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 .