Effective wellbore radius for finite-conductivity fractures
Input(s)
\(\mathrm{k}_{\mathrm{f}}\): Fracture Conductivity \((\mathrm{mD})\)
\(\mathrm{b}_{\mathrm{f}}\): Fracture Width \((\mathrm{ft})\)
k: Formation Conductivity \((\mathrm{mD})\)
\(\mathrm{x}_{\mathrm{f}}\): Fracture Half Length \((\mathrm{ft})\)
Output(s)
\(\mathrm{F}_{\mathrm{CD}}\): Dimensionless Fracture Conductivity (dimensionless)
\(\mathrm{r}_{\mathrm{w}}\): Effective Wellbore Radius ( \(\mathrm{ft}\) )
Formula(s)
\[
\begin{gathered}
\mathrm{F}_{\mathrm{CD}}=\frac{\mathrm{k}_{\mathrm{f}} * \mathrm{~b}_{\mathrm{f}}}{\mathrm{k} * \mathrm{x}_{\mathrm{f}}} \\
\mathrm{r}_{\mathrm{w}}=0.2807 * \frac{\mathrm{k}_{\mathrm{f}} * \mathrm{~b}_{\mathrm{f}}}{\mathrm{k}}
\end{gathered}
\]
Notes: \(\mathrm{r}_{\mathrm{w}}\) is valid if \(\mathrm{F}_{\mathrm{CD}}<0.1\).
Reference(s)
Joshi, S. D. 1991, Horizontal Well Technology. Tulsa, Oklahoma:PennWell Publishing Company. Chapter: 5, Page: 135 .