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.