Effective wellbore radius to calculate slant well productivity - van der Vlis et al.

Input(s)

h: Pay Zone Thickness (ft)

$\mathrm{r}_{\mathrm{w}}$ : Wellbore Radius (ft)

$\alpha$ : Slant Angle (degrees)

L: Length of Slant Wellbore $(\mathrm{ft})$

$\mathrm{r}_{\mathrm{w}}$ : Effective Wellbore Radius ( $\mathrm{ft}$ )

\begin{gathered} \mathrm{L}=\frac{\mathrm{h}}{\cos (\alpha)} \\ \mathrm{r}_{\mathrm{w}}=\frac{\mathrm{L}}{4} *\left[0.454 * \sin \left(360 *\left(\frac{\mathrm{r}_{\mathrm{w}}}{\mathrm{h}}\right)\right)\right]^{\frac{\mathrm{h}}{\mathrm{L}}} \end{gathered}

Joshi, S. D. 1991, Horizontal Well Technology. Tulsa, Oklahoma: PennWell Publishing Company. Chapter: 3, Page: 96.