# Skin factor due to partial penetration

## Input(s)

$$h_{t}$$: Total Formation Thickness $$(\mathrm{ft})$$

$$k_{v}$$: Vertical Permeability $$(\mathrm{mD})$$

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

$$h_{p}$$ : Height of Perforated interval (ft)

$$h_{a}$$ : Height (ft)

$$h_{p d}$$ : Dimensionless Perforated Thickness (fraction)

$$\mathrm{h}$$ : Thickness of reservoir ( $$\mathrm{ft}$$ )

## Output(s)

$$r_{d}$$: Permeability of altered zone $$(\mathrm{mD})$$

A: Dimensionless Constant A (dimensionless)

B: Dimensionless Constant B (dimensionless)

$$s_{p}$$ : Skin Factor from partial penetration (dimensionless)

## Formula(s)

$r_{d}=\left(\frac{r w}{h_{t}}\right) *\left(\frac{k_{v}}{k_{h}}\right)^{0.5}$
$\begin{gathered} A=\frac{h_{p}}{h_{t}} \\ B=\frac{h_{a}}{h_{t}} \\ s_{p}=\left(\frac{1}{h_{p d}}-1\right) * 2.303 * \log \left(0.5 * \frac{3.142}{\left.\left(\frac{r w}{h_{t}}\right) *\left(\frac{k_{v}}{k_{h}}\right)^{0.5}\right)}+\frac{1}{h_{p d}} * \ln \left(\frac{h_{p d}}{2+h_{p d}} *\left(\left(\frac{\left(\frac{h_{p}}{h_{t}}\right)-1}{\left(\frac{h_{a}}{h_{t}}\right)-1}\right)^{0.5}\right)\right)\right. \end{gathered}$

## Reference(s)

Pressure Transient Testing, Lee, Rollins & Spivey, Page: 44.

## Related

### Skin factor due to reduced crushed-zone permeability

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