathrm{u}}-1\right) \cdot \mathrm{e}^{-\mathrm{b}\left(\mathrm{F}-\mathrm{F}_{\mathrm{D}}\right)}\right] $$

Reference(s)

Serpen, U., Petroleum Economics, Course Notes, ITU Petroleum and Natural Gas Engineering, Istanbul, Turkey, (2008) Page: 79.