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.