Effective wellbore radius of a horizontal well - Method 1- Anisotropic reservoirs
Input(s)
L: Horizontal Well Length (ft)
h: Pay Zone Thickness (ft)
\(\mathrm{r}_{\mathrm{w}}\): Wellbore Radius ( \(\mathrm{ft}\) )
\(\mathrm{k}_{\mathrm{h}}\): Horizontal Permeability (mD)
\(\mathrm{k}_{\mathrm{v}}\): Vertical Permeability \((\mathrm{mD})\)
A: Drainage Area (acre)
Output(s)
\(\mathrm{r}_{\mathrm{eh}}\): Effective Drainage Radius (ft)
a: Horizontal wellbore variable from Joshi (dimensionless)
3: Permeability Ratio constant (dimensionless)
\(\mathrm{r}_{\mathrm{wd}}\): Effective Wellbore Radius (ft)
Formula(s)
\[
\begin{gathered}
r e h=\operatorname{sqrt}\left(A * \frac{43560}{3.14}\right) \\
a=\left(\frac{L}{2}\right) * \operatorname{sqrt}\left(.5+\operatorname{sqrt}\left(0.25+2 *\left(\frac{r e h}{L}\right)^{4}\right)\right) \\
\beta=\operatorname{sqrt}\left(\frac{k h}{k v}\right) \\
r w d=r e h * \frac{\frac{L}{2}}{a *\left(\left(1+\operatorname{sqrt}\left(1-\left(\frac{L}{2 * a}\right)^{2}\right)\right) *\left(h^{*} \frac{\beta}{2 * r w}\right)^{\beta * \frac{h}{L}}\right)}
\end{gathered}
\]
Reference(s)
Horizontal Well Technology, Joshi, Page: 90.