# Effective wellbore radius of a horizontal well - Method 1 - Isotropic reservoirs

## Input(s)

L: Horizontal Well Length (ft)

$$\mathrm{h}$$: Pay Zone Thickness $$(\mathrm{ft})$$

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

$$\mathrm{k}_{\mathrm{h}}$$: Horizontal Permeability $$(\mathrm{mD})$$

$$\mathrm{k}_{\mathrm{v}}$$: 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)

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

## Formula(s)

$\begin{gathered} \operatorname{reh}=\operatorname{sqrt}\left(A * \frac{43560}{3.14}\right) \\ a=\left(\frac{L}{2}\right) * \operatorname{sqrt}\left(.5+\operatorname{sqrt}\left(0.25+2 *\left(\frac{r e h}{L}\right)^{4}\right)\right) \\ r w d=r e h * \frac{\frac{L}{2}}{a *\left(\left(1+\operatorname{sqrt}\left(1-\left(\frac{L}{2 * a}\right)^{2}\right)\right) *\left(\frac{h}{2 * r w}\right)^{\frac{h}{L}}\right)} \end{gathered}$

## Reference(s)

Horizontal Well Technology, Joshi, Page: 90.

## Related

### Depth of a washout - Method 1

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